A beam of light from a monochromatic laser shines into a piece of glass. The glass has thickness L and index of refraction n=1.5 . The wavelength of the laser light in vacuum is L/10 and its frequency is f In this problem, neither the constant c nor its numerical value should appear in any of your answers. (1) How long does it take for a short pulse of light to travel from one end of the glass to the other?

Explanation:

For this case we know that the light without any obstruction and in the free space travels with a speed of

When we have a surface like a glass we know that the velocity is given by the following expression:

Where n is the refraction index, and on this case is given n = 1.5

For this case we know that the lenght of the glass is L and the wavalength is also given

We know the following relation between distance and time:

And if we solve for t we got:

For this case the value of D = L and v =c/n and if we replace we got:

 (1)

Now we need to found a way to incorporate the wavelength into this formula and we have the following expression:

If we replace this condition into equation (1) we got:

And we can use the condition that and we have this:

We can cancel the L terms and we have just:

And that would be the time that it takes a short pulse of light to travel from one end of the glass to the other.

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