2.1 Images Formed by Plane Mirrors
What are the differences between real and virtual images? How can you tell (by looking) whether an image formed by a single lens or mirror is real or virtual?
Can you see a virtual image? Explain your response.
Can you photograph a virtual image?
Can you project a virtual image onto a screen?
Is it necessary to project a real image onto a screen to see it?
Devise an arrangement of mirrors allowing you to see the back of your head. What is the minimum number of mirrors needed for this task?
If you wish to see your entire body in a flat mirror (from head to toe), how tall should the mirror be? Does its size depend upon your distance away from the mirror? Provide a sketch.
2.2 Spherical Mirrors
At what distance is an image always located: at or f ?
Under what circumstances will an image be located at the focal point of a spherical lens or mirror?
What is meant by a negative magnification? What is meant by a magnification whose absolute value is less than one?
Can an image be larger than the object even though its magnification is negative? Explain.
2.3 Images Formed by Refraction
Derive the formula for the apparent depth of a fish in a fish tank using Snell’s law.
Use a ruler and a protractor to find the image by refraction in the following cases. Assume an air-glass interface. Use a refractive index of 1 for air and of 1.5 for glass. (Hint: Use Snell’s law at the interface.)
(a) A point object located on the axis of a concave interface located at a point within the focal length from the vertex.
(b) A point object located on the axis of a concave interface located at a point farther than the focal length from the vertex.
(c) A point object located on the axis of a convex interface located at a point within the focal length from the vertex.
(d) A point object located on the axis of a convex interface located at a point farther than the focal length from the vertex.
(e) Repeat (a)–(d) for a point object off the axis.
2.4 Thin Lenses
You can argue that a flat piece of glass, such as in a window, is like a lens with an infinite focal length. If so, where does it form an image? That is, how are and related?
When you focus a camera, you adjust the distance of the lens from the film. If the camera lens acts like a thin lens, why can it not be a fixed distance from the film for both near and distant objects?
A thin lens has two focal points, one on either side of the lens at equal distances from its center, and should behave the same for light entering from either side. Look backward and forward through a pair of eyeglasses and comment on whether they are thin lenses.
Will the focal length of a lens change when it is submerged in water? Explain.
2.5 The Eye
If the lens of a person’s eye is removed because of cataracts (as has been done since ancient times), why would you expect an eyeglass lens of about 16 D to be prescribed?
When laser light is shone into a relaxed normal-vision eye to repair a tear by spot-welding the retina to the back of the eye, the rays entering the eye must be parallel. Why?
Why is your vision so blurry when you open your eyes while swimming under water? How does a face mask enable clear vision?
It has become common to replace the cataract-clouded lens of the eye with an internal lens. This intraocular lens can be chosen so that the person has perfect distant vision. Will the person be able to read without glasses? If the person was nearsighted, is the power of the intraocular lens greater or less than the removed lens?
If the cornea is to be reshaped (this can be done surgically or with contact lenses) to correct myopia, should its curvature be made greater or smaller? Explain.
2.8 Microscopes and Telescopes
Geometric optics describes the interaction of light with macroscopic objects. Why, then, is it correct to use geometric optics to analyze a microscope’s image?
The image produced by the microscope in Figure 2.38 cannot be projected. Could extra lenses or mirrors project it? Explain.
If you want your microscope or telescope to project a real image onto a screen, how would you change the placement of the eyepiece relative to the objective?