Solutions to Homework Problem Set #5

Chapter 3, Page 102: P11, P13, PH3

P11. The image is virtual, upright, smaller than the object. Draw the usual rays: a ray that strikes the lens parallel to the axis is refracted as if it came from the focal point and a ray headed for the focal point on the right side of the lens is refracted so as to emerge parallel. See following drawing.

P13. No, front-surface mirrors do not have chromatic aberration. Chromatic aberration occurs only in refraction because the index of refraction depends on wavelength. Front-surface mirrors reflect the light with no refraction so that the index of refraction does not enter into their operation.

PH3. A shaving/makeup mirror produces a magnified, erect, virtual image of your face. In order for this type of image to be produced by a concave mirror, the object must be closer to the mirror than the focal length. Thus the focal length of this kind of mirror must be large enough so that your face will be closer than this distance. The mirror will work if your face is at any distance from the mirror less than its focal length.

Chapter 4, Page 142: P1, P3

P1. You are focused at a far-away object when the lens is closest to the film. You can verify this by ray-tracing – the lens must be moved further and further away from the film as an object gets closer and closer.

P3. The field of view of a lens varies inversely with the focal length. To get the widest field of view you would use the shortest focal length lens. See the following drawing. Remember that as the focal length of a lens increases, you must move it further away from the film to focus on the same object.