Question

A light beam strikes a piece of glass at a 60◦incident angle. The beam contains two wavelengths,450 nm and 700 nm, for which the index of refraction of the glass is 1.4820 and 1.4742, respectively.What is the angle between the two refracted beams?

Answer 1

The angle between the two refracted beams is approximately 0.57°.

Step-by-step explanation:

To find the angle between the two refracted beams, we can use Snell's Law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the indices of refraction:

sin(incident angle) / sin(refracted angle) = index of refraction of incident material / index of refraction of refracted material

For the first wavelength (450 nm), the index of refraction of the glass is 1.4820. Plugging in the values:

sin(60°) / sin(refracted angle) = 1.4820 / 1

Using a calculator to solve for the refracted angle, we find that the refracted angle for the first wavelength is approximately 52.41°.

For the second wavelength (700 nm), the index of refraction of the glass is 1.4742. Plugging in the values:

sin(60°) / sin(refracted angle) = 1.4742 / 1

Again, using a calculator to solve for the refracted angle, we find that the refracted angle for the second wavelength is approximately 52.98°.

To find the angle between the two refracted beams, we subtract the two refracted angles:

Angle between refracted beams = refracted angle for second wavelength - refracted angle for first wavelength

Angle between refracted beams = 52.98° - 52.41° = 0.57°