Question

What is the time taken by light to cross a glass 2 mm thick? (Refractive index of glass = 1.5)
A. \[{10^{ - 10}}\,{\text{s}}\]
B. \[{10^{ - 12}}\,{\text{s}}\]
C. \[{10^{ - 11}}\,{\text{s}}\]
D. \[{10^{ - 9}}\,{\text{s}}\]

Answer 1

Hint:The change in the speed of light depends on the refractive index of the medium. Refractive index of the medium is the ratio of speed of light in free space to the speed of light in the given medium. Calculate the speed of light in glass and use the distance-velocity relation to determine the time taken.

Formula used:
Refractive index,\[\mu = \dfrac{c}{v}\],
where, c is the speed of light in free space and v is the speed of light in the given medium.
\[t = \dfrac{d}{v}\],
where, t is the time, d is the distance and v is the velocity.

Complete step by step answer:
We know that the speed of light decreases when its travels through a medium other than air. The change in the speed of light depends on the refractive index of the medium. We have expression for the refractive index of the medium,
\[\mu = \dfrac{c}{v}\]
Here, c is the speed of light in free space and v is the speed of light in the given medium.
Rearranging the above equation for v, we get,
\[v = \dfrac{c}{\mu }\]
Substituting \[c = 3 \times {10^8}\,{\text{m/s}}\] and \[\mu = 1.5\] in the above equation, we get,
\[v = \dfrac{{3 \times {{10}^8}}}{{1.5}}\]
\[ \Rightarrow v = 2 \times {10^8}\,{\text{m/s}}\]
Thus, the speed of light in the given glass will be \[v = 2 \times {10^8}\,{\text{m/s}}\].
Now, we have the relation between distance, velocity and time,
\[t = \dfrac{d}{v}\]
Here, d is the thickness of the glass and t is the time taken by the light to cross the glass.
Substituting \[d = 2\,{\text{mm}} = 2 \times {10^{ - 3}}\,{\text{m}}\] and \[v = 2 \times {10^8}\,{\text{m/s}}\] in the above equation, we get,
\[t = \dfrac{{2 \times {{10}^{ - 3}}}}{{2 \times {{10}^8}}}\]
\[ \therefore t = {10^{ - 11}}\,{\text{s}}\]
Therefore, the time taken by the light to cross the given thickness of the glass is \[{10^{ - 11}}\,{\text{s}}\].

So, the correct answer is option C.

Note:The speed of light in any medium other than air and vacuum is less than its speed in air and vacuum because the refractive index of every medium is greater than and equal to one. Make sure that you have converted the thickness of the glass into meters since we have expressed the speed of light in m/s. The time required to cross this thickness in air would be less than we have obtained for glass.