Assignment 1, Part 1: Pre-lab questions

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20.309: Biological Instrumentation and Measurement

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Pre-lab questions


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your answers to the following questions


  1. Snell's law:
    A laser beam shines on to a rectangular piece of glass of thickness $ T $ at an angle $ \theta $ of 45° from the surface normal, as shown in the diagram below. The index of refraction of the glass, ng, is 1.41 ≈√2. The index of refraction for air is 1.00.
    Optics bootcamp snells law problem.png

    (a) At what angle does the beam emerge from the back of the glass?

    (b) When the beam emerges, in what direction (up or down) is it displaced?
    Optional:
    (c) By how much will the beam be displaced from its original axis of propagation?

  2. Chelonian size estimation:
    In the diagram below, an observer at height $ S $ above the surface of the water looks straight down at a turtle swimming in a pool. The turtle has length $ L $, height $ H $, and swims at depth $ D $.
    Turtle problem.png

    (a) Use ray tracing and Snell's law to locate the image of the turtle. Show your work.
    (b) Is the image real or virtual?
    (c) Is the image of the turtle deeper, shallower, or the same depth as its true depth, $ D $?
    (d) Is the image of the turtle longer, shorter, or the same length as its true length, $ L $?
    (e) Is the image of the turtle taller, squatter, or the same height as its true height, $ H $?

  3. Ray tracing with thin, ideal lenses:
    Lenses L1 and L2 have focal lengths of f1 = 1 cm and f2 = 2 cm. The distance between the two lenses is 7 cm. Assume that the lenses are thin. The diagram is drawn to scale. (The gridlines are spaced at 0.5 cm.) Note: Feel free to print out this diagram so you can trace the rays directly onto it. Or maybe use one of those fancy tablet thingies that the kids seem to like so much these days.

    RayTracing1.png


    (a) Use ray tracing to determine the location of the image. Indicate the location on the diagram.
    (b) Is the image upright or inverted? Is the image real or virtual?
    (c) What is the magnification of this system?

    Optional:

    (d) Lens L1 is made of BK7 glass with a refractive index n1 of 1.5. Lens L2 is made of fluorite glass with a refractive index n2 of 1.4. Compute the focal lengths of L1 and L2 if they are submerged in microscope oil (refractive index no = 1.5).

  4. Measuring focal lengths (hint: this will be really useful later):
    In the two-lens system shown in the figure below, the rectangle on the left represents an unspecified lens L1 of focal length $ f_1 $ separated by 0.5 cm from another lens L2 with focal length $ f_2 $ of 1 cm.
    UnknownLens.png

    Find the value of $ f_1 $ such that all the rays incident parallel on this system will be focused at the observation plane, located at a distance d of 2 cm away from L2.