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Question

The ratio of the time taken by light to travel a distance of 100 m in air and water is 
(Given $$c = 3 \times 10^{8}$$ m/s ;  $$\mu _{air} =1.0003$$;   $$\mu _{water} = \dfrac{4}{3}$$)


A
1:1.1
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B
0.7502:1
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C
1:1.4
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D
1:1.5
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Solution

The correct option is B $$0.7502 : 1$$
Time taken in air $$=\dfrac{100}{c/\mu_{air}} = \dfrac{100 \mu_{air}}{C}$$
Time taken in water  $$=\dfrac{100}{c/\mu_{water}} = \dfrac{100 \mu_{water}}{C}$$
$$\dfrac{time\; taken\; in\; air} {time\; taken\; in\; water} = \dfrac{100 \mu_{air}/C}{100 \mu_{water}/C}$$                     
                                $$=\dfrac{\mu_{air}}{\mu_{water}}$$
 
                                $$=\dfrac{1.0003}{4/3}$$
 
                                $$=\dfrac{3 \times 1.0003}{4}$$
 
                                $$=\dfrac{0.7502}{1}$$ 

Physics

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