Question

Light takes $8$ minutes $20$ seconds to reach from the sun on the earth. If the whole atmosphere is filled with water, the light will take the time $({\mu }_w=\frac{4}{3})$:

• A. $8$ minutes $20$ seconds
• B. $8$ minutes
• C. $6$ minutes $11$ seconds
• D. $11$ minutes $6$ seconds

Answer 1

The correct option is D $11$ minutes $6$ seconds

The refractive index, $n$ is given as;

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

Where:

$c=$ speed of light in vacuum.

$v=$ speed of light in medium.

Therefore,

for water,

$\frac{4}{3}=\frac{c}{v}$

$v=\frac{3c}{4}$

With speed $c$, time taken $=8min20sec=500sec$

Therefore, with speed $\frac{3c}{4}$

Time taken $=666.67sec=11min6sec$

Thus, if the atmosphere is filled with water, the sunlight will take 11 min 6 seconds to reach to earth surface.