Question

Number of waves in $8cm$ of vacuum is same as number of waves in $xcm$ of a medium, RI of medium is $\dfrac{4}{3}$ , value of $x$ is
A. $\dfrac{32}{3}cm$
B. $12cm$
C. $6cm$
D. $4cm$

Answer 1

Hint: Refractive index is the ratio of the velocity of light in vacuum to its velocity in a medium. In the question, we will use the concept of Relative refractive index, which is the ratio of speed of light in two different media.

Complete step-by-step answer:
When we measure the value of speed of light in two different media, Relative refractive index of medium 1 with respect to medium 2 is defined as the ratio of speed of light in medium 2 to the speed of light in medium 1.
Expression for Relative refractive index-
${{n}_{12}}=\dfrac{\text{speed of light in medium 2}}{\text{speed of light in medium 1}}$
When a light ray propagates from one medium to another, then refractive index is known as Relative refractive index, while in case when light travels from vacuum to some other medium, then refractive index is called Absolute refractive index. Refractive index of vacuum is always taken as 1.
We are given the number of waves in $8cm$ of vacuum is the same as the number of waves in $xcm$ of a medium. As the refractive index of medium is given as $\dfrac{4}{3}$ ,
$\text{Refractive index of medium = }\dfrac{\text{speed of light in vacuum}}{\text{speed of light in medium}}$
Time taken by the wave is the same in both cases; the equation gets reduced to the ratio of distances travelled by the wave in vacuum and the medium.
Applying the equation of Refractive index we get,
$\begin{aligned} & \dfrac{4}{3}=\dfrac{8}{x} \\\ & x=\dfrac{8\times 3}{4}=6 \\\ \end{aligned}$
Value of $x$ is 6 cm
Hence, the correct option is C.

Note: Students should not get confused between the concept of Absolute refractive index and Relative refractive index. Absolute refractive index is taken in reference with the speed of light in vacuum while in case of relative refractive index; both the mediums are other than vacuum.