Question

How long does it take light to travel through a 2.5 mm thick piece of window glass?
t=? s
Through what thickness of water could light travel in the same amount of time?
d=? mm

Answer 1

Concepts and reason

The concepts required to solve the given problem are refractive index, velocity, distance, and time.

Initially, calculate the time taken by the light to travel in the glass by using the relation between velocity and distance. Finally, Calculate the distance travelled by the light in water by using the relation between velocity and distance.

Fundamentals

The refractive index is the ratio of the velocity of light in vacuum to the velocity of light in medium.

The expression for the refractive index is,

$n = \frac{c}{v}$

Here, c is the velocity of light in vacuum and v is the velocity of light in medium.

Velocity is the ratio of the distance to the time.

$v = \frac{d}{t}$

Here, v is the velocity, d is the distance, and t is the time.

The velocity of light is,

$v = \frac{c}{n}$

Substitute $3 \times {10^8}\;{\rm{m/s}}$ for c and 1.5 for n.

$\begin{array}{c}\\v = \frac{{3 \times {{10}^8}\;{\rm{m/s}}}}{{1.5\;}}\\\\ = 2 \times {10^8}\;{\rm{m/s}}\\\end{array}$

The velocity is,

$v = \frac{d}{t}$

From the above equation, the time taken by the light to travel in the glass is,

$t = \frac{d}{v}$

Substitute $2 \times {10^8}\;{\rm{m/s}}$ for v and $2.5 \times {10^{ - 3}}\;{\rm{m}}$ for d.

$\begin{array}{c}\\t = \frac{{2.5 \times {{10}^{ - 3}}\;{\rm{m}}}}{{2 \times {{10}^8}\;{\rm{m/s}}}}\\\\ = 1.25 \times {10^{ - 11}}\;{\rm{s}}\\\end{array}$

The velocity of light in water is,

$v = \frac{c}{n}$

Substitute $3 \times {10^8}\;{\rm{m/s}}$ for c and 1.33 for n.

$\begin{array}{c}\\v = \frac{{3 \times {{10}^8}\;{\rm{m/s}}}}{{1.33\;}}\\\\ = 2.26 \times {10^8}\;{\rm{m/s}}\\\end{array}$

The velocity is,

$v = \frac{d}{t}$

From the above equation, the distance travelled by the light in water is,

$d = vt$

Substitute $2.26 \times {10^8}\;{\rm{m/s}}$ for v and $1.25 \times {10^{ - 11}}\;{\rm{s}}$ for t.

$\begin{array}{c}\\d = \left( {2.26 \times {{10}^8}\;{\rm{m/s}}} \right)\left( {1.25 \times {{10}^{ - 11}}\;{\rm{s}}} \right)\\\\ = 2.83 \times {10^{ - 3}}\;{\rm{m}}\left( {\frac{{{{10}^3}\;{\rm{mm}}}}{{1\;{\rm{m}}}}} \right)\\\\ = 2.83\;{\rm{mm}}\\\end{array}$

Ans:

The time taken by the light to travel in the glass is $1.25 \times {10^{ - 11}}\;{\rm{s}}$ .

The distance travelled by the light in water is 2.83 mm.