33. Geometric Optics

An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Compute the image size, using Eq. 32–3.

(I) A solar cooker, really a concave mirror pointed at the Sun, focuses the Sun’s rays 17.2 cm in front of the mirror. What is the radius of the spherical surface from which the mirror was made?

An object is placed a distance r in front of a wall, where r exactly equals the radius of curvature of a certain concave mirror. At what distance from the wall should this mirror be placed so that a real image of the object is formed on the wall? What is the lateral magnification of the image?

Each student in a physics lab is assigned to find the location where a bright object may be placed in order that a concave mirror, with radius of curvature r = 54cm, will produce an image three times the size of the object. Two students complete the assignment at different times using identical equipment, but when they compare notes later, they discover that their answers for the object distance are not the same. Explain why they do not necessarily need to repeat the lab, and justify your response with a calculation.

An object is 18.0 cm from the center of a spherical silvered-glass Christmas tree ornament 6.00 cm in diameter. What are the position and magnification of its ?

A 2.0-cm-tall object is placed in front of a mirror. A 1.0-cm-tall upright image is formed behind the mirror, 150 cm from the object. What is the focal length of the mirror?

The place you get your hair cut has two nearly parallel mirrors 5.0 m apart. As you sit in the chair, your head is 2.0 m from the nearer mirror. Looking toward this mirror, you first see your face and then, farther away, the back of your head. (The mirrors need to be slightly nonparallel for you to be able to see the back of your head, but you can treat them as parallel in this problem.) How far away does the back of your head appear to be? Neglect the thickness of your head.

BIO A keratometer is an optical device used to measure the radius of curvature of the eye's cornea—its entrance surface. This measurement is especially important when fitting contact lenses, which must match the cornea's curvature. Most light incident on the eye is transmitted into the eye, but some light reflects from the cornea, which, due to its curvature, acts like a convex mirror. The keratometer places a small, illuminated ring of known diameter 7.5 cm in front of the eye. The optometrist, using an eyepiece, looks through the center of this ring and sees a small virtual image of the ring that appears to be behind the cornea. The optometrist uses a scale inside the eyepiece to measure the diameter of the image and calculate its magnification. Suppose the optometrist finds that the magnification for one patient is 0.049. What is the absolute value of the radius of curvature of her cornea?

(II) You are standing 2.7 m from a convex security mirror in a store. You estimate the height of your image to be half what it would be in a plane mirror at the same place. Estimate the radius of curvature of the mirror.

(a) In order to measure distances with parallax at 100 ly, what minimum angular resolution (in degrees) is needed?

(b) What diameter mirror or lens would be needed?

Suppose the mirrors in a Michelson interferometer are perfectly aligned and the path lengths to mirrors M₁ and M₂ are identical. With these initial conditions, an observer sees a bright maximum at the center of the viewing area. Now one of the mirrors is moved a distance x. Determine a formula for the intensity at the center of the viewing area as a function of x, the distance the movable mirror is moved from the initial position.