Question

Light travels through a glass plate of thickness $t$ and refractive index $n$. If $c$ is the velocity of light in a vacuum, then the time taken by light to travel through the thickness of the plate will be
(A) $\dfrac{nt}{c}$
(B) $\dfrac{t}{nc}$
(C) $\dfrac{tc}{n}$
(D) $\dfrac{c}{nt}$

Answer 1

Hint In this question, we have to find the time taken by light to travel through the thickness of the plate. As we know, the speed of light in the glass plate is $\dfrac{c}{n}$. Using this formula we find out the time taken by light to travel.

Complete step by step answer:
Given:
The thickness of the glass plate $=t$
Refractive index $=n$
The velocity of light in a vacuum $=c$
We use the following formula to solve this question
Speed of light in a glass plate $=\dfrac{c}{n}$
$v=\dfrac{c}{n}$
Time taken $=\dfrac{t}{v}$
Now we substitute the value of $v$ from the above equation,
Time taken $=\dfrac{t}{\dfrac{c}{n}}$
On further solving this we get,
Time taken $=\dfrac{nt}{c}$
The time taken by light to travel through the thickness of the plate is $\dfrac{nt}{c}$.

So option A is the correct answer.

Note: To solve this type of question we have to study the reflection and refraction of light. Reflection is the change in direction of a wavefront at an interface between two different media so that the wavefront returns into the medium from which it originated. And refraction of light is the bending of light as it passes from one transparent substance into another. This bending by refraction makes it possible for us to have lenses, prisms, magnifying glasses, rainbows. After studying these terms, you can easily solve this type of question.