Geometrical Optics Summary Questions

1. Two mirrors are set in the corner perpendicular to each other. A light ray, which travels in the plane perpendicular to both mirrors, hits one of the mirrors. Draw all resulting rays. Choose your own angle of incidence for the first ray (you don’t need necessarily to choose a numerical value, you can choose a graphical representation) and find angles of travel for all other rays.

2. A layer of water is on the top of a horizontal rectangular slab of glass. There is no wind or other perturbances on the surface of water. A light ray hits the water at some non-zero angle with the normal to the water surface. Draw all resulting rays. Choose your own angle of incidence for the first ray (you don’t need necessarily to choose a numerical value, you can choose a graphical representation) and find angles of travel for all other rays. The indexes of refraction of air, water and glass are: $n_1$, $n_2$, and $n_3$ correspondingly.

3. In the setup of the problem 2, light shines from the bottom of glass slab. Find critical angles of total internal reflection at the water-glass interface and the water-air interface. The glass is a crown glass (see the table in the lecture notes).

4. In a middle of the floor of a large 2 m deep swimming pool, there is an electric light. You are swimming in the middle lane (which goes directly above the light source). Will you always see the light looking from the air? Support your answer with the numerical calculations and ignore any waves in the swimming pool.

5. A coin of 3 cm in diameter is 12 cm away from a concave mirror with a radius of curvature of 6 cm. Find the image of the coin. You can choose an orientation of the coin.

6. A converting convex-concave glass lens is made with two spherical surfaces of 13 cm and 10 cm in radius. Find its focal length in air.

7. A biconvex glass lens is made with two spherical surfaces of 15 cm and 10 cm in radius. Find its focal length in air.

8. A coin of 1.2 cm in diameter is 4 cm away from a biconvex lens that has a focal length of 12 cm. Find the image of the coin. You can choose an orientation of the coin.

9. Light with 633-nm wavelength shines normally to a plane with two slits. We observe the first interference maximum 82 cm away from the central maximum on a screen 12 m away from the slits. What is the separation of slits? How many interference maxima one can, in principle, observe?

10. Two slits are 1 cm apart and 1 m away from the screen. Calculate the spacing between successive maxima near the central fringe on the screen for light with 500-nm wavelength.

11. Light is shining normally to $n_1-n_2$ interface. The intensity of reflected light is $I=(\frac{n_1-n_2}{n_1+n_2})I_0$, where $I_0$ is the incident intensity, and $n_i$ are the refraction indices for the two media.

    1. Find the intensities of the light transmitted through air-glass interface.
    2. Find the intensities of the light transmitted through a slab of glass in air.