Chapter 44: Problem 30

Question: An upright object is placed a distance in front of a converging lens. On the other side of the lens is a converging mirror of focal length f₂ seperated from the lens by a distance 2 (f₁+f₂), see Fig 35 Chap 44. Find the location, nature and relative size of the final image, as seen through the eye looking toward the mirror through the lens. Draw the appropriate ray diagram.

Solution:

$${1\over O}+{1\over I_1}~=~{1\over f_1}$$

O = 2 f₁ gives I₁ = 2 f₁. This gives an object for the mirror located at O₂ =  2(f₁+f₂)-2f₁ = 2f₂.

$${1\over O_2}+{1\over I}~=~{1\over f_2}$$

and hence I = 2 f₂. This provides the object for the lens again (as we are looking at it back through the lens). We see an inverted image at the location of the object, with magnification m = -1.