PHYSICS FOR NEET

GEOMETRICAL OPTICS

The branch optics in physics is related with the study of phenomenon of light. It is divided in two parts- geometrical and wave optics. In geometrical we deal with the rectilinear propagation of light. For e.g. Reflection, Refraction, Shadow formation etc. We will start with some basic definitions.

Source :

A body which emits light is called source.

(a) Selfluminous : The source which possess light of its own. For example sun.

(b) Non-luminous : It is a source of light which does not possess light of its own.

Ray :

Aray of light is the straight line path of transfer of light energy. It is represented by a straight line with an arrow - head indicating the direction of propagation.

Beam 

A bundle or bunch of rays is called a beam. It is of following three types :

(a) Convergent beam : In this case diameter of beam decreases in the direction of ray.

(b) Divergent beam : It is a beam in which all the rays meet at a point when produced backward and the diameter of beam goes on increasing as the rays proceed forward.

(c) Parallel beam : It is a beam in which all the rays constituting the beam move parallel to each other and diameter of beam remains same.

Shadow formation :

Parallel beam of light

Shadow formation is explained by the law of rectilinear propagation of light which state that in a homogeneous medium light travels along straight paths. Thus, an opaque object placed between a point source of light and screen will cast a shadow with a sharply defined boundary.

\section{PLANE MIRROR :}

It is a highly polished smooth surface from which most of the incident light gets reflected. It is represented by a line with hatches in the reverse side of the smooth surface.

OBJECT :}

Real Object 

If incident rays before event are diverging on the optical instrument then the point of divergence is real object with respect to the optical instrument.

\( Virtual Object \)

If incident rays before event are converging on optical instrument then the point of convergence is virtual object with respect to the optical instrument.

\section{Real Image :}

If rays after event are converging then the point of convergence is real image with respect to the optical instrument.

Virtual Image :

If rays after event are diverging then the point of the divergence is virtual image.

Note :

(i) Point at which reflected or refracted rays actually converge is called real image. Or point from which reflected or refracted rays appear to diverge is called virtual image.

(ii) Minimum two reflected or refracted rays are required to determine the image position. Law of Rectilinear Propagation of Light states that light propagates in straight lines in homogeneous media.

Law of Independence of Light Rays states that rays do not disturb each other upon intersection.

Law of Reversibility of Light Rays states that rays retrace their path when their direction is reversed.

Laws Of Reflection :

A. The incident - ray, reflected ray and normal to the reflecting surface at the point of incidence all lie in the same plane.

B. The angle of reflection is equal to the angle of incidence, i.e. \(\angle \mathrm{i}=\angle \mathrm{r}\).

CHARACTERISTICS OF REFLECTION AT PLANE MIRROR :

1. The image is always of same size and at same distance behind the mirror as the object in front of it.

2. When the object is real virtual image is formed and vice - versa.

3. The image is laterally inverted. The mirror actually reverses front and back in three dimensions (and not left to right ) i.e. only x-direction is reversed resulting in the change of left into right or vice - versa. A plane mirror changes right handed co-ordinate system to left handed one.

4. Though every part of a mirror forms complete image of an object, we usually see only that part of image from which light after reflection from the mirror reaches our eye. 5. Deviation \(\delta\) is defined as the angle between directions of incident ray and emergent ray. So if light is incident at an angle of incidence \(\mathrm{i}, \quad \delta=\pi-(\mathrm{i}+\mathrm{r})=\pi-2 \mathrm{i}\)

Deviation \(\delta\) produced by a plane mirror.

6. If keeping the incident ray fixed, the mirror is rotated by an angle \(\theta\), about an axis in the plane of mirror, The reflected ray is rotated through an angle \(2 \theta\).

7. To see complete image in a plane mirror the minimum length of plane mirror should be half the height of a person

Prove

\(\mathrm{H}=\) Height of the \(\operatorname{man}=2 \mathrm{x}+2 \mathrm{y}=2(\mathrm{x}+\mathrm{y})\)

Length of mirror \(\quad l=(\mathrm{x}+\mathrm{y})\)

From (i) and (ii)

\[

\begin{aligned}

& \mathrm{H}=2 l \\

& l=\frac{\mathrm{H}}{2}

\end{aligned}

\]

\section{Total number of image formed by two inclined mirror :}

When two plane mirrors are inclined at an angle \(\theta\) and an object is placed in between them due to multiple reflection more than one images are formed. This number of image \(\mathrm{n}\) is either even or odd.

\section{Locating all the images formed by two plane Mirrors :}

Consider two plane mirrors \(M_{1}\) and \(M_{2}\) inclined at an angle \(\theta=\alpha+\beta\) as shown in figure.

Point \(P\) is an object kept such that it makes angle \(\alpha\) with mirror \(M_{1}\) and angle \(\beta\) with mirror \(M_{2}\). Image of object \(P\) formed by \(M_{1}\), denoted by \(I_{1}\), will be inclined by angle \(\alpha\) on the other side of mirror \(M_{1}\). This angle is written in bracket in the figure besides I1. Similarly image of object \(\mathrm{P}\) formed by \(\mathrm{M}_{2}\), denoted by 

\section{GEOMETRICAL OPTICS}

\(\mathrm{I}_{2}\), will be inclined by angle \(\beta\) on the other side of mirror \(\mathrm{M}_{2}\). This angle is written in bracket in the figure besides \(\mathrm{I}_{2}\).

Now \(I_{2}\) will act as an obect for \(M_{1}\) which is at an angle \((\alpha+2 \beta)\) from \(M_{1}\). Its image will be formed at \((\alpha+2 \beta)\) on the opposite side of \(M_{1}\). This image will be denoted as \(I_{21}\), and so on. The process continuous till the angles reach \(180^{\circ}\).

Note :

(i) All the images lie on a circle whose radius is equal to the distance between object \(\mathrm{O}\) and the point of intersection of mirrors \(\mathrm{C}\).

(ii) The number of images seen may be different from number of images formed and depends on the position of the observer relative to object and mirrors.