Question

Light takes 8 min 20 sec to reach from sun on earth. If the whole atmosphere is filled with water, the light will take the time$\left( {\mu = \dfrac{4}{3}} \right)$:

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

Answer 1

Hint – Here we will proceed by using the formula for refractive index. Then by applying the conditions given in the question, we will get our answer.

Refractive index refers to the ratio between the speed of an electromagnetic wave in a vacuum and its speed in another medium. It refers to the measure of bending of rays of light when it passes from one medium to another medium.

Step By Step Answer:
Formula used- $\mu = \dfrac{{vc}}{{vm}}$

Where, $vc = $ speed of light in vacuum
$vm = $ speed of light in medium.

Let us suppose that between the earth and the sun will be d.

$ \Rightarrow vm = \dfrac{{\dfrac{{vc}}{4}}}{3}$
    $ = \dfrac{3}{4}vc$ …. (1)

As time taken will be constant then

$vm$ times $t1 = $ $vc$ time t (where t is 8 min 20 seconds)

$t1 = \dfrac{{vc}}{{vm}} \times t$

Put the value of equation in $vm$

=$\dfrac{{\dfrac{{vc}}{3}}}{4}vc \times t$

$vc,vc$ will be cancelled out,

$\dfrac{4}{3} \times t$

With t = 8 min 20 seconds
By converting time into seconds we will get

s

$
   = \dfrac{4}{3} \times 500 \\
   = \dfrac{{2000}}{3} \\
   = 666.666s \\
 $

By converting it into minutes we will get

=11 minute 20 seconds.

Note – In this particular question, it should be noted that the refractive index is generally written as $n = \dfrac{c}{v}$ which is the same as the formula we have mentioned in the question. In this type of question, we have to simply apply the formula of refractive index. Then in place of formula we have to put values. In this way we can solve questions related to refractive index.

$60 \times 8 + 20 = 500$