Question

A narrow beam of white light enters a prism made of crown glass at a 45.0° incident angle. a) At what angle does the red (660 nm) component of light emerge from the prism given that crown glass has an n = 1.512 index of refraction for this wavelength? Give your answer in degrees. b) At what angle does the violet (410 nm) component of light emerge from the prism given that crown glass has an n = 1.530 index of refraction for this wavelength? Give your answer in degrees.

Answer 1

The red light component emerges from the prism at an angle of approximately 29.1°, while the violet light component emerges at an angle of approximately 29.2°.

Step-by-step explanation:

The angle at which light is refracted when passing through a prism can be determined using Snell's law, which states that the ratio of the sine of the incident angle to the sine of the refracted angle is equal to the ratio of the indices of refraction. In this case, we can use this law to find the angles at which the red (660 nm) and violet (410 nm) light components emerge from the prism made of crown glass.

For the red light, we have an incident angle of 45.0° and an index of refraction of 1.512. Using Snell's law, we can solve for the refracted angle:

sin(45.0°)/sin(refracted angle) = 1.000/1.512

By rearranging the equation, we find that the refracted angle for the red light is approximately 29.1°.

For the violet light, we have the same incident angle of 45.0° but a different index of refraction of 1.530. Using Snell's law again, we can find the refracted angle for the violet light:

sin(45.0°)/sin(refracted angle) = 1.000/1.530

By rearranging the equation, we find that the refracted angle for the violet light is approximately 29.2°.