Question

A small object is embedded in a glass sphere (μ = 1.5) of radius 5.0 cm at a distance 1.5 cm left to the centre. Locate the image of the object as seen by an observer standing (a) to the left of the sphere and (b) to the right of the sphere.

Answer 1

Given,
Radius of the sphere = 5.0 cm
Refractive index of the sphere (μ₁) = 1.5
An object is embedded in the glass sphere 1.5 cm left to the centre.

(a)  
When the image is seen by observer from left of the sphere,
from surface the object distance (u) = − 3.5 cm
μ₁ = 1.5
μ₂ = 1
v₁ = ?
Using lens equation: 
\[\frac{\mu_2}{v_1} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}\]
\[\frac{1}{v_1} - \frac{1 . 5}{- (3 . 5)} = \frac{- 0 . 5}{- 5}\]
\[\frac{1}{v_1} = \frac{1}{10} - \frac{3}{7}\]
\[= \frac{7 - 30}{70}\]
\[= \frac{- 23}{70}\]
\[v_1  = \frac{- 70}{23} \simeq  - 3  \text{ cm }\] 
So the image will be formed at 2 cm (5 cm - 3cm) left to centre. 

(b) When the image is seen by observer from the right of the sphere,
u = −(5.0 + 1.5) = − 6.5,
R = −5.00 cm
μ₁ = 1.5, μ₂ = 1, v = ?

Using lens equation:
\[\frac{\mu_2}{v_1} - \frac{\mu_1}{u} = \frac{\mu_2 - \mu_1}{R}\] 
\[\frac{1}{v} - \frac{1 . 5}{6 . 3} = \frac{1}{10}\] 
\[\frac{1}{v} = \frac{1}{10} - \frac{3}{13}\]
\[= \frac{13 - 30}{130}\]
\[= \frac{- 17}{130}\]
\[v = \frac{- 130}{17} =  - 7 . 65  \text{ cm }\]
Therefore, the image will be formed 7.6 − 5 = 2.6 towards left from centre.