Question

There is a small air bubble inside a glass sphere $ (\mu = 1.5) $ of radius $ 10cm $ . The bubble is $ 4cm $ below the surface and is viewed normally from the outside the apparent depth of the bubble is:
(A) $ 3cm $ below the surface
(B) $ 5cm $ below the surface
(C) $ 8cm $ below the surface
(D) $ 10cm $ below the surface

Answer 1

Hint: This question is based on the concept of refraction and refractive index. Refraction is the change in direction of a wave passing from one medium to another or from a gradual change in the medium. The bending of the sun's rays as they enter raindrops is a perfect example of refraction.

Complete answer:
Refractive Index is a value calculated from the ratio of the speed of light in a vacuum to that in a second medium of greater density. Refractive index is represented by the symbol $ \mu $ .
According to the question,
Refractive index of glass sphere $ {\mu _1} = 1.5 $
Refractive index of air $ {\mu _2} = 1 $
Radius $ R = - 10cm $
Since the bubble is $ 4cm $ below the surface and it is also viewed from outside, so,
 $ u = - 4cm $
To solve this question the formula of refractive index will be used.
 $ \dfrac{{{\mu _2}}}{v} - \dfrac{{{\mu _1}}}{u} = \dfrac{{{\mu _2} - {\mu _1}}}{R} $
On putting the required values,
 $ \dfrac{1}{v} - \dfrac{{1.5}}{{ - 4}} = \dfrac{{1 - 1.5}}{{ - 10}} $
 $ \dfrac{1}{v} = \dfrac{{0.5}}{{10}} - \dfrac{{1.5}}{4} $
On further simplifying, we get,
 $ v = - 3.03cm $
Hence, The bubble will appear $ 3.03cm $ below the surface.
Now, $ 3.03cm $ can be approximated as $ 3cm $
So, the final answer is (A) $ 3cm $ below the surface.

Note:
Absolute refractive index is a special case of refractive index. The absolute refractive index is defined as the ratio of the speed of light in vacuum and in the given medium. Also, the absolute refractive index is never less than $ 1 $ as the speed of light in vacuum is the maximum.