Question

An air bubble in a glass slab (\[\mu =1.5\]) from one side is 5 cm and from the other side is 2 cm. The thickness of the glass slab in cm is?
(A)3.75
(B)3
(C)10.5
(D)2.5

Answer 1

Hint: This is a problem in which due to refraction of light an object appears of smaller length when viewed from above. This involves the use of depths- real and apparent. Refractive index is given so we may use Snell's law.

Complete step by step answer:
We know from the formula the relationship between real depth, apparent depth and refractive index is given by:
\[\mu =\dfrac{real depth}{apparent depth}\]
Here we need to find what is the thickness of the glass slab involved Also, we are viewing it first from one side and then from another side. Another assumption we are making is to let the real depth be x. Now the real depth will remain unchanged whether we consider it from one side or another.
From one side the apparent depth is 5 cm
\[\begin{align}
  & \mu =\dfrac{x}{5} \\
 & 1.5=\dfrac{x}{5} \\
 & x=7.5cm \\
\end{align}\]
So, when viewed from one side real depth comes out to be 7.5 cm.
Now from another side,
\[\begin{align}
  & \mu =\dfrac{x}{2} \\
 & 1.5=\dfrac{x}{2} \\
 & x=3cm \\
\end{align}\]
So, when viewed from one sidereal depth comes out to be 3 cm.
when viewed from one side appears at 5 cm and 2 cm from other side, then thickness of slab is therefore (3+7.5) cm which is 10.5 cm

So, the correct answer is “Option C”.

Note:
This question can also be done by first assuming the thickness of the glass slab is T. And then using the formula twice once by not taking into account the thickness and other by taking into account thickness. Because we are assuming that the bubble sits on closer to one face of the slab.