Chapter 18, Problem 96A

To determine

Extra time required for sunlight to reach the Earth.

Answer to Problem 96A

  $\Delta t=164\text{s}$

Explanation of Solution

Given:

Distance of the Sun from the Earth, $d=1.5\times {10}^8\text{km}=1.5\times {10}^{11}\text{m}$

Space between the Sun and the Earth is filled with water.

Formula Used:

The time, distance and speed relation is, $t=\frac{d}{s}$

Where $t$ is time, $d$ is distance and $s$ is speed.

And velocity of light through any medium is, $v=\frac{c}{n}$

Where, $c$ is speed of light in vacuum and $n$ is refractive index of the given medium.

Calculation:

Time taken by sunlight to reach the Earth through vacuum,

  $\begin{array}{c}t=\frac{d}{c}\\ =\frac{1.5\times {10}^{11}}{3\times {10}^8}\\ =50\text{s}\end{array}$

As the refractive index of water is $n=1.33$

So, velocity of light through water is

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

Now, time taken by sunlight to reach the Earth through water,

  $\begin{array}{c}t=\frac{d}{c}\\ =\frac{1.5\times {10}^{11}}{2.26\times {10}^8}\\ =664\text{s}\end{array}$

So, extra time required is

  $\begin{array}{c}\Delta t=664-500\\ =164\text{s}\end{array}$

Conclusion:

Therefore, the extra time require for sunlight to reach the Earth is $164\text{s}$ .