Question about lenses again?

Question

Thanks for the answers yesterday. A camera has a single convex lens of focal length 50.0mm. The lens may be moved relative to the film plane such that the lens-film distance may be varied between 50.0mm and 70.0mm. A photographer wishes to take some 'macro' photographs with high magnification of some small insects. To do this he places a convex magnifying lens of focal length 35.0mm directly in front of the lens. Find the shortest distance that the insect may be placed from the camera lens? Find the angular magnification that is achieved with the insect at this distance over what can be achieved without the magnifying lens? Explain your reasoning. Can anybody help me?

Answer 1

firt you need to find the focal length of the combination of the 2 lenses - change the focal length into dioptres (1/f in metres) tehn add the dioptres and then change them back into focal length.

This gives the 50mm = 0.05m = 20D

35mm = 0.035m = 28.67D

total = 48.57D which gives f = 1/48.57 = 20.5mm

This can then go into the lens formula

1/f= 1/u + 1/v

1/u = 1/20.5 - 1/70

so u = 29mm shortest distance from the combined lens