ME/CS 132a, Winter 2010, Homework 1 FAQ

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Problem 1

  • It looks like the units don't exactly cancel out in the exponential term in the Planck's law. Is this supposed to happen?
    • Answer: If you are using the old slides from lecture 2, the correct unit for the Planck constant is J·s, or W·s2 (but everything else is correct). The revised version has corrected this typo. [Shuo]

Problem 2

  • Is the answer going to have a dA_d term in it or would we have to integrate to get any of the phi's?
    • Answer: No, there won't be any integral involved (don't overthink!). The purpose of the problem is to let you learn how to "estimate" some of the quantities in radiometry for a real problem. [Shuo]
  • Once the laser reflects off the terrain, should we treat the reflected laser as an extended source, or a point source?
    • Answer: For simplicity, treat the reflected light as if it is coming from a point source. [Shuo]

Problem 3

  • Do we have to show that the focal length is equal to R/2/(n-1)?
    • Answer: No, you don't. This is a definition. On the other hand, you need to show that a ray travelling parallel to the optical axis will intersect with the focal point after being refracted by the lens (i.e. you cannot use Figure 1.9 directly). [Shuo]
  • Can we use the fact that the index of refraction of a vacuum (and approximately the index of refraction of air) is 1?
    • Answer: You can assume that the refractive index of the air is 1 when deriving the thin lens equation, but the first part (showing the ray is not refracted if it passes the center of a thin lens) shouldn't depend on this. [Shuo]

Problem 4

  • I am stuck on the derivation of part 2.
    • Answer: One trick you can try is to rewrite the condition that you obtained from part 1 in two separate inequalities (corresponding to the image plane is closer and farther away than ideal): 1 - z_hat'/z' < eps/d and 1 - z_hat'/z' > -eps/d. Then use the thin lens equation to replace z_hat'/z' with something in f, z, and z_hat. After this, do some algebra to rearrange things to get the following form: z_hat > (some term in f, d, eps, and z) and z_hat < (some other term in f, d, eps, and z). Then you can get D by taking the difference of the two. [Shuo]