Question

A ray of light enters a diamond from air. If the refractive index of diamond is 2.42. By what percent is the speed of light reduced on entering the diamond?

Answer 1

Hint: First we will define a ray. Later we will discuss the refractive index in short. We will then apply a simple formula that relates speed of air in vacuum, speed of air in any other medium and the refractive index and answer this question.

Formula Used:
\[n = \dfrac{c}{v}\]
Where,
\[n\] =refractive index
\[c\] =speed of light
\[v\] =phase velocity of light.

Complete step by step solution:
Have you ever been in a dark room with no lights at all when there is sunlight outside your room? What will happen when a little hole is made in the room? We will see that a little sunlight enters the room in a straight line . This is ray or in other words each of the lines in which light (and heat) may seem to stream from the sun or any luminous body when passed through a small opening.
Let us look at the refractive index: it is the ratio of the velocity of light in a vacuum to its velocity in a specified medium. Hence it is given by \[n = \dfrac{c}{v}\].
In this question it has been given that
\[{\text{n }} = {\text{ }}2.42\]
\[c = 3 \times {10^8}m{s^{ - 1}}\]
Using the value in the formula above,
\[n = \dfrac{c}{v}\]
On substituting the values we get
\[2.42 = \dfrac{{3 \times {{10}^8}}}{v}\]
On further solving we get
\[v = \dfrac{{3 \times {{10}^8}}}{{2.42}}\]
\[ \Rightarrow v = 1.23 \times {10^8}m{s^{ - 1}}\]
Speed of light in diamond is: \[1.23 \times {10^8}m{s^{ - 1}}\]
\[\% {\text{ }}of{\text{ }}speed{\text{ }}in{\text{ }}diamond = \dfrac{{1.23 \times {{10}^8}}}{{3.8 \times {{10}^8}}} \times 100\]
\[ \Rightarrow 0.3236 \times 100\]
Finally we get
\[ \Rightarrow 32.36\% \]
Thus there is \[32.36\% \] decrease in the speed of light in diamond than in air .

Note:
1) Do not forget to find the percentage of refractive index decreased after finding the speed of light in diamond.
2) do not write any units for refractive index and percentage found at last because, refractive index is a ratio and percentage is a mathematical operation.