Hand-held cameras (even fancy photographer\'s cameras), rarely use film any more

Question

Hand-held cameras (even fancy photographer's cameras), rarely use film any more, but the physics is nearly the same as an old fashioned camera: there is a lens, and a plane onto which the image focuses. (In the old days, the plane was where the film went, now there will likely be a solid state CCD array there. But we still call this the "film plane".) Suppose a 24.0mm focal length lens is used to focus an image onto the film plane. The maximum distance available in this (large!) camera between the lens and the film plane is 112mm.

A) How far ahead of the film plane should the lens be, if the object to be photographed is 1.5m away?

B) What is the smallest object distance for which this camera can produce a sharp image

Explanation / Answer

(a)
f = 24.0 mm
do = 1.5 m

Using thin lens eq,
1/f = 1/di + 1/do
1/24.0 = 1/di + 1/(1.5*10^3)
di = 24.4 mm

(b)
Let the smallest object distance be, do
di = 112 mm
1/f = 1/di + 1/do
1/24.0 = 1/112 + 1/do
do = 30.55 mm

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