Useful number(s): c=3.00x108 m/s, h=6.626x10-34 J·s
1) An object 8cm tall is placed 15cm in front of a mirror (f=-100mm).
a) Draw a diagram of this situation, including 2 rays, which originate from the top of the object and terminate on the top of the image.
b) Is the mirror concave or convex?
c) How far is the center of curvature from the mirror?
d) What are the height, position, and orientation of the image?
e) Is the image real or virtual?
2) You would like to know the focal length of your camera lens. So you set up an experiment. You place a meter stick 1m away from the center of the camera lens and take a picture. You then develop the film and measure the height of the image on the film to be 25.60mm. (Hint: you can assume that the lens is converging and the image is inverted.)
a) What is the focal length of the lens?
b) What is the distance from the lens to the image?
3) A 2m long fish is hovering directly in front of you in a large aquarium filled with water (n=1.33). The wall of the aquarium is 12cm thick with n=1.48. A horizontal meter stick is attached to air-side of the wall. When you stand 50cm in front of the wall with the center of the meter stick and the center of the fish directly in front of your eyes, the meter stick and the fish appear to be the same length. (See the diagram below. NB: Not drawn to scale) How far is the fish from the water-side of the wall. (i.e., the distance labeled X in the diagram.)
4) In the following circuit:
a) (9 pts.) What is the power in each element?
b) (3 pts.) Does the total current lead or lag the total voltage?
c) (4 pts.) What is the resonance frequency of the circuit?
d) (4 pts.) What would the power dissipated by the whole circuit if the frequency was changed to the resonance frequency?
5) A light ray traveling in air (n=1.00) hits a 2m by 3m rectangular piece of glass in the center of the short side at an incident angle of 55 degrees. The ray enters the glass and reflects off of the top surface and exits through the center of the opposite short side.
a) What is the index of refraction of the glass?
b) What is the critical angle for internal reflection for the ray inside the glass?
c) What angle (with respect to the normal) does the ray hit the top surface of the glass?
d) Are your answers to parts b) and c) consistent with the fact that the light is reflected at the top surface? Explain.
e) The air is replaced by water (n=1.33), but the ray still initially hits the same glass at the center of the short side at angle of incident of 55 degrees.
i) From what side of the glass will the ray emerge?
ii) At what angle with respect to the normal will it emerge?