Chapter 33, Problem 33.1DQ

Light requires about 8 minutes to travel from the sun to the earth. Is it delayed appreciably by the earth’s atmosphere? Explain.

To determine

To determine: Whether the light requires about $8$ minutes to travel from the sun to the earth is delayed appreciably by the earth’s atmosphere or not.

Explanation of Solution

Explanation:

The speed of light in a medium is,

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

$c$ is the speed of light.

$n$ is the refractive index.

The refractive index of the air is,

$n=1.000277$.

The refractive index of the vacuum is,

$n=1$.

The speed of light is,

$c=3\times {10}^8\text{m}/\text{s}$

The speed of the light in vacuum is $3\times {10}^8\text{m}/\text{s}$ because the refractive index of vacuum is 1.

$\begin{array}{c}v=\frac{3\times {10}^8\text{m}/\text{s}}{1}\\ =3\times {10}^8\text{m}/\text{s}\end{array}$

Substitute $1.000277$ for $n$ and $3\times {10}^8\text{m}/\text{s}$ for $c$ in above equation to calculate the speed of light in the air medium.

$\begin{array}{c}v=\frac{3\times {10}^8\text{m}/\text{s}}{1.000277}\\ =2.99\times {10}^9\text{m}/\text{s}\end{array}$

Refractive index of air is greater than the vacuum. The speed of light has an inverse relation with the refractive index. Hence, velocity of the light in air is decreased in earth’s atmosphere. Hence, the time taken by light from sun to earth is a little more than the time taken, if there were no atmosphere.

Conclusion:

The Light requires about $8$ minutes to travel from the sun to the earth, it is delayed appreciably by the earth’s atmosphere.