A luminous object is 500 m from a wall You are to use a conc

A luminous object is 5.00 m from a wall. You are to use a concave mirror to project an image of the object on the wall, with the image 2.27 the size of the object.

Part A

How far should the mirror be from the wall?

Part B

What should its radius of curvature be?

Solution

d_i = image distance, d_o = object distance, f = focus length

d_i = 2.27 * d_o , where d_o = d_i - 5

d_i= 2.27 (d_i - 5)

d_i = 8.94 m

d_o = 8.94 - 5 = 3.94 m

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1 / d_o + 1/ d_i = 2 / R

1 / 3.94 + 1/ 8.94 = 2 / R

R = 5.47 m