A simple camera telephoto lens consists of two lenses. The objective lens has a focal length f1 = +41.7 cm. Precisely 36.1 cm behind this lens is a concave lens with a focal length f2 = -13.9 cm. The object to be photographed is 4.06 m in front of the objective lens. How far behind the concave lens should the film be placed?
To determine the distance behind the concave lens where the film should be placed, we can use the thin lens equation:
1/f = 1/di - 1/do
Where:
f = the focal length of the lens
di = the image distance from the lens
do = the object distance from the lens
For the objective lens:
f1 = +41.7 cm
do1 = 4.06 m = 406 cm
We can use the equation above to find di1:
1/41.7 = 1/di1 - 1/406
Simplifying the equation:
1/di1 = 1/41.7 + 1/406
Finding the reciprocal:
di1 = 1 / ( (1/41.7) + (1/406) ) = 37.58 cm
Now, for the concave lens:
f2 = -13.9 cm
do2 = di1 = 37.58 cm
Using the thin lens equation again, we can find the image distance behind the concave lens, di2:
1/(-13.9) = 1/di2 - 1/37.58
Simplifying the equation:
-1/13.9 = 1/di2 - 1/37.58
Finding the reciprocal:
di2 = 1 / ( -1/13.9 + 1/37.58 ) = 14.86 cm
The final step is to determine the distance behind the concave lens where the film should be placed. This distance is equal to the image distance behind the concave lens, di2. Therefore, the film should be placed 14.86 cm behind the concave lens.