Light takes 8 min 20 sec to reach the Earth f | vedclass

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(D) The time taken by light to travel a distance $d$ in a medium is given by $t = d/v$,where $v$ is the speed of light in that medium.Since $v = c/\mu

Vedclass · Accepted Answer

$11$ min $6$ sec

Vedclass · Answer

(D) The time taken by light to travel a distance $d$ in a medium is given by $t = d/v$,where $v$ is the speed of light in that medium.Since $v = c/\mu$,where $c$ is the speed of light in vacuum and $\mu$ is the refractive index,we have $t = d\mu/c$.Let $t_a$ be the time taken in vacuum (or air) and $t_w$ be the time taken in water.Then,$t_a = d/c$ and $t_w = d/v_w = d\mu_w/c$.Therefore,$t_w = t_a 	imes \mu_w$.Given $t_a = 8$ min $20$ sec $= 500$ sec and $\mu_w = 4/3$.$t_w = 500 	imes (4/3) = 2000/3$ sec.$t_w = 666.67$ sec.Converting to minutes: $666.67 / 60 = 11.11$ min.$0.11$ min $= 0.11 	imes 60 = 6.6$ sec $\approx 6$ sec.Thus,$t_w = 11$ min $6$ sec.

Light takes $8$ min $20$ sec to reach the Earth from the Sun. If the whole atmosphere were filled with water,how much time would the light take to reach the Earth? (Given refractive index of water,$_a\mu_w = 4/3$)

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