Index of refraction

2010-06-23 6:40 am

Some modern optical devices are made with glass whose index of refraction changes with distance from the font surface. Figure shows the index of refraction as a function of the distance into a slab of glass of thickness L. The index of refraction increases linearly from n1 at the front surface to n2 at the rear surface.

圖片參考：http://imgcld.yimg.com/8/n/HA00140412/o/701006220176213873425500.jpg

Find an expression for the time light takes to travel through this piece of glass for normal incidence.

回答 (1)

天同

2010-06-23 10:02 pm

✔ 最佳答案

Let the refractive index n be in the form:
n = a + b.x, where a and b are constants.
Since n = n1 when x = 0, hence, a = n1
and n = n2 when x = L, hence b = (n2-n1)/L

But n = c/v, where c is the speed of light in vacuum, and v is the velocity in glass. Thus v = c/n = c/(a+bx)

From definition of velocity, v = dx/dt, i.e. dx = v.dt
dx = [c/(a+bx)].dt
i.e. (a+bx).dx = c.dt
Now, integrate both sides, with limits of x from 0 to L, and limits of t from 0 to T, say

After integration, substitute the values of a and b into the equation and solve for T.

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