Optics

Which of the following describes how to calculate the magnification?

(1) Find the Jones Matrix for apolarizer with the optic axis of 30°. (2) Find the Jones Matrix for a polarizer with the optic axis of - 60°. (3) Find the Jones Vector for the light at the point A after passing through the two polarizers. Find the Jones Vector for the light at the point A after passing through the two polarizers. (4) Find the transmittance of the light in (3).

The same arrow is placed 2 m from the same converging lens. a. Draw three rays to for man image. (See above for the diagram) b. Where is the image located? Is the image real or virtual?What is the magnification of the image? (c. Answer the same questions using the thin lens equation and the magnification.

A uniform collimated beam is focused by a lens whose focal length is 20 mm and whose diameter is 10 mm. The wavelength is 0.8 um. Compute the focused spot size.

In a three dimensional semiconductor crystal with a perfect lattice. Assume the distance between atoms is 'b' center meter. The reciprocal lattice is what we call k-space. It's Fourier transform of original lattice. We solve the Schrödinger equation of electron wave in original periodical lattice with one unit cube of side length of b and obtain the electron wave mode. We can represent all solutions in the k-space with each point of the k-value as one solution i.e. one mode. This problem is asking you to derive the mode density in this crystal. a). Assume the electrical potential distribution is infinite near the atoms. This results in a periodic solution with periodic unit (T/b, T/b, T/b) in kx, ky and kz directions of k-space. Write done the volume of the unit cell in the k-space. (5 points) c). How many cells in the spherical shell in total? (5 points) Due to k can only be positive, how many cells in the first quadrant? (5 points) Each k point can correspond to two modes for electron spin up and spin down. So how many modes in the first quadrant in k-space. (5 points) d). if we related the results to the density of modes, we can equal it to p(k)*dk, where the p(k) is the density of the modes. Please find the p(k) based on c) result. (5 points) e). Based on d) result, please normalized it to unit volume mode density. (5 points) b). Imagine in k-space, there is a spherical shell, the radius of the inner sphere is k, the thickness of the shell is the differential dk, write down the volume of the spherical shell. (5 points) f). Based on e), convert unit volume normalized p(k) to p(v) by using p(k)dk=p(v)dv relationship.It's more convenient to use frequency v instead of k in the real practice. (5 points)

5. Looking into the bowl of a spherical shape soup spoon, a man standing 25cm away sees his image reflected with a magnification of -0.064. Determine the radius of curvature of the spoon.

Calculate the magnification of an object placed 6.20 mm from a compound microscope (two conversing lenses) that has a 6.00 mm-focal length objective and a 50.0 mm-focal length eyepiece. The objective and eyepiece are separated by 23.0 cm.

- Let the focal length of an imaging lens be 20 mm. Plot the object distance versus the image distance.

6. A person is viewing a statue in a mirror. Her eyes are h metres above the ground, and thestatue is exactly h/2 metres tall. (b) Prove that the person needs a mirror of height h/4 m in order to view the whole statue[2 marks]at once. (The mirror does not need to start at floor level.) (c) On your diagram, sketch the virtual image of the statue which the person sees. (Size and-location are important, your ability to actually sketch the statue is not...) [1 mark] (a) On the diagram above (or your own hand-drawn approximation, if you do not have access to a printer), by hand draw at least two light rays from the statue to the person'sla

. Compute the divergence angle of a Gaussian beam of wavelength 0.8 um and spot size 1 mm. If this beam is aimed at the moon, what is its spot size on the moon's surface? (The distance between the earth and the moon is3.8 x 10 m.) What is its spot size at distances of 1 km and 10 km?