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Homework Help: Lenses and autocollimation

  1. Oct 13, 2009 #1
    1. The problem statement, all variables and given/known data

    a) In the autocollimation experiment of Sec. 3.5, a thin convex lens is placed 25 cm from a pinhole that acts as a point source of light. A plane mirror placed 20 cm behind the lens reflects the light back through the lens, and the reflected light forms a sharp spot beside the pinhole.
    What is the focal length of the lens (in cm)?

    b) Consider a symmetrical biconvex lens with r1 = r2 = r
    How would you alter the lens if you wanted to make the focal length longer?
    Make it flatter (more like a flat slide) or make it rounder (more like a sphere)?

    A. 1/f = 0
    B. 1/f = 2(n - 1)/r
    C. 1/f = 2(1 - n)/r
    D. 1/f = (n - 1)/r

    2. Relevant equations



    3. The attempt at a solution
    a)I used the lensmaker's equation but the answer was wrong. Shouldn't this formula apply?

    b) Increasing the focal length would occur if the radius was increased. Since it is a biconvex lens, they will increase if the lens is made to go outward more, such as if it was a sphere instead of flat.
    Last edited: Oct 13, 2009
  2. jcsd
  3. Oct 15, 2009 #2
    Something tells me that I know you :)


    for (a) Read page 42, section 3.1.2 in your physics lab book
    for (b) use equation 3.2 (see below)

    (n-1)(1/r' -1/r'') = 1/f
    for a biconvex lens, r'' is negative

    hence (n-1)(1/r' - 1/-r'') = 1/f
    (n-1)(1/r' + 1/r'') = 1/f
    but since r' = r'' = r, substitute and solve and you'll get your answer
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