Question

If it takes 8 minutes and 20 seconds for sunlight to reach the earth, find the distance between the earth and the sun. The velocity of light is \[3\times {{10}^{8}}m{{s}^{-1}}\].
\[\begin{align}
  & \text{A) 15}\times {{10}^{10}}m \\
 & \text{B) 25}\times {{10}^{10}}m \\
 & \text{C) 30}\times {{10}^{10}}m \\
 & \text{D) 5}\times {{10}^{10}}m \\
\end{align}\]

Answer 1

Hint: We need to understand the basic relationship between the time taken for any object or even the light rays to travel a distance with the velocity with which the object travels in the given medium. We can easily solve this problem with this idea.

Complete answer:
We know that the sun is the star which provides our planet earth with the sufficient heat and light energy for survival. The appropriate distance of the sun from the earth protects us from extreme heat or extreme cold conditions which will not support life. We are given the information on the time taken for the light to reach the earth from the sun at dawn. We already know the speed of light in vacuum. Using this information, we can find the distance travelled by the light rays, i.e., the distance between the sun and the earth.
We know that the velocity of a particle in a medium is the ratio of the distance travelled by the particle to the time taken for the travel. In our case, the time taken and the velocity of the light rays is given. So, we can find the distance travelled as –
\[\begin{align}
  & \text{Speed = }\dfrac{\text{Distance travelled}}{\text{Time taken}} \\
 & \Rightarrow \text{Distance travelled = Speed }\times \text{ Time taken} \\
 & \Rightarrow S=vt \\
 & \Rightarrow S=3\times {{10}^{8}}\times \{(8\times 60)+20\} \\
 & \Rightarrow S=3\times {{10}^{8}}\times 500 \\
 & \therefore S=15\times {{10}^{10}}m \\
\end{align}\]
This is the distance travelled by the light from the sun to the earth. So, the distance between the sun and the earth is given as \[15\times {{10}^{10}}m\].

The correct answer is option A.

Note:
The light always travels in a straight-line path unless there is an obstacle comparable to its wavelength that is present in the path of the light. So, it is easy for us to calculate the distance between the celestial bodies using the time taken for light to reach one to another.