Problem Set 2

Question 1:optical abberations (from previous problem set)

In lab, you are going to build a microscope. As discussed in lecture, a single lens can act as a magnifier. (You have certainly used a magnifying glass to look at something small.) But all modern microscopes that achieve very high magnifications use multiple lenses in series to make an image. This is clearly a much more expensive design. Why not use a single lens as a high-magnification microscope?

• List three potential problems with a single-lens, high-magnification microscope design. Explain the problems in few sentences and a simple sketch.

HINT: Use the information about the behavior of light in that was presented in lecture. Think about the underlying assumptions of geometric optics. Under what circumstances in a real microscope design would each assumption be violated? How do these violations impact the final image? (If you are stuck, go back to the lecture slides and take a close, logical look at each assumption. Where does each assumption break down? What is the effect of this breakdown in the assumption?)

Question 3:diffraction and interference

Collimated rays of light, with wavelength λ, shines on a square periodic structure at an angle θ relative to the structure normal. Assume that every surfaces of this structure, except the tops, are absorptive. The light rays are scattered off the top surface as spherical wavelets as described by the Huygen’s principle.

1. Find exit angles where the scattered light intensity is maximized as a function of λ, a, and θ. Explain how you come to this conclusion. (Hint, exit angle θ is one such angle where the exit rays are interfered in phase. The other exit angles, such as θ₂, correspond to the condition that the scattered rays are interfering constructively.)

1. If λ is 500 nm, a is 200 nm, and θ is 10 degrees, calculate the smallest three exit angles where the scattered light intensity is maximized. The scattered light exiting at angle θ is called the 0^th order diffraction spot, the light scattered at the next larger angle is called the 1^st order diffraction, and so on.

1. If the incident light is a mixture of two colors, λ₁ = 500 nm, λ₂ = 600 nm, what is the angular separation of the 0th order diffraction from rays of these two colors. What are the angular separations of the 1st and 2nd order diffractions of these two color rays?