Question

The average distance between Earth and the Sun is $1.496 \times {10^8}$ km and the speed of light coming from the Sun is $3 \times {10^8}\,m{s^{ - 1}}$ . How much time will it take for the Sun's rays to reach Earth?
A. $3$ min
B. $498.66$ s
C. $8$ min $30$ s
D. $554$ s

Answer 1

Hint: Speed is the ratio of distance travelled to the time taken to cover that distance. Rearrange the formula such that time is on one side and rest terms are on the other side. Then substitute the values to get the final answer.

Complete step by step solution:
We know that speed is total distance travelled divided by the total time taken to cover that distance. In the question, we are given the distance and speed. So, we can easily find the time taken.

Speed of light is denoted by the letter $c$ . Let the distance between the Sun and the Earth be denoted by $d$ and the time taken for the light to reach the Earth’s surface be denoted by $t$ .
So, we can have:
$c = \dfrac{d}{t}$
$ \Rightarrow t = \dfrac{d}{c}$

Substituting the values, we have:
$ t = \dfrac{{1.496 \times {{10}^8} \times {{10}^3}\,m}}{{3 \times {{10}^8}\,m{s^{ - 1}}}}$
$ \Rightarrow t = 498.66\,s$
$ \therefore t = 498.66\,s$
Therefore, the time taken for light to reach Earth’s surface from the Sun is $498.66\,s$.

Hence, option B is the correct answer.

Additional details:
The speed of light is constant in vacuum while this speed is different when light travels in different mediums. Also, gravity is known to be capable of bending light rays. The speed of light is little less than the one mentioned in the question.

Note: Don’t forget to convert the units in SI units. While calculating be careful that the distance is given in kilometres while speed of light has units in meters and seconds. Please remember that the distance between the Sun and the Earth is given as average. The distance between the Sun and the Earth is changing throughout the year.