Time taken by a laser beam to travel a distance of 5 km under water having refractive index 4343, will be Only one correct answerA.2 × 10–4 s B.2 × 10–5 s C.2.2 × 10–4 s D.2.2 × 10–5 s
Question
Time taken by a laser beam to travel a distance of 5 km under water having refractive index 4343, will be Only one correct answerA.2 × 10–4 s B.2 × 10–5 s C.2.2 × 10–4 s D.2.2 × 10–5 s
Solution
The speed of light in a medium is given by the formula:
v = c/n
where: v is the speed of light in the medium, c is the speed of light in vacuum (approximately 3 x 10^8 m/s), and n is the refractive index of the medium.
Given that the refractive index of water is 4343, the speed of light in water is:
v = (3 x 10^8 m/s) / 4343 = 6.91 x 10^4 m/s
The time taken for light to travel a distance is given by the formula:
t = d/v
where: t is the time taken, d is the distance, and v is the speed of light in the medium.
Given that the distance is 5 km = 5000 m, the time taken for the laser beam to travel this distance under water is:
t = 5000 m / (6.91 x 10^4 m/s) = 7.23 x 10^-2 s
None of the provided options (A. 2 x 10^-4 s, B. 2 x 10^-5 s, C. 2.2 x 10^-4 s, D. 2.2 x 10^-5 s) match this result. There seems to be a mistake in the question as the refractive index of water is typically close to 1.33, not 4343.
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