Question

The optical path of a monochromatic light is the same if it goes through 2.00 cm of glass or x cm of ruby. If the refractive index of glass is 1.510 and that of ruby is 1.760, the value of x is:
(A) 1.6 cm
(B) 1.68 cm
(C) 1.716 cm
(D) 1.74 cm

Answer 1

Hint: To answer this question, we have to start the answer by equating the two optical paths of the monochromatic light inside the glass and the ruby. Since, it is the same as mentioned in the question, the refractive index when compared will give us the answer. So developing the equation of the optical paths of the monochromatic light inside the glass and the ruby, and then comparing them will give us the answer.

Complete step by step answer:
We know that the optical path is given as $\mu t$.
Since it is mentioned in the question that the optical path remains the same for the monochromatic light inside the glass and ruby, we can say that:
${\mu _1}{t_1} = {\mu _2}{t_2}$
Here, ${\mu _1}$is the refractive index of the monochromatic light inside the glass. The thickness of glass is given as ${t_1}$. The ${\mu _2}$ is the refractive index of ruby and the thickness is given as x.
Now put the values in the above equation:
$
   \Rightarrow 1.510 \times 2 = 1.760 \times x \\
   \Rightarrow x = \dfrac{{1.510 \times 2}}{{1.760}} \\
   \Rightarrow x = 1.716cm \\
 $
Hence the thickness of the ruby is 1.716 cm.

So, option C is the correct answer.

Note: In the question, we have mentioned the refractive index. The meaning of refractive index should be, for the better understanding. Refractive index is defined as the measure of the bending which is experienced by a ray of light. This situation occurs when a ray of light passes from one medium to another.
The importance of the refractive index is that higher will be the value of the refractive index, the closer will be the ray of light travel from the normal.