Question

The ratio of the time taken by light to travel a distance of 100 m in air and water is

Answer 1

Answer:

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Answer 2

The ratio of the time taken by light to travel a distance of 100 m in air and water is 0.75 .

We need to find the ratio of the time taken by light to travel a distance of 100 m in air and water .

We know refractive index of air and water is $\mu_{air}=1$ and $\mu_{water}=\dfrac{4}{3}$ .

Also , we know ,

Speed of light in a medium is given as :

$v=\dfrac{c}{\mu}$   ( Here , c is speed of light and $\mu$ is the refractive index of material )

Now , we know , time taken $t=\dfrac{100}{\dfrac{c}{\mu}}$

Therefore , ratio  time taken by light to travel a distance of 100 m in air and water is :

$\dfrac{t_{air}}{t_{water}}=\dfrac{\dfrac{100}{\dfrac{c}{\mu_{air}}}}{\dfrac{100}{\dfrac{c}{\mu_{water}}}}\\\\\dfrac{t_{air}}{t_{water}}=\dfrac{\mu_{air}}{\mu_{water}}\\\\\dfrac{t_{air}}{t_{water}}=\dfrac{1}{\dfrac{4}{3}}\\\\\dfrac{t_{air}}{t_{water}}=\dfrac{3}{4}\\\\\dfrac{t_{air}}{t_{water}}=0.75$

Hence , this is the required solution .

Learn More :

Refraction

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