#12#16#18#22#26#30#32#34#38#42#46#48#54#58#6012. What effect(s) does enlarging the hole in a pinhole camera have on the image?
The greatest effect will be to brighten the image by letting more light through. It will also make the image somewhat fuzzier as the larger hole will act more like an extended light source and less like a point source.
16. If a 0.8 meter tall child stands 0.5 meter in front of a vertical plane mirror, how tall will the image of the child be?
The image in a plane mirror is the same size as the subject, so the child's image will be 0.8 meter tall regardless of the distance the child is from the mirror.
18. How does the height of the shortest mirror in which a person can see her entire body compare with her height? Does your answer depend on how far she stands from the mirror?
Looking straight ahead, she should be able to see her head at normal eye level. The top of the mirror must be about level with the top of her head. She must now be able to see her feet when looking at the bottom of the mirror. The law of reflection says that the angle of incidence equals the angle of reflection, so this will occur if the bottom of the mirror is at half of her height independent of her distance from the mirror. (You can sketch this to convince yourself.) The shortest mirror that will work is half of her height.
22. If you walk toward a flat mirror at a speed of 1.2 meters per second, with what speed does your image move?
Recall that a plane mirror forms a virtual image as far behind the mirror as the subject is in front of the mirror. As you walk toward the mirror, the image moves a distance equal to your motion. Since speed is distance divided by time, and the times are equal, the speed of the image is equal to your speed of 1.2 meters per second.
26. Why do the images produced by two opposing mirrors appear to get progressively smaller?
The first images are as far behind the mirrors as the subject is in front of them. These images, in turn, become the subjects for the next successive pair of images. Thus, the second pair of images will have their distance behind the mirrors multiplied by something like a factor of two. This multiplication of image distance behind the mirrors continues for each successive pair of images. Since we perceive distant objects as being smaller, we see the pattern of images as becoming smaller.
30. The image produced by a convex mirror is always closer to the mirror than the object. Then why is it that the convex mirrors used on cars and trucks often have the warning "Caution: Objects Are Closer Than They Appear" printed on them?
The image produced by a convex mirror is always smaller than the subject. Since we perceive distance in part by comparing the relative size of an image to our knowledge of its true size, we interpret these smaller images as being farther away.
32. What happens to a ray of light that passes through the focal point at an angle to the optic axis of a concave mirror?
A light ray passing through the focus of a concave mirror will be reflected back parallel to the optic axis. You can check that this agrees with the law of reflection by drawing a careful ray diagram for a concave mirror, knowing that its focus is at a distance of one-half R for a concave mirror with spherical radius R.
34. What type of mirror should a solar engineer use to concentrate light to boil water?
The engineer should use a concave mirror. Plane and convex mirrors only form virtual images that do not act to concentrate light from a wider area into a smaller area. Only a concave mirror can form a real image that is smaller than its subject, and so concentrate light.
38. Can real and virtual images be photographed?
Both real and virtual images can be photographed. In either case, light arrives at the camera from the direction of the image.
42. Argue that the reversible nature of light rays means that you can interchange an object and a real image.
A real image is formed when light travels from a subject, through a system of optical components, and ends up focused at a particular position. Along the way, the light rays change angle and direction according to the laws of optics. But, principles like the law of reflection yield the same result if we reverse the direction of the light rays! If the angle of incidence equals the angle of reflection for one direction of light travel, turning the light ray backwards causes the original angle of reflection to be the new angle of incidence, and the original angle of incidence to be the new angle of reflection. So, if these angles were originally equal, they will still be equal when the direction of the light is reversed. Taking this action with every light ray that makes up the original image from the original subject will let us make a new image (identical to the original subject) from a new subject (that is identical to the original image). Thus, we have just interchanged (the roles of) an object and a real image with each other.
46. Without asking, how could you tell whether you are talking to astronauts on the moon or on Mars?
You can tell by measuring the time between when you say something and when you hear a reply back. Remember that the speed of light is very large, but still finite. The distance from the Earth to the moon is much less than the distance from the Earth to Mars. Since light (or radio) waves travel at a constant speed, it will take longer for your voice to be transmitted to Mars from Earth, and a reply received back again, than it would between the Earth and the moon.
48. If you remove some of the green light from white light, what color would you expect to see?
Removing some of the green light would leave more of the other primary colors of light (red and blue) than is normally present in white light. So, you would see a color that is a mixture of red and blue, or magenta.
54. A Crest toothpaste tube viewed under white light has a red C on a white background. What would you see if you used red light?
The C on the toothpaste tube appears red when viewed under white light because it principally reflects red light. The surrounding background appears white because it reflects all components of white light equally. If only red light shines on the tube, only red light can be reflected. Since the C and the background will reflect red light about equally, the letter will blend into the background and may not be discernible.
58. A lens for a spotlight is coated so that it does not transmit yellow light. If the light source is white, what color is the spot?
White light is made up equally of the primary colors red, green, and blue. Yellow is a mixture of red and green light. Since the lens does not transmit yellow, the red and green components of white light have been reduced. Thus, mostly blue light would be transmitted through the lens giving a bluish spot.
60. Why is the sun yellow?
Light originating from the sun is basically white. As the sunlight passes through the Earth's atmosphere, the air molecules scatter more blue light than red. (This is also why the sky appears blue, from the scattered blue sunlight.) With some of the incoming blue sunlight removed, there is a greater amount of red and green light remaining. The sun then appears to be colored a mixture of red and some green, or yellow. Toward sunset, the sunlight passes through a greater amount of air scattering even more blue and a greater amount of green. That leaves the setting sun appearing reddish and gives rise to beautiful sunsets.