The Physics
Hypertextbook
Opus in profectus

Refraction

Problems

practice

1. Waves travel in all directions in the open ocean, but they always approach the land nearly perpendicular to the shore. Why does this happen?
2. A ray of light is traveling from air to crown glass. The angle that this ray makes with the surface of the glass is 30°. Determine each of the following angles…
1. the angle of incidence
2. the angle of reflection
3. the angle of refraction
4. the angle between the reflected and refracted rays
5. the angle between the incident and refracted rays
6. the angle between the incident and reflected rays
3. The diagram below shows a ray of light (A) incident upon an air-water interface. Several possible rays (B–K) are also shown. 1. Using the protractor in the diagram, measure the angle of incidence.
2. Using the law of reflection, determine the angle of reflection, then select the lettered ray that best represents the reflected ray.
3. Using Snell's law, determine the angle of refraction, then select the lettered ray that best represents the transmitted ray.
4. Write something completely different.

conceptual

1. refraction-drill.pdf
The diagrams on the accompanying pdf show a ray of light incident upon an interface. In some cases the ray is traveling through air and entering glass. In other cases it is traveling through glass and entering air. On each diagram, sketch the approximate path of the light in the second medium. Ignore any reflected light. It is not necessary to calculate any angles, but do clearly show the change in direction of the rays, if any, at each surface.
2. Three related questions.
1. Ice is transparent and so is water, but ice is visible in water. How is this possible?
2. Acrylic is transparent and so is mineral oil, but acrylic in mineral oil is nearly invisible. Why does this happen?
3. Find another pair of materials that have the same optical relationship as acrylic and mineral oil.
3. If you can see the face of a friend who is under water can your friend also see you? Justify your answer.
4. Is daytime a bit longer or a bit shorter because of atmospheric refraction? Justify your answer.
5. Under unusual atmospheric conditions, it is sometimes possible to see over the horizon. This results in a form of mirage called a Fata Morgana.
1. What optical phenomenon explains this natural phenomenon?
2. What atmospheric conditions are needed for a Fata Morgana to occur?
3. Explain why the light takes the path that it does in this kind of mirage.

numerical

1. Identify a likely material if the speed of light (v) in the material is the following fraction of the speed of light (c) in a vacuum…
1. v = ⅝c
2. v = ⅔c
3. v = ¾c
2. Antireflection coatings
High end lenses are often coated with a thin film of solid transparent material that reduces unwanted surface reflections. This has the effect of making the lens seem clearer and more transparent. The following chain of calculations will help you determine the characteristics of an effective antireflection coating for "old-fashioned" eyeglass lenses.
1. The index of the material is usually chosen so that its index is the square root of the index of the substrate (the material it is deposited on). What would be an appropriate index of refraction for an antireflection coating placed on crown glass (a kind of glass that is still sometimes used for eyeglasses)?
2. The index of refraction is usually stated for a color of light in the middle of the visible spectrum. What wavelength of light was used to determine the index of refraction you used in part a? What color is this light? Why do you suppose this type of light was chosen?
3. What is the wavelength of this light in the antireflection coating?
4. Antireflection coatings of the type described in this problem are usually one-quarter of a wavelength thick. How thick should this coating be?
5. About how big is an atom (an order of magnitude value will do)? How many atoms thick is the antireflection coating described in this problem (again, an order of magnitude value will do)?
3. Fish who spend a significant portion of their days near the surface of the water can actually see what's going on above the surface. The refraction of light gives them a field of vision that encompasses 180° on the surface even if their underwater field of vision is smaller. The diagram below illustrates what I am describing. What field of vision for a fish underwater corresponds to a 180° field of vision above the surface?

Magnify

4. The table on below gives the index of refraction in diamond for a few different colors of light.
Refractive indexes for diamond
designation color wavelength (nm) index
B red 686.7 2.40735
D yellow 589.3 2.41734
E green 527.0 2.42694
H violet 396.8 2.46476

Determine the angular separation between the red and violet components of a beam of white light traveling from diamond to air if the angle of incidence is…

1. 20°
2. 30°
5. Optical fibers are made from extremely pure silicon dioxide (also known as fused quartz). According to one manufacturer…

The two basic elements of optical fiber are its core and cladding. The core, or the axial part of the optical fiber, is the light transmission area of the fiber. The cladding is the layer completely surrounding the core. The difference in refractive index between the core and cladding is less than 0.5%. The refractive index of the core is higher than that of the cladding, so that light in the core strikes the interface with the cladding at a bouncing angle and is trapped in the core by total internal reflection

Corning Inc., 2008

Determine…

1. the index of refraction of the cladding
2. the critical angle at the core-cladding interface
3. the critical angle at the cladding-air interface
6. The diagram below shows an interface between an unspecified transparent liquid and a piece of Lucite. An incident ray of light that has been partially reflected and partially transmitted at the interface is also shown. 1. Determine the angle of incidence.
2. Determine the angle of reflection.
3. Determine the angle of refraction.
4. Determine the index of refraction of the unspecified liquid.
5. What is the unspecified liquid?

geometric

1. inverting-prism.pdf
The diagram below shows 11 parallel rays of light incident on a trapezoidal, crown glass prism. Choose one of the numbered rays at random. On the diagram, trace the transmitted portion of your ray until it emerges from the prism. Just as each incident ray was assigned a number, each emergent ray can be assigned a number. Determine this number. 2. The diagram below shows 18 rays of light from the Sun incident on an equilateral, triangular ice crystal. (The width of the crystal is much larger than the wavelength of the light incident on it.) Choose one of the rays at random. On the diagram, trace the transmitted portion of your ray until it emerges from the crystal. Determine the deviation angle between the incident ray and the emergent ray.

3. The diagram to the below shows 20 rays of light from the Sun incident on a spherical drop of water. (The diameter of the drop is much larger than the wavelength of the light incident on it.) Choose one of the rays at random. On the diagram, trace the portion of your ray that is transmitted at the interface, reflects once off the back of the drop, and then emerges. Determine the angle between the incident ray and the emergent ray.

4. Repeat the problem above, but this time trace the portion of your ray that is transmitted at the interface, reflects twice off the inside of the drop and then emerges.
5. An optical device is made out of a solid cylindrical rod of crown glass with a hemispherical, fire-polished end cap. The center of the hemisphere is indicated with a cross. Twelve lettered rays are shown traveling parallel to the axis of the device. 1. What is the critical angle for crown glass?
2. Which of the rays are refracted at the hemispherical end cap and which experience total internal reflection? (Hint: What is the easiest way to draw a line normal to the circumference of a circle? Second hint: Go find a protractor.)
3. Draw the refracted rays until they reach the axis. Do they focus?