# Optics – Modern Physics

**OPTICS**

Optics is the branch of physics which deals with the study of production, propagation and nature of light. It is divided into two branches :(i) Ray optics (ii) Wave optics

**REFLECTION OF LIGHT**

It is defined as, a part of incident light is turned back into the same medium.

In figure* i* and *r* represent incident ray and reflected ray respectively.

**Laws of Reflection**

The angle of incidence i equals the angle of reflection r.

Incident ray, the normal and the reflected ray lie in the same plane. The above laws of reflection are valid both in case of plane and curved reflecting surfaces.

For normal incidence i.e., ∠i = 0, ∠r = 0. Hence a ray of light falling normally on a mirror retraces its path on reflection.

**Reflection from Plane Surface**

– The image formed by a plane mirror is at the same distance behind the mirror as the object is in front of it.

– The image formed by a plane mirror is laterally inverted. The lateral inversion means that the right side of the object appears as the left side of the image and vice-versa.

– The image formed by a plane mirror is virtual, erect w.r.t. object and of the same size as the object.

– If keeping the incident ray fixed, the plane mirror is rotated through an angle θ, the reflected ray turns through double the angle i.e., 2θ in that very direction.

– If the object is fixed and the mirror moves relative to the object with a speed *v*, the image moves with a speed 2*v* relative to the object.

– If the mirror is fixed and the object moves relative to the mirror with a speed v, the image also moves with the same speed v relative to the mirror. Deviation suffered by a light ray incident at an angle *i* is given by

δ = (180° – 2*i*)

**Number of Images Formed by Two Inclined Mirrors**

If 360°/θ = even number; number of images = 360°/θ − 1

If 360°/θ = odd number; number of images = 360°/θ − 1 if the object is placed on the angle bisector.

If 360°/θ = odd number; number of images = 360°/θ, if the object is not placed on the angle bisector.

If 360°/θ ≠ integer, then count the number of images as explained above.

Illustration 1 : Two mirrors are inclined by an angle 30°. An object is placed making 10° with the mirror M1. Find the positions of first two images formed by each mirror. Find the total number of images.

**Soln.: Figure is self explanatory.**

Number of images 360°/30°= (evennumber)

Therefore number of images = 12 – 1 = 11

SPHERICAL MIRRORS

Spherical Mirror is formed by polishing one surface of a part of sphere.

D e p e n d i n g upon which part is shining the spherical mirror is classified as

– Concave mirror, if the side towards center of curvature is shining.

– Convex mirror, if the side away from the center of curvature is shining.

– Important Terms for Spherical Mirrors Pole (P), is the mid point of reflecting surface. Centre of curvature (C), is the centre of the sphere of which the mirror is a part.

– Radius of curvature, is the radius of the sphere of which the mirror is a part. Distance between P and C.

– Principal axis, is the straight line connecting pole P and centre of curvatrue C.

– Principal focus (F), is the point of intersection of all the reflected rays which strikes the mirror parallel to the principal axis. In concave mirror it is real and in the convex mirror it is virtual.

– Focal length (f), is distance from pole to focus. Aperture, the diameter of the mirror is called aperture of the mirror.

**Focal Plane :** Plane perpendicular to principal axis and passing through focus is known as focal plane.

Sign convention We follow Cartesian co-ordinate system conventions according to which

The pole of mirror is the origin.

The distance measured in the direction of the incident rays is considered as positive x-axis.

The heights measured in the vertically up direction are positive y-axis.

**Mirror Formula**

1/f = 1/v + 1/u

u = distance of object, v = image distance, f = focal length and f = R/2; R = radius of curvature.

**Ray Tracing**

Following facts are useful in ray tracing.

If the incident ray is parallel to the principal axis, the reflected ray passes through the focus.

If the incident ray passes through the focus, then the reflected ray is parallel to the principal axis.

Incident ray passing through centre of curvature will be reflected back through the centre of curvature (because it is a normally incident ray).

It is easy to make the ray tracing of a ray incident at the pole as shown below.

**Magnification**

Linear magnification : **m =h1/h2 = -v/u**

h1 = height of the object, h2 = height of the image. (h1 and h2 both are perpendicular to the principal axis of mirror)

Note: If the image is upright or erect with respect to the object then m is positive. And m is negative if the image is inverted with respect to the object.

Longitudinal magnification = **v2-v1/u2-u1 **[for small sized object]