Question

Time taken by the sunlight to pass through a window of thickness 4mm whose refractive index is 1.5, is?

Answer 1

Let S be the speed of light in the window
1/1.5 = S/3*10^8
Since speed of light in air is 3*10^8m/s and refractive index of air is 1
S = 2*10^8 m/s
Time = distance / speed
= 4*10^-3m/2*10^8 = 2*10^-11 s

Answer 2

Time taken by the sunlight to pass through a window of thickness 4mm whose refractive index is $2 \times 10^{-11}$ seconds.

Given:

Thickness (x) = 4mm = $4 \times 10^{-3} \ m$

Velocity of light in vacuum (c) = $3 \times 10^{8} \ \mathrm{ms}^{-1}$

Refractive index $(\mu)$ = 1.5

Formula to be used:

• $Refractive \ index =\frac{c}{v}$
• $Velocity =\frac{\text { Distance travelled }}{\text { Time taken }}$

Solution:

Refractive index $=\frac{c}{v}$

$1.5=\frac{3 \times 10^{8}}{v}$

$\mathrm{v}=\frac{3 \times 10^{8}}{1.5}$

$\Rightarrow \mathrm{v}=2 \times 10^{8} \mathrm{m} / \mathrm{s}$

Hence, from the above calculation, it is found that the distance travelled by the light is $2 \times 10^{8} \ \mathrm{m} / \mathrm{s}$.

When this value is substituted in the below given formula we get:

$Velocity =\frac{\text { Distance travelled }}{\text { Time taken }}$

$Time \ taken =\frac{\text { Distance travelled }}{\text { Time taken }}$

$Time \ taken =\frac{4 \times 10^{-3}}{2 \times 10^{8}}$

$\Rightarrow Time \ taken = 2 \times 10^{-11} \ s$