WAVES AND OPTICS
Go to: AP FREE RESPONSE PROBLEMS
WAVES AND SOUND
For problems involving standing waves in strings:
1. Complete a data table with the information given.
2. Draw a sketch for the harmonic described in the problem. Locate the position of the nodes and antinodes. Determine the wavelength of the wave.
3. If the frequency is known, or the tension and mass per unit length are known, solve for the velocity.
4. Solve for the frequency of the particular harmonic.
For problems involving harmonics produced in pipes:
1. Complete a data table with the information given and if necessary, solve for the speed of sound in the pipe.
2. Determine whether the problem involves an open or closed pipe. Draw a sketch locating the nodes and antinodes for the harmonic(s) requested.
3. Determine the wavelength of the waves producing the particular harmonic. Remember that closed pipes produce only odd harmonics.
4. Solve for the frequency of the particular harmonic. If the frequency is given solve for the length of the pipe.
For problems involving the Doppler effect:
1. Complete a data table with the information given.
2. Determine whether the source or the listener is moving; also note whether the source and listener are approaching each other or moving away from each other.
3. Solve for frequency heard by the listener.
4. Solve for the wavelength of the sound between the source and the listener.
REFRACTION
For problems involving refraction and Snell's law:
1. Complete a data table with the information given.
2. Draw an accurate labeled diagram locating the incident ray and normal to the surface. Determine the angle of incidence.
3. Use Snell's law to solve the problem.
4. If the problem involves total internal reflection, then at the critical angle, the angle of refraction is 90°. Use Snell's law to determine the magnitude of the critical angle.
GEOMETRIC OPTICS
For problems involving image formation by a convex or a concave mirror:
1. Complete a data table with the information given.
2. Identify whether the mirror is concave or convex. The focal length is positive for a concave mirror and negative for a convex mirror.
3. Solve the problem by:
A) Graphical Method:
1. Choose an appropriate scale to represent the focal length, object distance and height of the object.
2. Use the two rays to draw an accurate ray diagram. Draw in the image at the point where the two rays intersect after reflection from the mirror.
B) Mirror Equation:
1. Use the mirror equations and sign conventions to determine the image distance, image height, and magnification.
2. State the characteristics of the image: real or virtual; erect or inverted; magnified, diminished, or same size as the object.
For problems involving image formation by a concave or a convex lens:
1. Complete a data table with the information given.
2. Identify whether the lens is concave or convex. The focal length is positive for a convex lens and negative for a concave lens.
3. Solve the problem by:
A) Graphical Method:
1. Choose an appropriate scale to represent the focal length, object distance and height of the object.
2. Use the two rays to draw an accurate ray diagram. Draw in the image at the point where the two rays intersect after refraction from the lens.
B) Lens Equation:
1. Use the lens equations and sign conventions to determine the image distance, image height, and magnification.
2. State the characteristics of the image: real or virtual; erect or inverted; magnified, diminished, or same size as the object.
PHYSICAL OPTICS
For problems involving double slit interference, single slit diffraction, or a diffraction grating:
1. Complete a data table with the information given.
2. Determine whether the light is passing through a double slit, a single slit or a diffraction grating.
3. Draw an accurate labeled diagram.
4. Note whether the problem involves constructive interference (bright fringes) or destructive interference (dark fringes).
5. Choose the appropriate formula and solve the problem.
For problems involving thin film interference:
1. Complete a data table with the information given.
2. Assume a crest is incident on the top surface of the film.
3. Determine whether the subsequent reflections and transmissions from each interface will be a crest or trough.
4. Draw a diagram showing each position where the light is reflected and transmitted.
5. Determine the minimum thickness of the film in terms of a fraction of a wavelength of the incident light required to produce a) maximum reflection of the light and b) minimum reflection of the light.
6. Write a formula for film thickness that will produce a) maximum reflection of the light and b) minimum reflection of the light.
7. If the wavelength of the light in air is given, determine the wavelength of the light in the film.
WAVES AND OPTICS FREE RESPONSE AP PROBLEMS
The list of problems is given as follows:
Year of examination
Problem number
Topics covered in problem
1983, 5, concave mirror, graphical solution
1984, 5, thin film interference
1985, 5, double slit interference
1986, 6, converging and diverging lenses, graphical solutions
1987, 5, Snell's law, speed and wavelength
1989, 5, plano-convex lens, lens equation and graphical solution
1990, 6, Snell's law, critical angle, thin film interference
1991, 6, double slit interference, photoelectric effect
1992, 6, converging lens, graphical solution, lens equation, concave mirror graphical solution
1994, 5, velocity, Snell's law, critical angle, lens equation
1995, 6, sound, speed, frequency and wavelength
1996, 3, double slit interference
1997, 5, lens graphical solution, mirror graphical solution
2000, 4, Snell's law, thin film interference
2001, 4, Snell's law, critical angle
