A laser beam

2012-12-06 2:07 am

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A laser beam shines along the surface of a block of transparent
material. (See the figure (Figure 1) .) Half of the beam goes straight
to a detector, while the other half travels through the block and then
hits the detector. The time delay between the arrival of the two light
beams at the detector is 6.10 ns .

What is the index of refraction of this material?

回答 (1)

天同

2012-12-06 3:59 am

✔ 最佳答案

Let c and v be the speeds of light in air and in the material respectively.

Time (t1) for the light beam to travel the length of the material in air
t1 = 2.5/c

Time (t2) for the light beam to travel through the material
t2 = 2.5/v

Because there is a time delay of 6.1 ns (=6.1 x 10^-9 s) for the arrivals of the two light beams at the detector, hence
t2 - t1 = 6.1 x 10^-9
i.e. 2.5/v - 2.5/c = 6.1x10^-9
multiply both sides by c,
2.5(c/v) - 2.5 = (6.1x10^-9)c

Since c/v = n, the refractive index of the material, thus
2.5n = (6.1x10^-9)c + 2.5
n = (6.1x10^-9) x (3x10^8)/2.5 + 1
n = 1.732

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