Question

a medal in a plastic cube appears to be 12mm below its upper surface. if n=1.5 for the plastic, the depth of the medal is actually
a) 6mm
b) 8mm
c) 18mm
d) 5mm

correct option is c. but how?

Answer 1

A medal in plastic cube appears to be 12mm below its upper surface.
e.g., apparent depth = 12mm
let actual depth of medal in plastic cube is h ,
We know, actual depth/apparent depth = refractive index of plastic with respect to air
⇒ h/12mm = 1.5
⇒ h = 12 × 1.5 mm = 18 mm

Hence, actual depth of medal in plastic cube is 18mm

Answer 2

"The actual depth of the medal is 18mm.

Due to the refraction of light, the depth of an object may appear altered. This is called as apparent depth of the object.

The ratio of the actual depth to the apparent depth gives the refractive index of the material.  

Given

Apparent depth, $\mathrm{d}_{\mathrm{app}}=12 \mathrm{mm}$

Refractive index, n = 1.5

Actual depth, $\mathrm{d}_{\mathrm{act}}=?$

Solution:

$n=\frac{d_{act}}{d_{app}}$

$d_{a c t}=n \times d_{a p p}$

$d_{a c t}=1.5 \times 12$

$d_{a c t}=18 \mathrm{mm}$"