Question

The refractive index of diamonds is 2. The velocity of light (in cm/s) diamond will be:
A. $6 \times {10^{10}}$
B. $2 \times {10^{13}}$
C. $1.5 \times {10^{10}}$
D. $3 \times {10^{10}}$

Answer 1

Hint As the refractive index of solid is the ratio of the velocity of light ion air to the velocity of light in medium. As speed of light in air is an refractive index of diamond is given in the question then we can find the velocity of light in diamond by substituting the values in the formula and then convert the unit m/s into cm/s.

Step by step solution
We know that the velocity of light in vacuum is $c = 3 \times {10^8}m{s^{ - 1}}$
Given that the value of refractive index of diamond is $\eta = 2$
We know that the refractive index η of any medium is defined as the ratio of speed of air to the speed of light in medium i.e.
$ \Rightarrow \eta = \dfrac{c}{v}$……………………. (1)
Now, rearranging the above equation, we get
$ \Rightarrow v = \dfrac{c}{\eta }$………………………. (2)
Now, substitute the values in equation (2), we get
$ \Rightarrow v = \dfrac{{3 \times {{10}^8}}}{2}$
On solving above equation, we get
$ \Rightarrow v = 1.5 \times {10^8}m{s^{ - 1}}$
But in the question, it is mentioned that we need to write the velocity in cm/s, so we need to convert meter into centimeter multiply the value by 100, we get
$ \Rightarrow v = 1.5 \times {10^8}m{s^{ - 1}} = 1.5 \times {10^8} \times 100 = 1.5 \times {10^{10}}cm{s^{ - 1}}$
Therefore, the value of velocity of light in diamond in cm/s is $1.5 \times {10^{10}}$

Hence, option C is correct.

Note For these types of questions, firstly we need to recall the formula that is used in the question. Then we will write the value of the variables given in the question then solve for the result. Then do conversion of the unit if needed for the question.