A light beam contains two wavelengths of light of 700.0 nm and 400.0 nm as measu

Question

A light beam contains two wavelengths of light of 700.0 nm and 400.0 nm as measured in vacuum. The beam originates from a high index material and is incident upon an interface with vacuum. On the high-index side of the interface, the beam makes an angle of 30.0o to the normal of the interface. Find the difference in the angles of refraction for the two wavelengths as they pass through to the vacuum side of the interface if the index of refraction is 1.6 for 700.0 nm light and 1.7 for 400.0 nm light. If the angle of incidence is increased to 38.0o, do either of the rays of light make it through the interface? Explain your answer.

Explanation / Answer

a)

sin7 = n7 sin = 1.6 * sin30 = 0.8

==> 7 = 53.130 degrees

sin4 = n4 sin = 1.7 * sin30 = 0.85

==> 4 = 58.212 degrees

4 - 7 = 58.212 - 53.130 = 5.082 degrees

b)

n7 sin38 = 1.6 * 0.61566 = 0.985 < 1

Threrefore 700 nm light will passs through the interference.

n4 sin38 = 1.7 * 0.61566 = 1.046622 > 1

Threrefore 400 nm light will NOT passs through the interference.

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