25.7 Image Formation by Mirrors

A student is testing the properties of a mirror with an unknown radius of curvature. The student notices that no matter how far an object is placed from the mirror, the image seen in the mirror is always upright and smaller than the object. What can the student deduce about this mirror?

1. The mirror is convex.
2. The mirror is flat.
3. The mirror is concave.
4. More information is required to deduce the sha…

A mirror shows an upright image twice as large as the object when the object is 10 cm away from the mirror. What is the focal length of the mirror?

1. -10 cm
2. 10 cm
3. 20 cm
4. 40 cm

What is the focal length of a makeup mirror that has a power of 1.50 D?

(a) Calculate the focal length of the mirror formed by the shiny back of a spoon that has a 3.00 cm radius of curvature. (b) What is its power in diopters?

What is the focal length of a makeup mirror that produces a magnification of 1.50 when a person’s face is 12.0 cm away? Explicitly show how you follow the steps in the Problem-Solving Strategy for Mirrors.

An object 1.50 cm high is held 3.00 cm from a person’s cornea, and its reflected image is measured to be 0.167 cm high. (a) What is the magnification? (b) Where is the image? (c) Find the radius of curvature of the convex mirror formed by the cornea. (Note that this technique is used by optometrists to measure the curvature of the cornea for contact lens fitting. The instrument used is called a ke…

Show that for a flat mirror $h_{\text{i}} = h_{\text{o}}$, knowing that the image is a distance behind the mirror equal in magnitude to the distance of the object from the mirror.

Referring to the electric room heater considered in the first example in this section, calculate the intensity of IR radiation in $\text{W}/\text{m}^{2}$ projected by the concave mirror on a person 3.00 m away. Assume that the heating element radiates 1500 W and has an area of $\text{100} \text{ cm}^{2}$, and that half of the radiated power is reflected and focused by the mirror.

Light composed of multiple frequencies passes through crown glass. (a) How much faster does the violet component of the light with a wavelength of 410 nm travel in the crown glass than the component of orange light with a wavelength of 610 nm? (b) In a mechanical situation with friction, the longer one surface moves relative to the other, the more the friction acts, slowing the relative motion du…