A beam of white light is incident on the surface of a diamond at an angle .(Figu

Question

A beam of white light is incident on the surface of a diamond at an angle .(Figure 1) Since the index of refraction depends on the light's wavelength, the different colors that comprise white light will spread out as they pass through the diamond. The indices of refraction in diamond are for red light and for blue light. The surrounding air has . Note that the angles in the figure are not to scale.

Derive a formula for , the angle between the red and blue refracted rays in the diamond.
Express the angle in terms of , , and . Use . Remember that the proper way to enter the inverse sine of in this case is asin(x).

asin (sin theta a / n red) - asin ( sin theta a / n blue)

did not work and I do not understand why.

Explanation / Answer

Start with Snell’s law:

nair * sin(1) = ndiamond * sin(2)

For red light, the above becomes:

sin(1) = nred * sin(2, red)
2, red = asin(sin(1) / nred)

And for blue light:

sin(1) = nblue * sin(2, blue)
2, blue = asin(sin(1) / nblue)

Since we want the difference between the angles:

d = asin(sin(?1) / nred) – asin(sin(?1) / nblue)

d = asin(sin(?1) / nred) – asin(sin(?1) / nblue)

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