Answer to Question #2941 in Optics for morris

Question

The convex lens of a copy machine has a focal length of 25cm. A letter to be copied is placed 40 cm from the lens. How far from the lens is the copy paper located? How much larger will the copy be?

Answer 1

1/S₁ +1/S₂ =1/f

1/S₂ = -1/S₁ +1/f = (S₁-f)/(S₁ f)
S₂ = (S₁ f)/(S₁-f) = (40*25)/(40-25) = 1000/15 = 67cm.
Magnification is
M = -S₂/S₁ = -67/40 = -1.675.
Notice the sign convention here shows that, if M is negative, as it is for real images, the image is upside-down with respect to the object. For virtual images, M is positive and the image is oriented upright.