question_answer

A small coin is resting on the bottom of a beaker filled with a liquid. A ray of light from the coin travels upto the surface of the liquid and moves along its surface (see figure). [AIPMT (S) 2007]

How fast is the light travelling in the liquid?

A)  \[1.8\times {{10}^{8}}m/s\]    

B)  \[2.4\times {{10}^{8}}m/s\]

C)  \[3.0\times {{10}^{8}}m/s\]

D)       \[1.2\times {{10}^{8}}m/s\]

Correct Answer: A

Solution :

Key Idea : Critical angle is the angle of incidence in denser medium for which the angle of refraction in rarer medium is .

As shown in figure, a light ray from the coin will not emerge out of liquid, if .

Therefore, minimum radius R corresponds to . In

or

or

Given,

Hence,

or          or

But        or