A camera with a telephoto lens of focal length 125mm takes a picture of a 1.8m tall woman standing 5.0m away.
(1). What must be the distance between the film and the lens to get a properly focused picture?
(2). What is the magnification of the image
(3). What is the size of the woman's image on the film?
To answer these questions, I will explain the relevant formulas and steps involved in solving them.
(1) The distance between the film and the lens for a properly focused picture can be determined using the thin lens formula:
1/f = 1/v - 1/u
Where:
f = focal length of the lens
v = image distance (distance between the lens and the image)
u = object distance (distance between the lens and the object)
In this case, the focal length of the lens is given as 125mm (or 0.125m), and the object distance (u) is given as 5.0m.
To find the image distance (v), we rearrange the formula as follows:
1/v = 1/f + 1/u
Substituting the given values:
1/v = 1/0.125 + 1/5.0
Now we can solve for v by taking the reciprocal on both sides:
v = 1 / (1/0.125 + 1/5.0)
After evaluating the expression, v will be the distance between the film and the lens for a properly focused picture.
(2) The magnification of the image can be calculated using the magnification formula:
m = -v/u
Where:
m = magnification
v = image distance (from step 1)
u = object distance (given as 5.0m)
Using the calculated value of v from step 1 and the given value of u, we can plug in these values into the formula to find the magnification (m).
(3) The size of the woman's image on the film can be determined using the magnification formula:
Size of the image on the film = Magnification * Size of the object
In this case, the size of the object is given as the height of the woman, which is 1.8m. Use the calculated value of magnification (m) from step 2 and multiply it by the size of the object to find the size of the woman's image on the film.