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Angular magnification of flat and concave mirrors

  1. Mar 10, 2014 #1
    1. The problem statement, all variables and given/known data

    (a) I hold a flat mirror 22.4 cm in front of my face. There is a freckle on my
    face 1 mm in diameter. Find the angular size of the freckle on the image of my face as
    viewed by my eye. (b) Repeat for a concave mirror which has a focal length of 39 cm.
    (c) What is the angular magnification of the concave mirror, as compared to the flat
    mirror?


    2. Relevant equations

    m = θ/θ2
    M=h'/h=-q/p
    1/p+1/q=1/f

    3. The attempt at a solution

    For part a: I figured that θ is the angle with the mirror in use, and θ2 is the angle when the object is placed at the nearpoint without the mirror. I assumed I was looking for θ, so I drew a triangle and did the arctan of 0.1cm/44.8cm to get 0.128 degrees as my answer. I'm not sure if that is correct.

    For part b: I found q using 1/p+1/q=1/f, and it was -52.62650602 cm. I then calculated total distance, q+p = 52.62650602 cm + 22.4 cm = 75.02650602cm. Then using M=-q/p, i calculated the magnification to be 2.34939759, making h' 2.34939759 mm. Then to find theta, I did arctan(h'/totaldistance) to equal 0.179 degrees. Probably wrong.

    Part c: I took angular size from part b and divided it by the angular size in part a because i figured that theta2 is the same for both.
     
    Last edited: Mar 10, 2014
  2. jcsd
  3. Mar 11, 2014 #2

    Simon Bridge

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    Basically you have tried to remember how to use a bunch of memorized equations - so you are not sure you did it right. Have a go sketching the situation as a way of checking your results using geometry rather than rules.
     
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