Describe how rays change direction upon entering a medium
Apply the law of refraction in problem solving
The Propagation of Electromagnetic Waves in Matter
The Law of Refraction
If light travels from one medium into another, it will (in general) change its direction. This is called refraction. This fact is a property of waves. Nevertheless, the description of the effect doesn’t need to refer to the wavelength, or wave nature, of light, so this topic still belongs in this geometrical optics chapter. The math involved is fairly straightforward (one equation to learn), and there are many important consequences/applications ranging from simple eyeglass lenses, to fancy telescopes, to medical imaging equipment, fiber optics, etc…
In this photo, a laser shines a beam of light at a container of water. The interface is the boundary between air and water, and the light beam bends there.
Snell’s Law (The Law of Refraction)
There is a formula for the refraction of light, which is derivable from Maxwell’s Equations, called Snell’s Law:
Practice!
Practice 13.3.1
Light passes from a material with index of refraction 1.5 into one with index of refraction 1.1. Compared to the incident ray, the refracted ray does which of the following?
Check your answer: A. bends away from the normal
Practice 13.3.2
An oil layer that is 5.0 cm thick is spread smoothly and evenly over the surface of water on a windless day. What is the angle of refraction in the water for a ray of light that has an angle of incidence of 45° as it enters the oil from the air above? (The index of refraction for the oil is 1.15, and for water it is 1.33.)
Check your answer: B. 32°
Practice 13.3.3
In the figure, a laser positioned on a ship is used to communicate with a small research submarine resting on the bottom of a lake. The laser is positioned 12 m above the surface of the water, and it strikes the water 20 m from the side of the ship. The water is 76 m deep and has an index of refraction of 1.33. How far horizontally is the submarine from the side of the ship?
Check your answer: E. 64.1 m
Pause & Predict 13.3.1
What is the angle of refraction of the ray in the glass?
Pause & Predict 13.3.2
For total internal reflection to occur, what is the minimum glancing angle (β) of the incident ray, measured with respect to the core-cladding boundary?
Practice!
Practice 13.3.4
A thin layer of turpentine (n = 1.472) is floating on water (n = 1.333). Light of wavelength 589 nm initially traveling in air is incident on the turpentine at an angle of 24.8° measured with respect to the air-turpentine interface. What is the light’s refraction angle in the turpentine?
Check your answer: C. 38.1°
Practice 13.3.5
A thin layer of turpentine (n = 1.472) is floating on water (n = 1.333). Light of wavelength 589 nm initially traveling in air is incident on the turpentine at an angle of 24.8° measured with respect to the air-turpentine interface. After the light passes through the turpentine, what is its refraction angle in the water?
Check your answer: C. 42.9°
Practice 13.3.6
A thin layer of turpentine (n = 1.472) is floating on water (n = 1.333). Light of wavelength 589 nm travels from air into the turpentine. At what angle should the light be incident on the turpentine-water interface so that all the light totally internally reflects in the turpentine and does not travel into the water?
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