Additional Problems

| 30 | An object is placed in front of a convex mirror. Draw the convex mirror (radius of curvature = 15 cm) to scale, and place the object 25 cm in front of it. Make the object height 4 cm. Using a ray diagram, locate the image and measure its height. Now move the object closer to the mirror, so the object distance is 5 cm. Again, locate its image using a ray diagram. As the object moves closer to the mirror, (a) does the magnitude of the image distance become larger or smaller, and (b) does the magnitude of the image height become larger or smaller? (c) What is the ratio of the image height when the object distance is 5 cm to its height when the object distance is 25 cm? Give your answer to one significant figure.

| 31 | ssm The image produced by a concave mirror is located 26 cm in front of the mirror. The focal length of the mirror is 12 cm. How far in front of the mirror is the object located?

| 32 | You are trying to photograph a bird sitting on a tree branch, but a tall hedge is blocking your view. However, as the drawing shows, a plane mirror reflects light from the bird into your camera. For what distance must you set the focus of the camera lens in order to snap a sharp picture of the bird’s image?

Problem 32

| 33 | A clown is using a concave makeup mirror to get ready for a show and is 27 cm in front of the mirror. The image is 65 cm behind the mirror. Find (a) the focal length of the mirror and (b) the magnification.

| 34 | An object that is 25 cm in front of a convex mirror has an image located 17 cm behind the mirror. How far behind the mirror is the image located when the object is 19 cm in front of the mirror?

| 35 | ssm A concave mirror has a focal length of 42 cm. The image formed by this mirror is 97 cm in front of the mirror. What is the object distance?

* | 36 | A ray of light strikes a plane mirror at a 45° angle of incidence. The mirror is then rotated by 15° into the position shown in red in the drawing, while the incident ray is kept fixed. (a) Through what angle does the reflected ray rotate? (b) What is the answer to part (a) if the angle of incidence is 60° instead of 45°?

* | 37 | Multiple-Concept Example 7 reviews the concepts that are needed to solve this problem. In Figure 25-21b the head-up display is designed so that the distance between the digital readout device and virtual image 1 is 2.00 m. The magnification of virtual image 1 is 4.00. Find the focal length of the concave mirror. (Hint: Remember that the image distance for virtual image 1 is a negative quantity.)

* | 38 | A candle is placed 15.0 cm in front of a convex mirror. When the convex mirror is replaced with a plane mirror, the image moves 7.0 cm farther away from the mirror. Find the focal length of the convex mirror.

* | 39 | ssm An object is located 14.0 cm in front of a convex mirror, the image being 7.00 cm behind the mirror. A second object, twice as tall as the first one, is placed in front of the mirror, but at a different location. The image of this second object has the same height as the other image. How far in front of the mirror is the second object located?

** | 40 | A spherical mirror is polished on both sides. When the convex side is used as a mirror, the magnification is +1/4. What is the magnification when the concave side is used as a mirror, the object remaining the same distance from the mirror?

** | 41 | ssm A lamp is twice as far in front of a plane mirror as a person is. Light from the lamp reaches the person via two paths, reflected and direct. It strikes the mirror at a 30.0° angle of incidence and reflects from it before reaching the person. The total time for the light to travel this path includes the time to travel to the mirror and the time to travel from the mirror to the person. The light also travels directly to the person without reflecting. Find the ratio of the total travel time along the reflected path to the travel time along the direct path.

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