Question

Problem As the resident physics expert, you’ve been called in to take care of some hornets that have been terrorizing your dorm. You find their nest is located high up in a tree. Your flamethrower is on backorder, so you’ll have to find another way to burn them out. In the deep recesses of the physics and astronomy basement, you find a very large concave spherical mirror from an old telescope. The mirror is 2 m across with an unknown radius of curvature. A solar furnace1 will certainly do the trick. Because this is just a small piece of such a large sphere, the angle of incidence for on-axis rays will always be below 5°, minimizing spherical aberration.

a) You first test out the mirror as a full-length wall mirror to determine its specifications. Placing a meter stick 2 m away, and observing the virtual image is upright with a new height of 1.5m, determine the image distance, the focal length, and the radius of curvature (Start with a ray diagram showing the object, mirror, and image.)

b) You determine that the nest is 7 m high. At what height above the ground should you place the mirror to do away with the hornet’s nest? Explain your reasoning, and support with a diagram using the sun’s rays.

c) Word of your success spreads quickly, and you’re called to eradicate another nest. But this nest is located only 5 m off the ground. To make matters worse, the ground is concrete so digging isn’t an option. But wait! You can fill the mirror bowl with water to change the focal length. Determine the new focal length with water. At what height above the ground should you place the mirror filled with water so that your fame lives on? Hint: trace a couple of reflected rays as they converge toward focus, with and without water in the mirror bowl; use Snell’s Law. (Include a ray diagram showing incoming, reflected, and refracted light.)

Answer 1