A concave mirror (f = 45 cm) produces an image whose distance from the mirror is one-third the object distance. Determine (a) the object distance and (b) the (positive) image distance.

A spherical mirror is polished on both sides. When the concave side mirror, the magnification is +2.0. What is the magnification when the convex side is used as a mirror, the object remaining the same distance from the mirror?

A concave mirror with a focal length of 4.8 cm produces an image 8.9 cm in front of the mirror. What is the object distance?

The image of a very distant car is located 12 cm behind a convex mirror. (a) What is the radius of curvature of the mirror? (b) Draw a ray diagram to scale showing this situation.

A plane mirror and a concave mirror (f = 8.0 cm) are facing each other and are separated by a distance of 20.0 cm. An object is placed 10.0 cm in front of the plane mirror. Consider the light from the object that reflects first from the plane mirror and then from the concave mirror. Using a ray diagram drawn to scale, find the location of the image that this light produces in the concave mirror. Specify this distance relative to the concave mirror.

A drop of water on a countertop reflects light from a flower held 3.0 cm directly above it. The flower's diameter is 2.0 cm, and the diameter of the flower's image is 0.10 cm. What is the focal length of the water drop, assuming that it may be treated as a convex spherical mirror?

A diverging lens (f = -10.0 cm) is located 20.0 cm to the left of a converging lens (f = 30.0 cm). A 3.00-cm-tall object stands to the left of the diverging lens, exactly at its focal point. (a) Determine the distance of the final image relative to the converging lens. (b) What is the height of the final image (including the proper algebraic sign)?

A laser emits a narrow beam of light. The radius of the beam is

$$1.0 \times 10 ^ { - 3 } \mathrm { m }$$

and the power is

$$1.2 \times 10 ^ { - 3 } \mathrm { W }$$

What is the intensity of the laser beam?

In a dentist's office an X-ray of a tooth is taken using X-rays that have a frequency of $6.05 \times 10^{18} \mathrm{Hz}$. What is the wavelength in vacuum of these X-rays?

A tall tree is growing across a river from you. You would like to know the distance between yourself and the tree, as well as its height, but are unable to make the measurements directly. However, by using a mirror to form an image of the tree, and then measuring the image distance and the image height, you can calculate the distance to the tree, as well as its height. (a) What kind of mirror, concave or convex, must you use? Why? (b) You will need to know the focal length of the mirror. The sun is shining. You aim the mirror at the sun and form an image of it. How is the image distance of the sun related to the focal length of the mirror? (c) Having measured the image distance

$$d_i$$

and the image height

$$h_i$$

of the tree, as well as the image distance of the sun, describe how you would use these numbers to determine the distance and height of the tree. A mirror produces an image of the sun, and the image is located 0.9000 m from the mirror. The same mirror is then used to produce an image of the tree. The image of the tree is 0.9100 m from the mirror. (a) How far away is the tree? (b) The image height of the tree has a magnitude of 0.12 m. How tall is the tree?

An object is placed in front of a convex mirror, and the size of the image is one-fourth that of the object. What is the ratio

$$d _ { \mathrm { o } } / f$$

of the object distance to the focal length of the mirror?

A concave mirror has a focal length of 12 cm. This mirror forms an image located 36 cm in front of the mirror. What is the magnification of the mirror?

An object is placed at a known distance in front of a mirror whose focal length is also known. You apply the mirror equation and find that the image distance is a negative number. This result tells you that ____. (a) the image is larger than the object (b) the image is smaller than the object (c) the image is inverted relative to the object (d) the image is real (e) the image is virtual

Two cars have identical horns, each emitting a frequency

$$f _ { \mathrm { s } }.$$

One of the cars is moving toward a bystander waiting at a corner, and the other is parked . The two horns sound simultaneously. (a) From the moving horn, does the bystander hear a frequency that is greater than, less than, or equal to

$$f _ { \mathrm { s } }?$$

(b) From the stationary horn, does the bystander hear a frequency that is greater than, less than, or equal to

$$f _ { \mathrm { s } }?$$

(c) Does the bystander hear a beat frequency from the combined sound of the two horns? Account for your answers. The frequency that the horns emit is

$$f _ { \mathrm { s } } = 395 \mathrm { Hz }$$

The speed of the moving car is 12.0 m/s, and the speed of sound is 343 m/s. What is the beat frequency heard by the bystander?