Numerical problems

Problem 4

Speed of light in air is 3 × 108 m s-1 and the speed of light in a medium is 2 ×108 ms-1. Find the refractive index of the medium with respect to air.

Solution

Refractive index (μ) = Speed of light in air (c) / Speed of light in the medium (v)

μ = 3×108 / 2×108 = 1.5

Problem 5

Refractive index of water is 4/3 and the refractive index of glass is 3/2. Find the refractive index of glass with respect to the refractive index of water.

Solution

wμg = Refractive index of glass / Refractive index of water

 = (3/2) / (4/3) = 9/8 = 1.125

1. The radius of curvature of a spherical mirror is 25 cm. Find its focal length.

Answer:

Given : Radius of curvature = 25 cm

To find : f = ?

Solution : f = R/2 = 25/2

f = 12.5 cm

2. If two plane mirrors are inclined to each other at an angle of 45°, find the number of images formed.

Answer:

Given :  Angle of inclination = 45o

To find : Number of images formed = [ 360o / angle ] − 1

Solution :

= [ 360o / 45o ] −1

= 8 – 1 = 7 images

3. Speed of light in air is 3 × 108 m s–1 and the refractive index of a medium is 1. 5. Find the speed of light in the medium.

Answer:

Given : Speed of light in air c = 3 × 108 ms-1

Refractive index of a medium μ = 1.5

To find : Speed of light in medium v = ? 

Formula : μ= c/v

Solution : 1.5 = [ 3 × 108 ] / v

V = [3×108] / 1.5

v = 2 × 108 ms-1

Speed of light in medium v = 2 × 108 ms-1