Question

You must use the ray tracing equations to trace the appropriate rays through the system.

A thin lens is used to image a real object located 90 mm from the lens to produce a real image on a detector 60 mm from the lens in air. A second thin lens is inserted at 40 mm before the first lens in order to image a distant object at the detector (40 mm from the original lens). Determine the effective focal length of the second lens.

Answer 1

For the first lens, L1

1/f = 1/v + 1/u

1/f = 1/90 + 1/60

=> f = 36 mm

now, image distance from L1 in the 2nd case is: v' = 40 mm

therefore, object distance can be found using:

1/36 = 1/40 + 1/u'

=> u' = 360 mm

and distance between first lens L1 and the newly introduced lens L2 is 40 mm

therefore, image distance of L2 is:

v'' = - (360-40) = - 320 mm

u'' = 60 - 40 = 20 mm

so, 1/f' = 1/20 - 1/320

=> f' = 21.33 mm

this is the focal length of the 2nd lens L2.