Question

The distance travelled by light in glass (refractive index = 1.5) in a nanosecond will be
A. \[45\,cm\]
B. \[40\,cm\]
C. \[30\,cm\]
D. \[20\,cm\]

Answer 1

Hint: The distance travelled by the light in glass is equal to the product of the speed of light in glass and the given time. So first find the speed of light in glass.

Complete step by step solution:
Let \[{\mu _g}\] be the refractive index of glass and \[c'\] be the speed of light in glass.
It is given that \[{\mu _g} = 1.5 = \dfrac{3}{2}\]
The speed of light in glass is given by the relation
\[c' = \dfrac{c}{{{\mu _g}}} \Rightarrow c' = \dfrac{{2c}}{3}\] , As the speed of light in air is \[3 \times {10^8}\,m/s\]
\[\therefore c' = \dfrac{{2 \times 3 \times {{10}^8}}}{3} = 2 \times {10^8}\,m/s\]
Distance travelled by the light in 1 nanosecond or \[1 \times {10^{ - 9}}\,s\]is given by
\[2 \times {10^8} \times 1 \times {10^{ - 9}}m = 0.2\,m = 20\,cm\]
The distance travelled by light in glass (refractive index = 1.5) in a nanosecond will be \[20{\text{ }}cm\] .

Hence, the correct option is (D).

Additional Information: Light while travelling in a uniform substance, or medium, propagates in a straight line at a relatively constant speed, unless it is refracted, reflected, diffracted in some other manner. However, the intensity of light and other electromagnetic radiation is inversely proportional to the square of the distance travelled.

Note: When light travelling through the air enters a different medium, such as glass or water, the speed and wavelength of light are reduced. Light travels at approximately 300,000 kilometers per second in a vacuum, which has a refractive index of 1.0, but it slows down to 225,000 kilometers per second in water which have a refractive index of 1.3 and 200,000 kilometers per second in glass which have a refractive index of 1.5.