A beam of white light is Incident on the surface of a diamond at an angle theta.

Question

A beam of white light is Incident on the surface of a diamond at an angle theta.(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 n_red = 2.410 for rod light and n_blue = 2.450 for blue light The Surrounding air has n_air = 1.000. Note that the angles in the figure am not to scale. Derive a formula for S the angle between n_red and blue refracted rays in the diamond. Express the angle In terms of Use = 1 Remember that the proper way to enter the Inverse sine of x In this case is asin(x).

Explanation / Answer

The speed of light in a medium is:

c = (2.998 * 10^8) * (1.00 / nmedium)

For red light in diamond:

c = (2.998 * 10^8) * (1.00 / 2.410)
c = 1.244*10^8 m/s

1.244*10^8 m/s

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:

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

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

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