\section{EXERCISE-1}

Q.1 A light bulb is placed between two mirrors (plane) inclined at an angle of \(60^{\circ}\). Number of images formed are

(1) 2

(2) 4

(3) 5

(4) 6

Q.2 Two plane mirrors are inclined at an angle of \(72^{\circ}\). The number of images of a point object placed between them will be

(1) 2

(2) 3

(3) 4

(4) 5

Q.3 To get three images of a single object, one should have two plane mirrors at an angle of

(1) \(30^{\circ}\)

(2) \(60^{\circ}\)

(3) \(90^{\circ}\)

(4) \(120^{\circ}\)

Q.4 A man of length \(h\) requires a mirror of length at least equal to, to see his own complete image

(1) \(\frac{\mathrm{h}}{4}\)

(2) \(\frac{h}{3}\)

(3) \(\frac{\mathrm{h}}{2}\)

(4) \(\mathrm{h}\)

Q.5 An object is at a distance of \(0.5 \mathrm{~m}\) in front of a plane mirror. Distance between the object and image is

(1) \(0.5 \mathrm{~m}\)

(2) \(1 \mathrm{~m}\)

(3) \(0.25 \mathrm{~m}\)

(4) \(1.5 \mathrm{~m}\)

Q.6 The light reflected by a plane mirror may form a real image

(1) If the rays incident on the mirror are diverging

(2) If the rays incident on the mirror are converging

(3) If the object is placed very close to the mirror

(4) Under no circumstances

Q.7 When a plane mirror is rotated through an angle \(\theta\), then the reflected ray turns through the angle \(2 \theta\), then the size of the image

(1) Is doubled

(2) Is halved

(3) Remains the same

(4) Becomes infinite

Q.8 It is desired to photograph the image of an object placed at a distance of \(3 \mathrm{~m}\) from the plane mirror. The camera which is at a distance of \(4.5 \mathrm{~m}\) from the mirror should be focussed for a distance of

(1) \(3 \mathrm{~m}\)

(2) \(4.5 \mathrm{~m}\)

(3) \(6 \mathrm{~m}\)

(4) \(7.5 \mathrm{~m}\)

Q.9 An object is initially at a distance of \(100 \mathrm{~cm}\) from a plane mirror. If the mirror approaches the object at a speed of \(5 \mathrm{~cm} / \mathrm{s}\), then after \(6 \mathrm{~s}\) the distance between the object and its image will be

(1) \(60 \mathrm{~cm}\)

(2) \(140 \mathrm{~cm}\)

(3) \(170 \mathrm{~cm}\)

(4) \(150 \mathrm{~cm}\)

Q.10 An object placed in front of a plane mirror is displaced by \(0.4 \mathrm{~m}\) along a straight line at an angle of \(30^{\circ}\) to mirror plane. The change in the distance between the object and its image is

(1) \(0.20 \mathrm{~m}\)

(2) \(0.40 \mathrm{~m}\)

(3) \(0.25 \mathrm{~m}\)

(4) \(0.80 \mathrm{~m}\)

Q.11 A point object \(\mathrm{O}\) is placed between two plan mirrors as shown is fig. The distance of the first three images formed by mirror \(\mathrm{M}_{2}\) from it are

(1) \(2 \mathrm{~mm}, 8 \mathrm{~mm}, 18 \mathrm{~mm}\)

(2) \(2 \mathrm{~mm}, 18 \mathrm{~mm}, 28 \mathrm{~mm}\)

(3) \(2 \mathrm{~mm}, 18 \mathrm{~mm}, 22 \mathrm{~mm}\)

(4) \(2 \mathrm{~mm}, 18 \mathrm{~mm}, 58 \mathrm{~mm}\)

Q.12 Figure shows a cubical room \(\mathrm{ABCD}\) will the wall \(\mathrm{CD}\) as a plane mirror. Each side of the room is \(3 \mathrm{~m}\). We place a camera at the midpoint of the wall \(\mathrm{AB}\). At what distance should the camera be focused to photograph an object placed at A

(1) \(1.5 \mathrm{~m}\)

(2) \(3 \mathrm{~m}\)

(3) \(6 \mathrm{~m}\)

(4) More than \(6 \mathrm{~m}\)

Q.13 A man having height \(6 \mathrm{~m}\), want to see full height in mirror. They observe image of \(2 \mathrm{~m}\) height erect, then used mirror is

(1) Concave

(2) Convex

(3) Plane

(4) None of these

Q.14 Convergence of concave mirror can be decreased by dipping in

(1) Water

(2) Oil

(3) Both

(4) None of these

Q.15 In an experiment of find the focal length of a concave mirror a graph is drawn between the magnitudes of u and v. The graph looks like

Q.16. An object \(2.5 \mathrm{~cm}\) high is placed at a distance of \(10 \mathrm{~cm}\) from a concave mirror of radius of curvature 30 \(\mathrm{cm}\) The size of the image is

(1) \(9.2 \mathrm{~cm}\)

(2) \(10.5 \mathrm{~cm}\)

(3) \(5.6 \mathrm{~cm}\)

(4) \(7.5 \mathrm{~cm}\)

Q.17 An object is placed \(40 \mathrm{~cm}\) from a concave mirror of focal length \(20 \mathrm{~cm}\). The image formed is

(1) Real, inverted and same in size

(2) Real, inverted and smaller

(3) Virtual, erect and larger

(4) Virtual, erect and smaller

Q.18 Which of the following forms a virtual and erect image for all positions of the object

(1) Convex lens

(2) Concave lens

(3) Convex mirror

(4) Concave mirror

Q.19 A convex mirror has a focal length \(\mathrm{f}\). A real object is placed at a distance \(\mathrm{f}\) in front of it from the pole produces an image at

(1) Infinity

(2) \(\mathrm{f}\)

(3) \(f / 2\)

(4) \(2 \mathrm{f}\)

Q.20 All of the following statements are correct except

(1) The magnification produced by a convex mirror is always less than one

(2) A virtual, erect, same-sized image can be obtained using a plane mirror

(3) A virtual, erect, magnified image can be formed using a concave mirror

(4) A real, inverted, same-sized image can be formed using a convex mirror Q.21 An object \(1 \mathrm{~cm}\) tall is placed \(4 \mathrm{~cm}\) in front of a mirror. In order to produce an upright image of \(3 \mathrm{~cm}\) height one needs a

(1) Convex mirror of radius of curvature \(12 \mathrm{~cm}\)

(2) Concave mirror of radius of curvature \(12 \mathrm{~cm}\)

(3) Concave mirror of radius of curvature \(4 \mathrm{~cm}\)

(4) Plane mirror of height \(12 \mathrm{~cm}\)

Q.22 An object \(5 \mathrm{~cm}\) tall is placed \(1 \mathrm{~m}\) from a concave spherical mirror which has a radius of curvature of \(20 \mathrm{~cm}\). The size of the image is

(1) \(0.11 \mathrm{~cm}\)

(2) \(0.50 \mathrm{~cm}\)

(3) \(0.55 \mathrm{~cm}\)

(4) \(0.60 \mathrm{~cm}\)

Q.23 For the largest distance of the image from a concave mirror of focal length \(10 \mathrm{~cm}\), the object should be kept at

(1) \(10 \mathrm{~cm}\)

(2) Infinite

(3) \(40 \mathrm{~cm}\)

(4) \(60 \mathrm{~cm}\)

Q.24 A dentist uses a small mirror that gives a magnification of 4 when it is held \(0.60 \mathrm{~cm}\) from a tooth. The radius of curvature of the mirror is

(1) \(1.60 \mathrm{~cm}(\) convex)

(2) \(0.8 \mathrm{~cm}\) (concave)

(3) \(1.60 \mathrm{~cm}\) (concave)

(4) \(0.8 \mathrm{~cm}\) (convex)

Q.25 A concave mirror is used to focus the image of a flower on a nearby well \(120 \mathrm{~cm}\) from the flower. If a lateral magnification of 16 is desired, the distance of the flower from the mirror should be

(1) \(8 \mathrm{~cm}\)

(2) \(12 \mathrm{~cm}\)

(3) \(80 \mathrm{~cm}\)

(4) \(120 \mathrm{~cm}\)

Q.26 A thin rod of \(5 \mathrm{~cm}\) length is kept along the axis of a concave mirror of \(10 \mathrm{~cm}\) focal length such that its image is real and magnified and one end touches the rod. Its magnification will be

(1) 1

(2) 2

(3) 3

(4) 4

Q.27 A cube of side \(2 \mathrm{~m}\) is placed in front of a concave mirror focal length \(1 \mathrm{~m}\) with its face \(P\) at a distance of \(3 \mathrm{~m}\) and face \(Q\) at a distance of \(5 \mathrm{~m}\) from the mirror. The distance between the images of face \(P\) and \(Q\) and height of images of \(P\) and \(Q\) are

(1) \(1 \mathrm{~m}, 0.5 \mathrm{~m}, 0.25 \mathrm{~m}\)

(2) \(0.5 \mathrm{~m}, 1 \mathrm{~m}, 0.25 \mathrm{~m}\)

(3) \(0.5 \mathrm{~m}, 0.25 \mathrm{~m}, 1 \mathrm{~m}\)

(4) \(0.25 \mathrm{~m}, 1 \mathrm{~m}, 0.5 \mathrm{~m}\)

Q.28 A concave mirror of focal length \(10 \mathrm{~cm}\) and a convex mirror of focal length \(15 \mathrm{~cm}\) are placed facing each other \(40 \mathrm{~cm}\) apart. A point object is placed between the mirrors, on their common axis and \(15 \mathrm{~cm}\) from the concave mirror. Find the position and nature of the image produced by the successive reflections, first at concave mirror and then at convex mirror

(1) \(2 \mathrm{~cm}\)

(2) \(4 \mathrm{~cm}\)

(3) \(6 \mathrm{~cm}\)

(4) \(8 \mathrm{~cm}\)

Q.29 When a light ray incident from air to glass and reflected, angle of incidence is \(57^{\circ}\). What will be the incident angle for reflection again when incident from water to glass

(1) \(\theta<57^{\circ}\)

(2) \(\theta>57^{\circ}\)

(3) \(\theta=57^{\circ}\)

(4) Can't be determined

Q.30 When light travels from glass to air, the incident angle is \(\theta_{1}\) and the refracted angle is \(\theta_{2}\). The true relation is

(1) \(\theta_{1}=\theta_{2}\)

(2) \(\theta_{1}<\theta_{2}\)

(3) \(\theta_{1} \geq \theta_{2}\)

(4) Not predictable (s)

Q.31 White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains

(1) Yellow, Orange, Red

(2) Violet, Indigo, Blue

(3) All colours

(4)All colours except green GEOMETRICAL OPTICS

Q.32 A plane glass slab is kept over various coloured letters, the letter which appears least raised is

(1) Blue

(2) Violet

(3) Green

(4) Red

Q.33 Monochromatic light is refracted from air into the glass of refractive index \(\mu\). The ratio of the wavelength of incident and refracted waves is

(1) \(1: \mu\)

(2) \(1: \mu^{2}\)

(3) \(\mu: 1\)

(4) \(1: 1\)

Q.34 The refractive index of water is 1.33 . The direction in which a man under water should look to see the setting sun is

(1) \(49^{\circ}\) to the horizontal

(2) \(90^{\circ}\) with the vertical

(3) \(49^{\circ}\) to the vertical

(4) Along the horizontal

Q.35 Why sun has elliptical shape on the time when rising and sun setting

(1) Refraction

(2) Reflection

(3) Scattering

(4) Dispersion

Q.36 Which of the following statement is true

(1) Velocity of light is constant in all media

(2) Velocity of light in vacuum is maximum

(3) Velocity of light is same in all reference frames

(4) Laws of nature have identical form in all reference frames

Q.37 A ray of light is incident on a transparent glass slab of refractive index 1.62. The reflected and the refracted rays are mutually perpendicular. The angle of incidence is

(1) \(58.3^{\circ}\)

(2) \(50^{\circ}\)

(3) \(35^{\circ}\)

(4) \(30^{\circ}\)

Q.38 An under water swimmer is at a depth of \(12 \mathrm{~m}\) below the surface of water. A bird is at a height of \(18 \mathrm{~m}\) from the surface of water, directly above his eyes. For the swimmer the bird appears to be at a distance from the surface of water equal to (Refractive Index of water is \(4 / 3\) )

(1) \(24 \mathrm{~m}\)

(2) \(12 \mathrm{~m}\)

(3) \(18 \mathrm{~m}\)

(4) \(9 \mathrm{~m}\)

Q.39 Consider the following statements

Assertion (A) : The frequencies of incident, reflected and refracted beam of monochromatic light incident from one medium to another are same

Reason (R): The incident, reflected and refracted rays are coplanar of these statements

(1) Both \(A\) and \(R\) are true and the \(R\) is a correct explanation of the \(A\)

(2) Both \(A\) and \(R\) are true but the \(R\) is not a correct explanation of the \(A\)

(3) A is true but the \(\mathrm{R}\) is false

(4) Both A and \(\mathrm{R}\) are false

Q.40 The refractive indices of glass and water w.r.t. air are \(3 / 2\) and \(4 / 3\) respectively. The refractive index of glass w.r.t. water will be

(1) \(8 / 9\)

(2) \(9 / 8\)

(3) \(7 / 6\)

(4) None of these Q.41 Light of wavelength is 7200 A in air has a wavelength in glass \((\mu=1.5)\) equal to (when the refractive index of glass is 1.5)

(1) \(7200 \AA\)

(2) \(4800 \AA\)

(3) \(10800 \AA\)

(4) \(7201.5 \AA\)

Q.42 The distance travelled by light in glass (refractive index \(=1.5\) ) in a nanosecond will be

(1) \(45 \mathrm{~cm}\)

(2) \(40 \mathrm{~cm}\)

(3) \(30 \mathrm{~cm}\)

(4) \(20 \mathrm{~cm}\)

Q.43 The splitting of white light into several colours on passing through a glass prism is due to

(1) Refraction

(2) Reflection

(3) Interference

(4) Diffraction

Q.44 Absolute refractive indices of glass and water are \(\frac{3}{2}\) and \(\frac{4}{3}\). The ratio of velocity of light in glass and water will be

(1) \(4: 3\)

\((2) 8: 7\)

(3) \(8: 9\)

(4) \(3: 4\)

Q.45 The ratio of thickness of plates of two transparent mediums \(A\) and \(B\) is \(6: 4\). If light takes equal time in passing through them, then refractive index of \(\mathrm{B}\) with respect to \(A\) will be

(1) 1.4

(2) 1.5

(3) 1.75

(4) 1.33

Q.46 Which of the following is a correct relation

(1) \({ }_{\mathrm{a}} \mu_{\mathrm{r}}={ }_{\mathrm{a}} \mu_{\mathrm{w}} \times{ }_{\mathrm{r}} \mu_{\mathrm{w}}\)

(2) \({ }_{\mathrm{a}} \mu_{\mathrm{r}} \times{ }_{\mathrm{r}} \mu_{\mathrm{w}}={ }_{\mathrm{w}} \mu_{\mathrm{a}}\)

(3) \({ }_{\mathrm{a}} \mu_{\mathrm{r}}{ }_{\mathrm{r}} \mu_{\mathrm{a}}=0\)

(4) \({ }_{\mathrm{a}} \mu_{\mathrm{r}} /{ }_{\mathrm{w}} \mu_{\mathrm{r}}={ }_{\mathrm{a}} \mu_{\mathrm{w}}\)

Q.47 If \(\varepsilon_{0}\) and \(\mu_{0}\) are respectively, the electric permittivity and the magnetic permeability of free space, \(\varepsilon\) and \(\mu\) the corresponding quantities in a medium, the refractive index of the medium is

(1) \(\sqrt{\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}}\)

(2) \(\frac{\mu \varepsilon}{\mu_{0} \varepsilon_{0}}\)

(3) \(\sqrt{\frac{\mu_{0} \varepsilon_{0}}{\mu \varepsilon}}\)

(4) \(\sqrt{\frac{\mu \mu_{0}}{\varepsilon \varepsilon_{0}}}\)

Q.48 At sun rise or sunset, the sun looks more red than at mid-day because

(1) The sun is hottest at these times

(2) Of the scattering of light

(3) Of the effects of refraction

(4) Of the effects of diffraction

Q.49 The refractive index of a piece of transparent quartz is the greatest for

(1) Red light

(2) Violet light

(3) Green light

(4) Yellow light

Q.50 On heating a liquid, the refractive index generally

(1) Decreases

(2) Increases or decreases depending on the rate of heating

(3) Does not change

(4) Increases

Q.51 At what angle does the diver in water see the setting sun, when the refractive index of water is 1.33

(1) \(0^{\circ}\)

(2) \(41^{\circ}\)

(3) \(90^{\circ}\)

(4) \(60^{\circ}\)

Q.52 A beam of light is converging towards a point I on a screen. A plane parallel plate of glass whose thickness in the direction of the beam \(=\mathrm{t}\), refractive index \(=\mu\), is introduced in the path of the beam. The convergence point is shifted by

(1) \(\mathrm{t}\left(1-\frac{1}{\mu}\right) a w a y\)

(2) \(\mathrm{t}\left(1+\frac{1}{\mu}\right)\) away

(3) \(t\left(1-\frac{1}{\mu}\right)\) nearer

(4) \(\mathrm{t}\left(1+\frac{1}{\mu}\right)\) nearer Q.53 \(\mathrm{V}_{1}\) is velocity of light in first medium, \(\mathrm{V}_{2}\) is velocity of light in second medium, then refractive index of second medium with respect to first medium is

(1) \(\mathrm{V}_{1} / \mathrm{V}_{2}\)

(2) \(\mathrm{V}_{2} / \mathrm{V}_{1}\)

(3) \(\sqrt{\mathrm{V}_{1} / \mathrm{V}_{2}}\)

(4) \(\sqrt{\mathrm{V}_{2} / \mathrm{V}_{1}}\)

Q.54 A rectangular block of glass is placed on a printed page lying on a horizontal surface. Then the minimum value of refractive index of glass for which the letters on the page are not visible from any of the vertical faces of the block is

(1) Equal to \(\sqrt{2}\)

(2) More than \(\sqrt{2}\)

(3) Less than

(4) \(>=<\sqrt{2}\)

Q.55 The critical angle for diamond (refractive index \(=2\) ) is

(1) About \(20^{\circ}\)

(2) \(60^{\circ}\)

(3) \(45^{\circ}\)

(4) \(30^{\circ}\)

Q.56 Consider telecommunication through optical fibres. Which of the following statements is not true

(1) Optical fibres may have homogeneous core with a suitable cladding

(2) Optical fibres can be graded refractive index

(3) Optical fibres are subject to electromagnetic interference from outside

(4) Optical fibres have extremely low transmission loss

Q.57 Light wave enters from medium 1 to medium 2. Its velocity in \(2^{\text {nd }}\) medium is double from \(1^{\text {st }}\). For total internal reflection the angle of incidence must be greater than

(1) \(30^{\circ}\)

(2) \(60^{\circ}\)

(3) \(45^{\circ}\)

(4) \(90^{\circ}\)

Q.58 Critical angle of light passing from glass to air is minimum for

(1) Red

(2) Green

(3) Yellow

(4) Violet

Q.59 If critical angle for a material to air is \(30^{\circ}\), the refractive index of the material will be

(1) 1.0

(2) 1.5

(3) 2.0

(4) 2.5

Q.60 The reason for shining of air bubble in water is

(1) Diffraction of light

(2) Dispersion of light

(3) Scattering of light

(4) Total internal reflection

Q.61 With respect to air critical angle in a medium for light of red colour \(\left[\lambda_{1}\right]\) is \(\theta\). Other facts remaining same, critical angle for light of yellow colour \(\left[\lambda_{2}\right]\) will be

(1) \(\theta\)

(2) More than \(\theta\)

(3) Less than \(\theta\)

(4) \(\frac{\theta \lambda_{1}}{\lambda_{2}}\)

Q.62 The velocity of light in a medium is half its velocity in air. If ray of light emerges from such a medium into air, the angle of incidence, at which it will be totally internally reflected, is

(1) \(15^{\circ}\)

(2) \(30^{\circ}\)

(3) \(45^{\circ}\)

(4) \(60^{\circ}\)

Q.63 For total internal reflection to take place, the angle of incidence \(i\) and the refractive index \(\mu\) of the medium must satisfy the inequality

(1) \(\frac{1}{\sin i}<\mu\)

(2) \(\frac{1}{\sin i}>\mu\)

(3) \(\sin i<\mu\)

(4) \(\sin i>\mu\) Q.64 When a ray of light emerges from a block of glass, the critical angle is

(1) Equal to the angle of reflection

(2) The angle between the refracted ray and the normal

(3) The angle of incidence for which the refracted ray travels along the glass-air boundary

(4) The angle of incidence

Q.65 For which of the following pairs the critical angle is smallest

(1) Water to air

(2) Glass to water

(3) Glass to air

(4) Glass to glass

Q.66 A fish is a little away below the surface of a lake. If the critical angle is \(49^{\circ}\) then the fish could see things above the water surface within an angular range of \(\theta^{\circ}\) where

(1) \(\theta=49^{\circ}\)

(2) \(\theta=90^{\circ}\)

(3) \(\theta=98^{\circ}\)

(4) \(\theta=24 \frac{1^{0}}{2}\)

Q.67 A diver in a swimming pool wants to signal his distress to a person lying on the edge of the pool by flashing his water proof flash light

(1) He must direct the beam vertically upwards

(2) He has to direct the beam horizontally

(3) He has to direct the beam at an angle to the vertically which is slightly less than the critical angle of incidence for total internal reflection

(4) He has to direct the beam at an angle to the vertical which is slightly more than the critical angle of incidence for the total internal reflection

Q.68 A ray of light propagates from glass (refractive index \(=3 / 2\) ) to water (refractive index \(=4 / 3\) ). The value of the critical angle

\[

\sin ^{-1}(1 / 2) \quad \text { (2) } \sin ^{-1}\left(\frac{\sqrt{8}}{9}\right)

\]

(3) \(\sin ^{-1}(8 / 9)\)

(4) \(\sin ^{-1}(5 / 7)\)

Q.69 A ray of light travels from an optically denser to rarer medium. The critical angle for the two media is \(C\). The maximum possible deviation of the ray will be

(1) \(\left(\frac{\pi}{2}-C\right)\)

(2) \(2 C\)

(3) \(\pi-2 C\)

(4) \(\pi-C\)

Q.70 A plano-convex lens of refractive index 1.5 and radius of curvature \(30 \mathrm{~cm}\) is silvered at the curved surface. Now this lens has been used to form the image of an object. At what distance from this lens an object be placed in order to have a real image of the size of the object

(1) \(20 \mathrm{~cm}\)

(2) \(30 \mathrm{~cm}\)

(3) \(60 \mathrm{~cm}\)

(4) \(80 \mathrm{~cm}\)

Q.71 At what distance from a convex lens of focal length \(30 \mathrm{~cm}\), an object should be placed so that the size of the image be \(1 / 2\) th of the object

(1) \(30 \mathrm{~cm}\)

(2) \(60 \mathrm{~cm}\)

(3) \(15 \mathrm{~cm}\)

(4) \(90 \mathrm{~cm}\) Q.72 A beam of parallel rays is brought to a focus by a plano-convex lens. A thin concave lens of the same focal length is joined to the first lens. The effect of this is

(1) The focal point shifts away from the lens by a small distance

(2) The focus remains undisturbed

(3) The focus shifts to infinity

(4) The focal point shifts towards the lens by a small distance

Q.73 A double convex lens \(\left(R_{1}=R_{2}=10 \mathrm{~cm}\right)\) having focal length equal to the focal length of a concave mirror. The radius of curvature of the concave mirror is

(1) \(10 \mathrm{~cm}\)

(2) \(20 \mathrm{~cm}\)

(3) \(40 \mathrm{~cm}\)

(4) \(15 \mathrm{~cm}\)

Q.74 Two lenses of power \(6 D\) and \(-2 D\) are combined to form a single lens. The focal length of this lens will be

(1) \(\frac{3}{2} m\)

(2) \(\frac{1}{4} m\)

(3) \(4 m\)

(4) \(\frac{1}{8} m\)

Q.75 A biconvex lens with equal radii curvature has refractive index 1.6 and focal length \(10 \mathrm{~cm}\). Its radius of curvature will be

(1) \(20 \mathrm{~cm}\)

(2) \(16 \mathrm{~cm}\)

(3) \(10 \mathrm{~cm}\)

(4) \(12 \mathrm{~cm}\)

Q.76 A plano convex lens is made of glass of refractive index 1.5. The radius of curvature of its convex surface is \(R\). Its focal length is

(1) \(R / 2\)

(2) \(R\)

(3) \(2 R\)

(4) \(1.5 R\)

Q.77 If two +5 diopter lenses are mounted at some distance apart, the equivalent power will always be negative if the distance is

(1) Greater then \(40 \mathrm{~cm}\)

(2) Equal to \(40 \mathrm{~cm}\)

(3) Equal to \(10 \mathrm{~cm}\)

(4) Less then \(10 \mathrm{~cm}\)

Q.78 A convex lens is made up of three different materials as shown in the figure. For a point object placed on its axis, the number of images formed are

(1) 1

(2) 5

(3) 4

(4) 3

Q.79 A point object \(O\) is placed in front of a glass rod having spherical end of radius of curvature \(30 \mathrm{~cm}\). The image would be formed at

(1) \(30 \mathrm{~cm}\) left

(2) Infinity

(3) \(1 \mathrm{~cm}\) to the right

(4) \(18 \mathrm{~cm}\) to the left

Q.80 An object is placed \(12 \mathrm{~cm}\) to the left of a converging lens of focal length \(8 \mathrm{~cm}\). Another converging lens of \(6 \mathrm{~cm}\) focal length is placed at a distance of \(30 \mathrm{~cm}\) to the right of the first lens. The second lens will produce

(1) No image

(2) A virtual enlarged image

(3) A real enlarged image

(4) A real smaller image

Q.81 A plano-convex lens \((f=20 \mathrm{~cm})\) is silvered at plane surface. Now it's focal length will be

(1) \(20 \mathrm{~cm}\)

(2) \(40 \mathrm{~cm}\)

(3) \(30 \mathrm{~cm}\)

(4) \(10 \mathrm{~cm}\) 

\section{GEOMETRICAL OPTICS}

Q.82 If the central portion of a convex lens is wrapped in black paper as shown in the figure

(1) No image will be formed by the remaining portion of the lens

(2) The full image will be formed but it will be less bright

(3) The central portion of the image will be missing

(4) There will be two images each produced by one of the exposed portions of the lens

Q.83 An object has image thrice of its original size when kept at \(8 \mathrm{~cm}\) and \(16 \mathrm{~cm}\) from a convex lens. Focal length of the lens is

(1) \(8 \mathrm{~cm}\)

(2) \(16 \mathrm{~cm}\)

(3) Between \(8 \mathrm{~cm}\) and \(16 \mathrm{~cm}\)

(4) Less then \(8 \mathrm{~cm}\)

Q.84 A convex lens forms a real image of an object for its two different positions on a screen. If height of the image in both the cases be \(8 \mathrm{~cm}\) and \(2 \mathrm{~cm}\), then height of the object is

(1) \(16 \mathrm{~cm}\)

(2) \(8 \mathrm{~cm}\)

(3) \(4 \mathrm{~cm}\)

(4) \(2 \mathrm{~cm}\)

Q.85 The radius curvature of a thin plano-convex lens is \(10 \mathrm{~cm}\) (of curved surface) and the refractive index is 1.5. If the plane surface is silvered, then the focal length will be

(1) \(15 \mathrm{~cm}\)

(2) \(20 \mathrm{~cm}\)

(3) \(5 \mathrm{~cm}\)

(4) \(10 \mathrm{~cm}\)

Q.86 A convex lens of focal length \(40 \mathrm{~cm}\) is an contact with a concave lens of focal length \(25 \mathrm{~cm}\). The power of combination is

(1) \(-1.5 \mathrm{D}\)

\((2)-6.5 \mathrm{D}\)

\((3)+6.5 \mathrm{D}\)

\((4)+6.67 \mathrm{D}\)

Q.87 A double convex thin lens made of glass (refractive index \(\mu=1.5\) ) has both radii of curvature of magnitude \(20 \mathrm{~cm}\). Incident light rays parallel to the axis of the lens will converge at a distance \(L\) such that

(1) \(L=20\)

(2) \(L=10\)

(3) \(L=40\)

(4) \(L=20 / 3\)

Q.88 An equiconvex lens of glass of focal length 0.1 metre is cut along a plane perpendicular to principle axis into two equal parts. The ratio of focal length of new lenses formed is

(1) \(1: 1\)

(2) \(1: 2\)

(3) \(2: 1\)

(4) \(2: \frac{1}{2}\)

Q.89 A convex lens of focal length \(0.5 \mathrm{~m}\) and concave lens of focal length \(1 \mathrm{~m}\) are combined. The power of the resulting lens will be

(1) \(1 \mathrm{D}\)

\((2)-1 \mathrm{D}\)

(3) \(0.5 \mathrm{D}\)

(4) \(-0.5 \mathrm{D}\)

Q.90 Two thin lenses of focal lengths \(f_{1}\) and \(f_{2}\) are in contact and coaxial. The combination is equivalent to a single lens of power

(1) \(\mathrm{f}_{1}+\mathrm{f}_{2}\)

(2) \(\frac{\mathrm{f}_{1} \mathrm{f}_{2}}{\mathrm{f}_{1}+\mathrm{f}_{2}}\)

(3) \(\frac{1}{2}\left(f_{1}+f_{2}\right)\)

(4) \(\frac{f_{1}+f_{2}}{f_{1} f_{2}}\)

Q.91 A candle placed \(25 \mathrm{~cm}\) from a lens, forms an image on a screen placed \(75 \mathrm{~cm}\) on the other end of the lens. The focal length and type of the lens should be

(1) \(+18.75 \mathrm{~cm}\) and convex lens

(2) \(-18.75 \mathrm{~cm}\) and concave lens

(3) \(+20.25 \mathrm{~cm}\) and convex lens

(4) \(-20.25 \mathrm{~cm}\) and concave lens

Q.92 We combined a convex lens of focal length \(f_{1}\) and concave lens of focal lengths \(f_{2}\) and their combined focal length was \(F\). The combination of these lenses will behave like a concave lens if

(1) \(f_{1}>f_{2}\)

(2) \(f_{1}<f_{2}\)

(3) \(f_{1}=f_{2}\)

(4) \(f_{1} \leq f_{2}\) Q.93 A double convex thin lens made of glass of refractive index 1.6 has radii of curvature \(15 \mathrm{~cm}\) each. The focal length of this lens when immersed in a liquid of refractive index 1.63 is

(1) \(-407 \mathrm{~cm}\)

(2) \(250 \mathrm{~cm}\)

(3) \(125 \mathrm{~cm}\)

(4) \(25 \mathrm{~cm}\)

Q.94 The relation between \(n_{1}\) and \(n_{2}\), if behaviour of light rays is as shown in figure is

(1) \(n_{1}>>n_{2}\)

(2) \(n_{2}>n_{1}\)

(3) \(n_{1}>n_{2}\)

(4) \(n_{1}=n_{2}\)

Q.95 The focal length of a lens is \(10 \mathrm{~cm}\) and its refractive index is 1.5 . If the radius of curvature of one surface is \(7.5 \mathrm{~cm}\), the radius of curvature of the second surface will be

(1) \(7.5 \mathrm{~cm}\)

(2) \(15.0 \mathrm{~cm}\)

(3) \(75 \mathrm{~cm}\)

(4) \(5.0 \mathrm{~cm}\)

Q.96 The object distance \(u\), the image distance \(v\) and the magnification \(m\) in a lens follow certain linear relations. These are

(1) \(\frac{1}{u} \operatorname{versus} \frac{1}{v}\)

(2) \(m\) versus \(u\)

(3) \(u\) versus \(v\)

(4) \(m\) versus \(v\)

Q.97 A lens of power +2 diopters is placed in contact with a lens of power -1 diopter. The combination will behave like

(1) A convergent lens of focal length \(50 \mathrm{~cm}\)

(2) A divergent lens of focal length \(100 \mathrm{~cm}\)

(3) A convergent lens of focal length \(100 \mathrm{~cm}\)

(4) A convergent lens of focal length \(200 \mathrm{~cm}\)

Q.98 A lens of refractive index \(n\) is put in a liquid of refractive index \(n\) ' of focal length of lens in air is \(f\), its focal length in liquid will be

(1) \(-\frac{f n^{\prime}(n-1)}{n^{\prime}-n}\)

(2) \(-\frac{f\left(n^{\prime}-n\right)}{n^{\prime}(n-1)}\)

(3) \(-\frac{n^{\prime}(n-1)}{f\left(n^{\prime}-n\right)}\)

(4) \(\frac{f n^{\prime} n}{n-n^{\prime}}\)

Q.99 An object of height \(1.5 \mathrm{~cm}\) is placed on the axis of a convex lens of focal length \(25 \mathrm{~cm}\). A real image is formed at a distance of \(75 \mathrm{~cm}\) from the lens. The size of the image will be

(1) \(4.5 \mathrm{~cm}\)

(2) \(3.0 \mathrm{~cm}\)

(3) \(0.75 \mathrm{~cm}\)

(4) \(0.5 \mathrm{~cm}\)

Q.100 A concave lens of focal length \(20 \mathrm{~cm}\) placed in contact with a plane mirror acts as a

(1) Convex mirror of focal length \(10 \mathrm{~cm}\)

(2) Concave mirror of focal length \(40 \mathrm{~cm}\)

(3) Concave mirror of focal length \(60 \mathrm{~cm}\)

(4) Concave mirror of focal length \(10 \mathrm{~cm}\)

Q.101 A achromatic combination is made with a lens of focal length \(f\) and dispersive power \(\omega\) with a lens having dispersive power of \(2 \omega\). The focal length of second will be

(1) \(2 f\)

(2) \(f / 2\)

(3) \(-f / 2\)

(4) \(-2 f\)

Q.102 A convex lens forms a real image of a point object placed on its principal axis. If the upper half of the lens is painted black, the image will

(1) Be shifted downwards

(2) Be shifted upwards

(3) Not be shifted

(4) Shift on the principal axis Q.103 In the figure an air lens of radii of curvature \(10 \mathrm{~cm}\left(R_{1}=R_{2}=10 \mathrm{~cm}\right)\) is cut in a cylinder of glass \((\mu=1.5)\). The focal length and the nature of the lens is

(1) \(15 \mathrm{~cm}\), concave

(2) \(15 \mathrm{~cm}\), convex

(3) \(\infty\), neither concave nor convex

(4) 0 , concave

Q.104 A biconvex lens forms a real image of an object placed perpendicular to its principal axis. Suppose the radii of curvature of the lens tend to infinity. Then the image would

(1) Disappear

(2) Remain as real image still

(3) Be virtual and of the same size as the object

(4) Suffer from aberrations

Q.105 An object is placed first at infinity and then at \(20 \mathrm{~cm}\) from the object side focal plane of the convex lens. The two images thus formed are \(5 \mathrm{~cm}\) apart. The focal length of the lens is

(1) \(5 \mathrm{~cm}\)

(2) \(10 \mathrm{~cm}\)

(3) \(15 \mathrm{~cm}\)

(4) \(20 \mathrm{~cm}\)

Q.106 An object is placed \(9 \mathrm{~cm}\) from a magnifying lens of focal length \(24 \mathrm{~cm}\). What is the magnitude of magnification

(1) 1.2

(2) 1.6

(3) 2.0

(4) 2.4

Q.107 Two lenses are placed in contact with each other and the focal length of combination is \(80 \mathrm{~cm}\). If the focal length of one is \(20 \mathrm{~cm}\), then the power of the other will be

(1) \(1.66 D\)

(2) \(4.00 D\)

(3) \(-1.00 D\)

(4) \(-3.75 D\)

Q.108 Sixteen thin convex lenses focal lengths \(f, 2 f, 4 f, 8 f \ldots \ldots\). are placed in contact with each other. The combination will behave as a convex lens of focal length approximately

(1) \(136 f\)

(2) \(39 f\)

(3) \(2 f\)

(4) \(f / 2\)

Q.109 For getting enlarged and real image by a convex lens of focal length \(15 \mathrm{~cm}\), the object is to be placed at a distance of ..... from the optical centre

(1) Between 0 and \(15 \mathrm{~cm}\)

(2) Between 15 and \(30 \mathrm{~cm}\)

(3) Between 30 and \(45 \mathrm{~cm}\)

(4) Between 45 and \(60 \mathrm{~cm}\)

Q.110 The angle of a prism is \(30^{\circ}\). The rays incident at \(60^{\circ}\) at one refracting face suffer a deviation of \(30^{\circ}\). The angle of emergence is

(1) \(0^{\circ}\)

(2) \(30^{\circ}\)

(3) \(60^{\circ}\)

(4) \(90^{\circ}\)

Q.111 When a glass prism of refracting angle \(60^{\circ}\) is immersed in a liquid its angle of minimum deviation is \(30^{\circ}\). The critical angle of glass with respect to the liquid medium is

(1) \(42^{\circ}\)

(2) \(45^{\circ}\)

(3) \(50^{\circ}\)

(4) \(52^{\circ}\)

Q.112 Which one of the following alternative is FALSE for a prism placed in a position of minimum deviation

(1) \(i_{1}=i_{2}\)

(2) \(r_{1}=r_{2}\)

(3) \(i_{1}=r_{1}\)

(4) All of these

Q.113 The dispersive powers of crown and flint glasses are 0.02 and 0.04 respectively. In an achromatic combination of lenses the focal length of flint glass lens is \(40 \mathrm{~cm}\). The focal length of crown glass lens will be

(1) \(-20 \mathrm{~cm}\)

\((2)+20 \mathrm{~cm}\)

(3) \(-10 \mathrm{~cm}\)

(4) \(+10 \mathrm{~cm}\)

Q.114 Under minimum deviation condition in a prism, if a ray is incident at an angle \(30^{\circ}\), the angle between the emergent ray and the second refracting surface of the prism is

(1) \(0^{\circ}\)

(2) \(30^{\circ}\)

(3) \(45^{\circ}\)

(4) \(60^{\circ}\) 

\section{GEOMETRICAL OPTICS}

Q.115 A ray of light passes through an equilateral glass prism in such a manner that the angle of incidence is equal to the angle of emergence and each of these angles is equal to \(3 / 4\) of the angle of the prism. The angle of deviation is

(1) \(45^{\circ}\)

(2) \(39^{\circ}\)

(3) \(20^{\circ}\)

(4) \(30^{\circ}\)

Q.116 The refracting angle of a prism \(A\) is small. The correct statement for the dispersive power of a prism is that dispersive power

(1) Depends upon the material of the prism

(2) Depends upon both material and angle of prism

(3) Depends only upon refracting angle of prism

(4) Is same for all colors of white light

Q.117 If a thin prism of glass is dipped into water then minimum deviation (with respect to air) of light produced by prism will be left \(\left({ }_{w} \mu_{g}=\frac{3}{2}\right.\) and \(\left.{ }_{a} \mu_{w}=\frac{4}{3}\right)\)

(1) \(\frac{1}{2}\)

(2) \(\frac{1}{4}\)

(3) 2

(4) \(\frac{1}{5}\)

Q.118 Dispersion of light is due to

(1) Wavelength

(2) Intensity of light

(3) Density of medium

(4) None of these

Q.119 A thin prism \(P_{1}\) of angle of prism \(4^{\circ}\) and refractive index 1.54 is combined with another thin prism \(P_{2}\) of refractive index 1.72 for dispersion without deviation. The angle of prism of \(P_{2}\) is

(1) \(5.33^{\circ}\)

(2) \(4^{\circ}\)

(3) \(3^{\circ}\)

(4) \(2.6^{\circ}\)

Q.120 White light is passed through a prism whose angle is \(5^{\circ}\). If the refractive indices for rays of red and blue colour are respectively 1.64 and 1.66 the angle of deviation between the two colours will be

(1) 0.1 degree

(2) 0.2 degree

(3) 0.3 degree

(4) 0.4 degree

Q.121 We use flint glass prism to disperse polychromatic light because light of different colours

(1) Travel with same speed

(2) Travel with same speed but deviate differently due to the shape of the prism

(3) Have different anisotropic properties while travelling through the prism

(4) Travel with different speeds

Q.122 The angle of minimum deviation measured with a prism is \(30^{\circ}\) and the angle of prism is \(60^{\circ}\). The refractive index of prism material is

(1) \(\sqrt{2}\)

(2) 2

(3) \(3 / 2\)

(4) \(4 / 3\)

Q.123 The minimum deviation produced by a hollow prism filled with a certain liquid is found to be \(30^{\circ}\). The light ray is also found to be refracted at angle of \(30^{\circ}\). The refractive index of the liquid is

(1) \(\sqrt{2}\)

(2) \(\sqrt{3}\)

(3) \(\sqrt{\frac{3}{2}}\)

(4) \(\frac{3}{2}\)

Q.124 The dispersion for a medium of wavelength \(\lambda\) is \(D\), then the dispersion for the wavelength \(2 \lambda\) will be

(1) \(D / 8\)

(2) \(D / 4\)

(3) \(D / 2\)

(4) \(D\) Q.125 A real image of a distant object is formed by a plano-convex lens on its principal axis. Spherical aberration

(1) Is absent

(2) Is smaller if the curved surface of the lens faces the object

(3) Is smaller if the plane surface of the lens faces the object

(4) Is the same whichever side of the lens faces the object

Q.126 Near and far points of human eye are

(1) \(25 \mathrm{~cm}\) and infinite

(2) \(50 \mathrm{~cm}\) and \(100 \mathrm{~cm}\)

(3) \(25 \mathrm{~cm}\) and \(50 \mathrm{~cm}\)

(4) \(0 \mathrm{~cm}\) and \(25 \mathrm{~cm}\)

Q.127 A defective eye cannot see close objects clearly because their image is formed

(1) On the eye lens

(2) Between eye lens and retina

(3) On the retina

(4) Beyond retina

Q.128 A person who can see things most clearly at a distance of \(10 \mathrm{~cm}\). Requires spectacles to enable him to see clearly things at a distance of \(30 \mathrm{~cm}\). What should be the focal length of the spectacles

(1) \(15 \mathrm{~cm}\) (concave)

(2) \(15 \mathrm{~cm}\) (convex)

(3) \(10 \mathrm{~cm}\)

(4) 0

Q.129 A person suffering from 'presbyopia' should use

(1) Aconcave lens

(2) A convex lens

(3) A bifocal lens whose lower portion is convex

(4) A bifocal lens whose upper portion is convex

Q.130 A person uses spectacles of power \(+2 D\). He is suffering from

(1) Short sightedness or myopia

(2) Long sightedness or hypermetropia

(3) Presbyopia

(4) Astigmatism

Q.131 A person can see a thing clearly when it is at a distance of 1 metre only. If he wishes to see a distance star, he needs a lens of focal length

(1) \(+100 \mathrm{~cm}\)

(2) \(-100 \mathrm{~cm}\)

(3) \(+50 \mathrm{~cm}\)

(4) \(-50 \mathrm{~cm}\)

Q.132 A person can see clearly objects at \(100 \mathrm{~cm}\) distance. If he wants to see objects at \(40 \mathrm{~cm}\) distance, then the power of the lens he shall require is

(1) \(+1.5 \mathrm{D}\)

(2) \(-1.5 D\)

(3) \(+3.0 D\)

(4) \(-3.0 \mathrm{D}\)

Q.133 If the distance of the far point for a myopia patient is doubled, the focal length of the lens required to cure it will become

(1) Half

(2) Double

(3) The same but a convex lens

(4) The same but a concave lens

Q.134 One can take pictures of objects which are completely invisible to the eye using camera film which are invisible to

(1) Ultra-violet rays

(2) Sodium light

(3) Visible light

(4) Infra-red rays

Q.135 The maximum focal length of the eye-lens of a person is greater than its distance from the retina. The eye is

(1) Always strained in looking at an object

(2) Strained for objects at large distances only

(3) Strained for objects at short distances only

(4) Unstrained for all distances

Q.136 The focal length of a normal eye-lens is about

(1) \(1 \mathrm{~mm}\)

(2) \(2 \mathrm{~cm}\)

(3) \(25 \mathrm{~cm}\)

(4) 1 

Q.137 If the eye is taken as a spherical ball of radius \(1 \mathrm{~cm}\), the range of accommodated focal length of eye-lens is

(1) \(1.85 \mathrm{~cm}\) to \(2.0 \mathrm{~cm}\)

(2) \(1.0 \mathrm{~cm}\) to \(2.8 \mathrm{~cm}\)

(3) \(1.56 \mathrm{~cm}\) to \(2.5 \mathrm{~cm}\)

(4) \(1.6 \mathrm{~cm}\) to \(2.0 \mathrm{~cm}\)

Q.138 A person cannot read printed matter within \(100 \mathrm{~cm}\) from his eye. The power of the correcting lens required to read at \(20 \mathrm{~cm}\) from his eye if the distance between the eye lens and the correcting lens is 2 \(\mathrm{cm}\) is

(1) \(4.8 D\)

(2) \(1.25 D\)

(3) \(4.25 \mathrm{D}\)

(4) \(4.55 \mathrm{D}\)

Q.139 In a simple microscope, if the final image is located at \(25 \mathrm{~cm}\) from the eye placed close to the lens, then the magnifying power is

(1) \(\frac{25}{f}\)

(2) \(1+\frac{25}{f}\)

(3) \(\frac{f}{25}\)

(4) \(\frac{f}{25}+1\)

Q.140 Wavelength of light used in an optical instrument are \(\lambda_{1}=4000 \AA\) and \(\lambda_{2}=5000 \AA\), then ratio of their respective resolving power (corresponding to \(\lambda_{1}\) and \(\lambda_{2}\) ) is

(1) \(16: 25\)

(2) \(9: 1\)

(3) \(4: 5\)

(4) \(5: 4\)

Q.141 The angular magnification of a simple microscope can be increased by increasing

(1) Focal length of lens

(2) Size of object

(3) Aperture of lens

(4) Power of lens

Q.142 Relative difference of focal lengths of objective and eye lens in the microscope and telescope is given as

(1) It is equal in both

(2) It is more in telescope

(3) It is more in microscope

(4) It may be more in any one

Q.143 If the red light is replaced by blue light illuminating the object in a microscope the resolving power of the microscope

(1) Decreases

(2) Increases

(3) Gets halved

(4) Remains unchanged

Q.144 In case of a simple microscope, the object is placed at

(1) Focus \(f\) of the convex lens

(2) A position between \(f\) and \(2 f\)

(3) Beyond \(2 f\)

(4) Between the lens and \(f\)

Q.145 In a compound microscope cross-wires are fixed at the point

(1) Where the image is formed by the objective

(2) Where the image is formed by the eye-piece

(3) Where the focal point of the objective lies

(4) Where the focal point of the eye-piece lies

Q.146 To produce magnified erect image of a far object, we will be required along with a convex lens, is

(1) Another convex lens

(2) Concave lens

(3) A plane mirror

(4) A concave mirror

Q.147 In a compound microscope, if the objective produces an image \(I_{o}\) and the eye piece produces an image \(I_{e}\), then

(1) \(I_{o}\) is virtual but \(I_{e}\) is real

(2) \(I_{o}\) is real but \(I_{e}\) is virtual

(3) \(I_{o}\) and \(I_{e}\) are both real

(4) \(I_{o}\) and \(I_{e}\) are both virtual Q.148 The focal length of the objective of a compound microscope is \(f_{0}\) and its distance from the eyepiece is \(L\). The object is placed at a distance \(u\) from the objective. For proper working of the instrument

(1) \(L<u\)

(2) \(L>u\)

(3) \(f_{0}<L<2 f_{0}\)

(4) \(L>2 f_{0}\)

Q.149 Find the maximum magnifying power of a compound microscope having a 25 diopter lens as the objective, a 5 diopter lens as the eyepiece and the separation \(30 \mathrm{~cm}\) between the two lenses. The least distance for clear vision is \(25 \mathrm{~cm}\)

(1) 8.4

(2) 7.4

(3) 9.4

(4) 10.4

Q.150 The focal length of the objective and the eye-piece of a microscope are \(2 \mathrm{~cm}\) and \(5 \mathrm{~cm}\) respectively and the distance between them is \(30 \mathrm{~cm}\). If the image seen by the eye is \(25 \mathrm{~cm}\) from the eye-piece, the distance of the object from the objective is

(1) \(0.8 \mathrm{~cm}\)

(2) \(2.3 \mathrm{~cm}\)

(3) \(0.4 \mathrm{~cm}\)

(4) \(1.2 \mathrm{~cm}\)

Q.151 If the focal length of objective and eye lens are \(1.2 \mathrm{~cm}\) and \(3 \mathrm{~cm}\) respectively and the object is put 1.25 \(\mathrm{cm}\) away from the objective lens and the final image is formed at infinity. The magnifying power of the microscope is

(1) 150

(2) 200

(3) 250

(4) 400

Q.152 When the object is self-luminous, the resolving power of a microscope is given by the expression

(1) \(\frac{2 \mu \sin \theta}{\lambda}\)

(2) \(\frac{\mu \sin \theta}{\lambda}\)

(3) \(\frac{2 \mu \cos \theta}{\lambda}\)

(4) \(\frac{2 \mu}{\lambda}\)

Q.153 A telescope of diameter \(2 m\) uses light of wavelength \(5000 \AA\) for viewing stars. The minimum angular separation between two stars whose image is just resolved by this telescope is

(1) \(4 \times 10^{-4} \mathrm{rad}\)

(2) \(0.25 \times 10^{-6} \mathrm{rad}\)

(3) \(0.31 \times 10^{-6} \mathrm{rad}\)

(4) \(5.0 \times 10^{-3} \mathrm{rad}\)

Q.154 To increase both the resolving power and magnifying power of a telescope

(1) Both the focal length and aperture of the objective has to be increased

(2) The focal length of the objective has to be increased

(3) The aperture of the objective has to be increased

(4) The wavelength of light has to be decreased

Q.155 A telescope has an objective of focal length \(50 \mathrm{~cm}\) and an eye piece of focal length \(5 \mathrm{~cm}\). The least distance of distinct vision is \(25 \mathrm{~cm}\). The telescope is focussed for distinct vision on a scale \(200 \mathrm{~cm}\) away. The separation between the objective and the eye-piece is

(1) \(75 \mathrm{~cm}\)

(2) \(60 \mathrm{~cm}\)

(3) \(71 \mathrm{~cm}\)

(4) \(74 \mathrm{~cm}\)

Q.156 The focal lengths of the objective and the eyepiece of an astronomical telescope are \(20 \mathrm{~cm}\) and \(5 \mathrm{~cm}\) respectively. If the final image is formed at a distance of \(30 \mathrm{~cm}\) from the eye piece, find the separation between the lenses for distinct vision

(1) \(32.4 \mathrm{~cm}\)

(2) \(42.3 \mathrm{~cm}\)

(3) \(24.3 \mathrm{~cm}\)

(4) \(30.24 \mathrm{~cm}\)

Q.157 The magnifying power of a telescope is \(M\). If the focal length of eye piece is doubled, then the magnifying power will become

(1) \(2 M\)

(2) \(M / 2\)

(3) \(\sqrt{2 M}\)

(4) \(3 M\)

Q.158 The final image in an astronomical telescope is

(1) Real and errect

(2) Virtual and inverted

(3) Real and inverted

(4) Virtual and errect Q.159 The focal length of objective and eye-piece of a telescope are \(100 \mathrm{~cm}\) and \(5 \mathrm{~cm}\) respectively. Final image is formed at least distance of distinct vision. The magnification of telescope is

(1) 20

(2) 24

(3) 30

(4) 36

Q.160 The diameter of the objective of the telescope is 0.1 metre and wavelength of light is \(6000 \AA\). Its resolving power would be approximately

(1) \(7.32 \times 10^{-6}\) radian

(2) \(1.36 \times 10^{6}\) radian

(3) \(7.32 \times 10^{-5}\) radian

(4) \(1.36 \times 10^{5}\) radian

Q.161 The length of a telescope is \(36 \mathrm{~cm}\). The focal length of its lenses can be

(1) \(30 \mathrm{~cm}, 6 \mathrm{~cm}\)

(2) \(-30 \mathrm{~cm},-6 \mathrm{~cm}\)

(3) \(-30 \mathrm{~cm},-6 \mathrm{~cm}\)

(4) \(-30 \mathrm{~cm}, 6 \mathrm{~cm}\)

Q.162 The image of a star (effectively a point source) is made by convergent lens of focal length \(50 \mathrm{~cm}\) and diameter of aperture \(5.0 \mathrm{~cm}\). If the lens is ideal, and the effective wavelength in image formation is taken as \(5 \times 10^{-5} \mathrm{~cm}\), the diameter of the image formed will be nearest to

(1) Zero

(2) \(10^{-6} \mathrm{~cm}\)

(3) \(10^{-5} \mathrm{~cm}\)

(4) \(10^{-3} \mathrm{~cm}\)

Q.163 The limit of resolution of a \(100 \mathrm{~cm}\) telescope \(\left(\lambda=5.5 \times 10^{-7} \mathrm{~m}\right)\) is

(1) \(0.14 "\)

(2) \(0.3 "\)

(3) \(1^{\prime}\)

(4) 1 "

Q.164 A planet is observed by an astronomical refracting telescope having an objective of focal length \(16 \mathrm{~m}\) and an eyepiece of focal length \(2 \mathrm{~cm}\)

(1) The distance between the objective and the eyepiece is \(16.02 \mathrm{~m}\)

(2) The angular magnification of the planet is 800

(3) The image of the planet is inverted

(4) The objective is larger than the eyepiece

Q.165 The focal length of the objective and eye piece of a telescope are respectively \(60 \mathrm{~cm}\) and \(10 \mathrm{~cm}\). The magnitude of the magnifying power when the image is formed at infinity is

(1) 50

(2) 6

(3) 70

(4) 5

Q.166 The focal length of an objective of a telescope is 3 metre and diameter \(15 \mathrm{~cm}\). Assuming for a normal eye, the diameter of the pupil is \(3 \mathrm{~mm}\) for its complete use, the focal length of eye piece must be

(1) \(6 \mathrm{~cm}\)

(2) \(6.3 \mathrm{~cm}\)

(3) \(20 \mathrm{~cm}\)

(4) \(60 \mathrm{~cm}\)

Q.167 An observer looks at a tree of height \(15 m\) with a telescope of magnifying power 10 . To him, the tree appears

(1) 10 times taller

(2) 15 times taller

(3) 10 times nearer

(4) 15 times nearer

Q.168 The magnification produced by an astronomical telescope for normal adjustment is 10 and the length of the telescope is \(1.1 \mathrm{~m}\). The magnification when the image is formed at least distance of distinct vision \((D\) \(=25 \mathrm{~cm})\) is

(1) 14

(2) 6

(3) 16

(4) 18

Q.169 The objective of a telescope has a focal length of \(1.2 \mathrm{~m}\). it is used to view a \(10.0 \mathrm{~m}\) tall tower \(2 \mathrm{~km}\) away. What is the height of the image of the tower formed by the objective

(1) \(2 \mathrm{~mm}\)

(2) \(4 \mathrm{~mm}\)

(3) \(6 \mathrm{~mm}\)

(4) \(8 \mathrm{~mm}\) Q.170 An eye-piece of a telescope with a magnification of 100 has a power of 20 diopters. The object of this telescope has a power of

(1) 2 diopters

(2) 0.2 diopters

(3) 2000 diopters

(4) 20 diopters

Q.171 A Galilean telescope measures \(9 \mathrm{~cm}\) from the objective to the eye-piece. The focal length of the objective is \(15 \mathrm{~cm}\). Its magnifying power is

(1) 2.5

(2) \(2 / 5\)

(3) \(5 / 3\)

(4) 0.4

Q.172 For seeing a cricket match, we prefer binoculars to the terrestrial telescope, because

(1) Binoculars give three-dimensional view

(2) Terrestrial telescope gives inverted image

(3) To avoid chromatic aberration

(4) To have larger magnification

Q.173 A simple two lens telescope has an objective of focal length \(50 \mathrm{~cm}\) and an eye-piece of \(2.5 \mathrm{~cm}\). The telescope is pointed at an object at a very large distance which subtends at an angle of 1 milliradian on the naked eye. The eye piece is adjusted so that the final virtual image is formed at infinity. The size of the real image formed by the objective is

(1) \(5 \mathrm{~mm}\)

(2) \(1 \mathrm{~mm}\)

(3) \(0.5 \mathrm{~mm}\)

(4) \(0.1 \mathrm{~mm}\)

Q.174 The objective of a telescope, after focussing for infinity is taken out and a slit of length \(L\) is placed in its position. A sharp image of the slit is formed by the eye-piece at a certain distance from it on the other side. The length of this image is \(l\), then magnification of telescope is

(1) \(\frac{l}{2 L}\)

(2) \(\frac{2 L}{l}\)

(3) \(\frac{l}{L}\)

(4) \(\frac{L}{l}\)