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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

Some modern optical devices are made with glass whose index of refraction changes with distance from the front surface. FIGURE CP16.84 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. a. Find an expression for the time light takes to travel through this piece of glass. b. Evaluate your expression for a 1.0-cm-thick piece of glass for which n1 = 1.50 and n2 = 1.60.



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Step by Step Solution

Given Information

We have a glass slab whose refractive index increases as a function of distance. (from n1 to n2)

Forming equation of n as a function of x

Now we know slope of the line is

Forming the equation of line as y = mx + c

where n(x) is value of n at y axis at any given value of distance in x axis.

Finding time taken:

We know that integral of inverse of velocity gives time taken.

also, velocity of light in a medium is defined as

In our case velocity of light is a function of distance

Part b:

n1 = 1.50

n2 = 1.60

L = 1cm = 0.001m

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