Question

Your camera has a lens with a 35.0 mm focal length and film that is 36.0mm wide. In taking a picture of an airplane 22.7m in length, you find that the image of the airplane fills only three-fourths of the width of the film.

a.) How far are you from the airplane?

b.) How close should you stand if you want to fill the width of the film with the airplane's image?

Please show all work, thank you!

Answer 1

A.

The image length is,

        h' = (3/4)W = (3/4)(36 mm) = 27 mm = 27x10^-3 m

The image distance is,

       di = (h' / h)d₀ = (27x10^-3 m /22.7 m)d₀ = (1.1894x10^-3)d0

The thin lens equation is,

     1/d0 + 1/di = 1/f

     1/d0 + 1/[(1.1894x10^-3)d0] = 1/f

Then,

     d0 = f [1 + {1 / (1.1894x10^-3)}] = (35x10^-3 m)[1 + {1 / (1.1894x10^-3)}] = 29.46 m

Answer: The required distance is, 29.46 m

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b.

The image of the airplane is,

        di = [W / h]d0

            = (36x10^-3 m/ 22.7 m)d0

           = [1.5859x10^-3]d0

The thin lens equation is,

     1/d0 + 1/di = 1/f

     1/d0 + 1/[[1.5859x10^-3]d0] = 1/f

Then,

     d0 = f [1 + {1 / (1.5859x10^-3)}] = (35x10^-3 m)[1 + {1 / (1.5859x10^-3)}] = 22.10 m

Hence, the distance from the airplane is,

    Distance = 29.46 m - 22.10 m = 7.36 m