33. Geometric Optics

(I) How far from a concave mirror (radius 30.0 cm) must an object be placed if its image is to be at infinity?

(II) The image of a distant tree is virtual, very small, and 13.0 cm behind a curved mirror. What kind of mirror is it, and what is its radius of curvature?

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.

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.

You hold a spherical salad bowl 60 cm in front of your face with the bottom of the bowl facing you. The bowl is made of polished metal with a 35-cm radius of curvature. Where is the of your 5.0-cm tall nose located?

(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?

An object 4.0 mm high is placed 18 cm from a convex mirror of radius of curvature 18 cm. Show that the (negative) image distance can be computed from Eq. 32–2 using a focal length of -9.0 cm.

An object is placed 21 cm from a certain mirror. The image is half the height of the object, inverted, and real. How far is the image from the mirror, and what is the radius of curvature of the mirror?

When walking toward a concave mirror you notice that your image flips at a distance of 0.80 m from the mirror. What is the radius of curvature of the mirror? [Hint: Carefully examine Section 32–4.]

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 4 cm tall object is placed 15 cm in front of a concave mirror with a focal length of 5 cm. Where is the image produced? Is this image real or virtual? Is it upright or inverted? What is the height of the image?

(II) A 4.2-cm-tall object is placed 26 cm in front of a spherical mirror. It is desired to produce a virtual image that is upright and 3.2 cm tall.

(a) What type of mirror should be used?

(b) Where is the image located?

(c) What is the focal length of the mirror?

(d) What is the radius of curvature of the mirror?

A 2.0-cm-tall candle flame is 2.0 m from a wall. You happen to have a lens with a focal length of 32 cm. How many places can you put the lens to form a well-focused image of the candle flame on the wall? For each location, what are the height and orientation of the image?

A 1.80-m-tall person stands 4.20 m from a convex mirror and notices that he looks precisely half as tall as he does in a plane mirror placed at the same distance. What is the radius of curvature of the convex mirror? (Assume that θ ≈ θ .) [Hint: The viewing angle is half.]

The thin glass shell shown in Fig. E34.15 has a spherical shape with a radius of curvature of 12.0 cm, and both of its surfaces can act as mirrors. A seed 3.30 mm high is placed 15.0 cm from the center of the mirror along the optic axis, as shown in the figure. Calculate the location and height of the of this seed.