Question

A glass slab of thickness $12\,mm$ is placed on a table. The lower surface of the slab has a black spot. At what depth from the upper surface will the spot appear when viewed from above? Refractive index of glass $ = 1.5$ .
A) $9\,mm$
B) $8\,mm$
C) $18\,mm$
D) $12\,mm$

Answer 1

Hint:Here we have to use the relation between real depth, apparent depth and refractive index. Real depth is the real distance of an object below the surface, which can be calculated by submerging the ideal ruler along with it. The depth of an object in the rarer medium which is seen from the rarer medium is known as the apparent depth.

Complete step by step solution:
Given,
Real depth $ = 12\,mm$

Refractive index, $\mu = 1.5$

We know that,
Refractive index,
$
  \mu = \dfrac{{{\text{real}}\,{\text{depth}}}}{{{\text{apparent}}\,{\text{depth}}}} \\
  1.5 = \dfrac{{12\,mm}}{{{\text{apparent}}\,{\text{depth}}}} \\
  {\text{apparent}}\,{\text{depth}} = \dfrac{{12\,mm}}{{1.5}} = 8\,mm \\
$

The depth from the upper surface will the spot appear when viewed from above is $8\,mm$.

Additional information: As a ray of light passes from one medium to another, there is a difference in the velocity and path of the ray due to a refraction that results in a false appearance of the depth of the material. The approximate depth that the translucent medium is known as the actual depth.
Refractive index: the refractive index is a value determined by the ratio of the velocity of light in the vacuum to that of the second medium of higher density.
The higher the refractive index, the slower the light passes, resulting in a correspondingly improved change in the path of light inside the object. What this means for lenses is that a higher refractive index film will bend the light further to make a lower profile of the lens.

Note: We should always remember that the apparent depth is smaller than the real depth. Also we have to carefully remember the formula for refractive index. If we change the numerator and denominator, we shall get a different answer.