PROBLEMS
- You will notice if you look in a mirror that your left and right sides are inverted, but your feet and head (bottom and top) are not inverted. How can this be? A mirror can't possibly know your orientation. Explain why this is so via careful ray tracing. Hint: Draw two different views of a person standing in front of a mirror - one overhead view and one side view and do the ray tracing. Recall that you need two rays to be emitted from any single point on an object in order to find the image!
- Reflectors are simple devices that accomplish a pretty cool thing. They send light back the way it came (anti-parallel to the incoming light) regardless of the orientation of the surface normal. There is a limit to the angle that the surface normal can have, but you will see what that limit is after you figure out the geometry of reflectors. Please find the angle required between two planar mirrors such that they will act like a reflector.
- In which of the following cases is a real image possible: Planar mirror, concave mirror, convex mirror? In which case is a virtual image possible? Can a real image be upright in any of these scenarios?
- Draw an orientation of a room that could be at a carnival to make real image of a mannequin like a ghost while leaving the mannequin out of sight.
- Which planet has the highest albedo? What is the cause of its high value?
- Draw a diagram and show mathematically that for small angles of reflection of rays near the principal axis on spherical mirror, that the focal length should be half of the radius of curvature.
- What is spherical aberration?
- What is the role of an aperture in a cheap camera?
- A 10cm tall cup is placed 30cm away from a convex mirror with a 40cm radius of curvature. a. Where does the image arise? b. How tall is the image? c. Is it upright or inverted?
- Using the mirror equation, indicate where must an object be placed such that no image forms near a concave mirror?
- What is the sign of: a. The focal length of a convex mirror? b. The focal length of a concave mirror? c. The image distance for a real image? d. The image distance for a virtual image? e. The magnification for a real image using a mirror? f. The magnification for a virtual image using a mirror?
- At what wavelength is the absorption of water highest? Lowest? What fraction of light at wavelength 350 nm will pass through 30cm of water?
- How many times stronger is the scattering of violet light at 400 nm wavelength vs green light at 500 nm? Recall that wavelength is inversely proportional to frequency.
ANSWERS
1. Mirror symmetry is different than a rotation by pi. If you don't see this from your ray tracing, see me.
2. Two options: parabolic mirror and rectangular prism. The latter you should at least in two dimensions be able to show with ray tracing and simple geometry.
3. concave; all; no
4. Like the real image in lecture using a concave mirror... except a bigger version.
5. Venus due to its dense atmosphere
6. We did this in class.
7. See section 7.2
8. ditto
9. -12cm; 4cm; upright
10. no image means di=infinity, so when do=f.
11. -++--+
12. 70nm; 500nm; 97%
13. 2.44