Optics Practice Problems for AP Physics B
Review the following concepts if necessary:
- In an aquarium, light traveling through water (n = 1.3) is incident upon the glass container (n = 1.5) at an angle of 36° from the normal. What is the angle of transmission in the glass?
- The light will not enter the glass because of total internal reflection.
- Which of the following optical instruments can produce a virtual image with magnification 0.5?
- convex mirror
- concave mirror
- convex lens
- concave lens
- I and IV only
- II and IV only
- I and II only
- III and IV only
- I, II, III, and IV
- Light waves traveling through air strike the surface of water at an angle. Which of the following statements about the light's wave properties upon entering the water is correct?
- The light's speed, frequency, and wavelength all stay the same.
- The light's speed, frequency, and wavelength all change.
- The light's speed and frequency change, but the wavelength stays the same.
- The light's wavelength and frequency change, but the light's speed stays the same.
- The light's wavelength and speed change, but the frequency stays the same.
- An object is placed at the center of a concave spherical mirror. What kind of image is formed, and where is that image located?
- A real image is formed at the focal point of the mirror.
- A real image is formed at the center of the mirror.
- A real image is formed one focal length beyond the center of the mirror.
- A virtual image is formed one focal length behind the mirror.
- A virtual image is formed one radius behind the mirror.
- Light traveling through air encounters a glass aquarium filled with water. The light is incident on the glass from the front at an angle of 35°.
- At what angle does the light enter the glass?
- At what angle does the light enter the water?
- On the diagram above, sketch the path of the light as it travels from air to water. Include all reflected and refracted rays; label all angles of reflection and refraction.
- At what angle does light enter the glass on the side of the aquarium?
- Does the light travel out of the glass and into the air, or does total internal reflection occur? Justify your answer.
After entering the water, the light encounters the side of the aquarium, hence traveling back from water to glass. The side of the tank is perpendicular to the front.
- B—If you had a calculator, you could use Snell's law, calling the water medium "1" and the glass medium "2": 1.3·sin 36° = 1.5·sin θ2. You would find that the angle of transmission is 31°. But, you don't have a calculator … so look at the choices. The light must bend toward the normal when traveling into a material with higher index of refraction, and choice B is the only angle smaller than the angle of incidence. Choice A is silly because total internal reflection can only occur when light goes from high to low index of refraction.
- A—The converging optical instruments—convex lens and concave mirror—only produce virtual images if the object is inside the focal point. But when that happens, the virtual image is larger than the object, as when you look at yourself in a spoon or a shaving mirror. But a diverging optical instrument—a convex mirror and a concave lens—always produces a smaller, upright image, as when you look at yourself reflected in a Christmas tree ornament.
- E—The speed of light (or any wave) depends upon the material through which the wave travels; by moving into the water, the light's speed slows down. But the frequency of a wave does not change, even when the wave changes material. This is why tree leaves still look green under water—color is determined by frequency, and the frequency of light under water is the same as in air. So, if speed changes and frequency stays the same, by v = λf, the wavelength must also change.
- B—You could approximate the answer by making a ray diagram, but the mirror equation works, too:
Because the radius of a spherical mirror is twice the focal length, and we have placed the object at the center, the object distance is equal to 2f. Solve the mirror equation for di by finding a common denominator:
This works out to ( f )(2f )/(2f – f ) which is just 2f. The image distance is twice the focal length, and at the center point. This is a real image because di is positive.
- Use Snell's law: n1 sin θ1 = n2 sin θ2. This becomes 1.0 sin 35° = 1.5 sin θ2. Solve for θ2 to get 22°.
- Use Snell's law again. This time, the angle of incidence on the water is equal to the angle of refraction in the glass, or 22°. The angle of refraction in water is 25°. This makes sense because light should bend away from normal when entering the water because water has smaller index of refraction than glass.
- Important points:
- The angle of incidence on the side must be measured from the normal. The angle of incidence is not 25°, then, but 90 – 25 = 65°. Using Snell's law, 1.33 sin 65° = 1.50 sin θ2. The angle of refraction is 53°.
- The critical angle for glass to air is given by sin θc = 1.0/1.5. So θc = 42°. Because the angle of incidence from the glass is 53° [calculated in (d)], total internal reflection occurs.
*Light both refracts and reflects at both surfaces. You must show the reflection, with the angle of incidence equal to the angle of reflection.
*We know you don't have a protractor, so the angles don't have to be perfect. But the light must bend toward normal when entering glass, and away from normal when entering water.
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