Question

If the index of refraction of diamond is 2.0, velocity of light in diamond in cm/second is approximately
A. \[6 \times {10^{10}}\;{\rm{cm/s}}\]
B. \[3 \times {10^{10}}\;{\rm{cm/s}}\]
C. \[2 \times {10^{10}}\;{\rm{cm/s}}\]
D. \[1.5 \times {10^{10}}\;{\rm{cm/s}}\]

Answer 1

Hint: The above problem can be resolved by applying the formula of the refractive index of the diamond, that is numerically given by taking the fraction of the speed of light in air and the speed of light while entering into the diamond. From this formula, the speed of light ray in the diamond can be determined, following the substitution of the known as well as the standard values.

Complete step by step answer:
The refractive index of diamond is. \[\mu = 2.0\].
The expression for the velocity of light in diamond is,
\[{v_d} = \dfrac{c}{\mu }\]
Here, c is the velocity of light in air and its value in cm/s is, \[3 \times {10^{10}}\;{\rm{cm/s}}\].
Solve by substituting the values as,
\[\begin{array}{l}
{v_d} = \dfrac{c}{\mu }\\
{v_d} = \dfrac{{3 \times {{10}^{10}}\;{\rm{cm/s}}}}{{2.0}}\\
{v_d} = 1.5 \times {10^{10}}\;{\rm{cm/s}}
\end{array}\]
Therefore, the speed of light in diamond is \[1.5 \times {10^{10}}\;{\rm{cm/s}}\]

So, the correct answer is “Option D”.

Note:
 Try to remember the mathematical relation for the refractive index of the medium and the speed of light, entering the same medium. The refractive index is one of the major properties of any material that determines the nature of light rays travelling down the medium. Moreover, the concept of refractive index can be applied in determining the path of light rays, while travelling from any specific media into another medium. Besides, the refractive index always depends on the material of the medium. Moreover, the concept of velocity of light for the different medium is also necessary to take such consideration as possible.