Due Wednesday May 7th by 5 pm.

Note that clear diagrams are vital components of good answers to questions 1-6 (and most other physics questions!).

1) You hold your pen at about eye level 10 cm in front of a plane mirror. You are behind it, 30 cm from the mirror.
a) What is the distance between your eyes and the apparent position of the pen's image in the mirror?
b) Draw a ray diagram with two rays showing the pen and its image. Is the image real or virtual?

2) An object is 20 cm in front of a thin diverging lens having a 30 cm focal length.
a) What is the image distance d_i? Is the image inverted or not?
b) Is the image real or virtual?
c) What is the absolute value of the magnification?

3) An object is 40 cm in front of a thin converging lens having a 30 cm focal length.
a) What is the image distance d_i?
b) Is the image inverted or not?
c) Is the image real or virtual?
d) What is the absolute value of the magnification?

4) An object is 10 cm in front of a concave mirror having a 30 cm focal length.
a) What is the image distance d_i?
b) Is the image inverted or not?
c) Is the image real or virtual?
d) What is the absolute value of the magnification?

5) An object is 30 cm in front of a convex mirror having a 30 cm focal length.
a) What is the image distance d_i?
b) Is the image inverted or not?
c) Is the image real or virtual?
d) What is the absolute value of the magnification?

6) A white point-sized object is imaged by a lens onto a piece of paper. The index of refraction of the glass is shown below. What does the spot look like if the paper is placed at the point where the blue light is focused?

7) Why do stars shimmer and sparkle?
Consider the reason that we see mirages, and that the atmosphere is not a uniform density, but rather a turbulent mix of densities.

8) Use geometry and similar triangles to derive the thin lens equation. where d_o is the distance between the object and the lens, d_i is the distance between the image and the lens, and f is the focal length of the lens. Use two of the rays shown below including the middle ray, and a geometrical argument.
Hint: for two rays find expressions relating d_o, d_i, f, h_o, and h_i, then eliminate h_o.

9) Briefly describe near sightedness and farsightedness. Which one makes it easier to read the fine print on the above graph?

10) Why do lenses have different focal lengths under water and in air? This is true of our eyes as well, and is why we need swimming goggles to properly focus under water.

11) A lens of focal length f is placed in front of your eye (ignore the distance between the lens and your eye). An object is placed at the focal length of the lens so that its image appears to be at infinity and can be seen by a relaxed eye. Show that the lens’s angular magnification for a typical user is given by m=25cm/f.

12) Show that the magnification of a microscope is given by m=s*25cm/(f_o*f_i) where s is the tube length, f_o and f_i are the focal lengths of the objective lens and eyepiece, respectively.

13) Show that the angular magnification of a refracting telescope is given by m=f_o/f_e where f_o and f_i are the focal lengths of the objective lens and eyepiece, respectively.