Snell's law

Practice problem:

 

Which quantity doesn't change when light enters the glass?

A. wavelength

 

B. frequency

 

C. speed

The index of refraction, n, is the ratio of the speed of light in vacuum to the speed of light in the medium. This gives rise to Snell's law n1 sin q1 = n2 sin q2

The index of refraction is a property of a medium. It describes how light propagates in that medium.

 

When light crosses from one medium into another medium with a different index of refraction, the ray bends to minimize time.

Practice problem:

 

Which index of refraction is bigger, n1 or n2?

A. n1

 

B. n2

 

C. can't tell

 

 

 

 

 

 

 

Practice problem:

 

A light ray travels through the media as shown. Which of the following statements is true, regarding n1 and n3?

A. n3 = n1

 

B. n3 > n1

 

C. n3 < n1

 

D. Can't tell

Total internal reflection

Transmission gets weaker as the angle of incidence increases. Internal reflection gets stronger. When the angle of transmission reaches 90 degrees, no light is transmitted - it is all reflected internally. The incident angle that results in total internal reflection for two media is called the critical angle, qc. Notice that total internal reflection only happens when n2 < n1

Fiber optics utilizes total internal reflection to propagate light along a long, narrow glass tube. The tube can bend slightly, as long as the bending doesn't increase the angle of incidence beyond the critical angle (or break the glass!)

Practice problem:

 

Use Snell's law to calculate the critical angle  between glass and air.

 

Take the index of refraction for glass to be 1.5.

Image formation by refraction

The refraction of light rays as they pass from the water to air cause the virtual image of the fish at P' to appear closer than the fish really is.

Angles are measured with respect to the optical axis. Note that the distance l is common to both the incident and reflected rays.

The fact that the relationship between the image distance and the object distance is independent of the angle means that all paraxial rays diverge from the same point P' (in the small angle approximation).

Practice problem:

 

Tom Hanks is new to the island, and has just made a spear. He is very hungry, and aims at a fish.

 

Should the fish be smiling? The fish knows Snell's law means that Tom is looking at a virtual image at a different location. Is the fish far enough from where Tom thinks he is to be safe?

 

The dashed line shows where Tom thinks he sees the fish. Take the angle with respect to the normal to be 50 degrees, and the index of refraction for water to be 1.33. Find the angle with respect to the normal in the water.

Color and dispersion

The index of refraction of glass is higher for short wavelength light than for long wavelength light. This means that violet light refracts more than red.

Colors of light spread out through a prism because the index of refraction depends on wavelength.

The incident angle of light upon a spherical raindrop can mean that there is a lot of internally reflected light. The internally reflected light undergoes dispersion, separating out the colors of light. The light emerges at different angles for different wavelengths. Since red light refracts less, we need to look higher to see refracted red rays.

Image source

The index of refraction, n, is the ratio of the speed of light in vacuum to the speed of light in the medium. This gives rise to Snell's law n1 sin q1 = n2 sin q2 Transmission gets weaker as the angle of incidence increases. Internal reflection gets stronger. When the angle of transmission reaches 90 degrees, no light is transmitted - it is all reflected internally. The incident angle that results in total internal reflection for two media is called the critical angle, qc. Notice that total internal reflection only happens when n2 < n1