Question

In the figure given below, APB is a curved surface of radius of curvature 10 cm separating air and a transparent material $(μ = \frac{4}{3} ).$ A point object O is placed in air on the principal axis of the surface 20 cm from P. The distance of the image of O from P will be _____.
Fill in the blank with the correct answer from the options given below

• A. 16 cm left of P in air
• B. 16 cm right of P in water
• C. 20 cm right of P in water
• D. 20 cm left of P in air

Answer 1

Answer: (A)

16 cm left of P in air

Answer 2

The refraction at a spherical surface is governed by the formula

$\frac{μ2}{v} −\frac{ μ1}{ u} = \frac{μ2 − μ1}{ R}$

where, $\mu_1 = 1 \ (\text{for air}), \ \mu_2 = \frac{4}{3}, \ u = -20 \ \text{cm}, \ R = 10 \ \text{cm}$

Substitute the values into the formula

$\frac{4}{3v} - \frac{1}{-20} = \frac{\frac{4}{3} - 1}{10}$

Simplifying, $\frac{4}{3v} + \frac{1}{20} = \frac{1}{30}$

$\frac{4}{3v} = \frac{1}{30} - \frac{1}{20} = \frac{2 - 3}{60} = \frac{-1}{60}$

Thus, $v = -16 \ \text{cm}$,
This means the image is 16 cm to the left of P in air.