Physics help. I don't know how to approach this one. Re: Lenses help.?

Question

A bright object and a viewing screen are separated by a distance of 72.0 cm. At what location(s) between the object and the screen should a lens of focal length 12.0 cm be placed in order to produce a crisp image on the screen? [Hint: First draw a diagram.]

smallest possible distance from object:
_____ cm
largest possible distance from object:
_______ cm

Answer 1

It depends on the diameter of the lens.

If the lens is very small, that is, it has a high numerical f-stop, the range of acceptable distances for a crisp image is much greater.

If the rays from the object are parallel, then 12 cm is the optimum distance from the lens, 60cm from the object.

This is called depth of field, or more accurately, depth of focus in photography.

Since all objects are 3 dimensional, part of the object is always closer or further from the lens and viewing screen. The screen and/or lens of a professional view camera can be tilted and adjusted to compensate, putting more of the object into a crisp image.

Answer 2

If the distance from bright object to lens is x, and the distance from lens to screen is y, the following formulas apply:

1/x +1/y = 1/f

x + y = d

f is the focal length of the lens, 12.0cm and d is the distance between object and screen, 72 cm

Substitute y = d - x to eliminate y in the first eq.

1/x + 1/(d-x) = 1/f mult both sides by x(d-x)

d-x + x = x(d-x)/f mult both sides by f and expand parens

d*f = d*x - x^2

x^2 - d*x + d*f = 0

Plug in the numbers and solve the quadratic equation. You will get the two values of x