A narrow beam of light containing red (660 nm) and blue (470 nm) wavelengths travels from air

step 1 So here we have a piece of glass, let's say a rays incident at an angle theta, and here we have

A narrow beam of light containing red (660 nm) and blue...

A narrow beam of light containing red $(660 \mathrm{~nm})$ and blue $(470 \mathrm{~nm})$ wavelengths travels from air through a $1.00 \mathrm{~cm}$ thick flat piece of crown glass and back to air again. The beam strikes at a $30.0^{\circ}$ incident angle. (a) At what angles do the two colors emerge? (b) By what distance are the red and blue separated when they emerge?

Key Concepts

Snell's Law

Snell's Law describes how light rays bend when they pass from one medium into another with a different refractive index. It relates the sine of the incident angle to the sine of the refracted angle, with the ratio given by the refractive indices of the media. This principle is essential for predicting the change in direction of light as it enters and exits a material such as glass.

Refractive Index

The refractive index is a measure of how much a medium slows down light relative to vacuum. It is the ratio of the speed of light in a vacuum to the speed of light in the medium. Different materials—and even different wavelengths within the same material—have distinct refractive indices, which influence the angle of refraction according to Snell's Law.

Chromatic Dispersion

Chromatic dispersion refers to the phenomenon where different wavelengths of light travel at different speeds in a medium, resulting in different refractive indices for each color. This wavelength-dependence causes the separation of colors in a light beam when it passes through a medium such as crown glass, leading to effects such as the splitting of white light into its constituent colors.

Lateral Displacement in a Parallel Slab

When a light ray enters a parallel-sided slab, even though the emerging ray is parallel to the incident ray, it is laterally displaced. This displacement arises due to the finite thickness of the slab and the bending of the ray at the interfaces, and it can be quantitatively determined by combining geometrical optics principles with Snell's Law.

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