Question

The velocity of light in air is $3 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$ . If the refractive index of glass with respect to air is $1.5$ , then velocity of light in glass is:
A. $2 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$
B. $4.5 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$
C. $3 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$
D. $1 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$

Answer 1

The given speed of light in SI units is $3 \times {10^8}\,m\,{\sec ^{ - 1}}$ . This is the maximum speed any known object or wave can travel with. Therefore, eliminate the options which have value greater than the speed of light in air. Refractive index of a medium is the ratio of the speed of light in vacuum to the speed of light in the medium. Use this formula and solve accordingly.

Complete step by step answer:
We are given the speed of light in air which has the same value as the speed of light in vacuum. We are required to calculate the speed of light in glass having a refractive index $1.5$ .The given quantities are: velocity of light in air is $3 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$, refractive index of glass with respect to air is $1.5$ .We are required to find the speed of light in glass.Refractive index $\mu$ for any substance is defined as the ratio of the speed of light in vacuum $c$ to speed of light in that substance $v$ . This is represented as:
$\mu = \dfrac{c}{v}$
$\Rightarrow v = \dfrac{c}{\mu }$
Substituting the given values, we get
$v = \dfrac{{3 \times {{10}^{10}}\,cm\,{{\sec }^{ - 1}}}}{{1.5}}$
$\therefore v = 2 \times {10^{10}}\,cm\,{\sec ^{ - 1}}$
This the required velocity of light in glass.

Therefore, option A is the correct option.

Note: The given unit of speed of light in air was in $cm\,{\sec ^{ - 1}}$ and the options were also in the same units. Hence, we did not convert the units in SI, to avoid more unnecessary steps. Remember that the speed of light in vacuum has the maximum value and nothing in the universe can have speed greater than that.