Pdf of a camera with telephoto lens of focal length 125 mm takes a picture of 1.8m tall woman standing 5.0m away. what must be the distance between the film and the lens to get a properly focused picture
To determine the distance between the film and the lens in order to get a properly focused picture, we can make use of the thin lens formula:
1/f = 1/v - 1/u
where:
- f is the focal length of the lens
- v is the distance between the lens and the image (film or sensor)
- u is the distance between the lens and the object
In this case, the focal length is given as 125 mm, the object distance (u) is 5.0 m, and we want to find the image distance (v).
To begin, we need to convert 125 mm to meters:
f = 125 mm = 0.125 m
Now, let's substitute the given values into the thin lens formula:
1/0.125 = 1/v - 1/5
Simplifying the equation:
8 = 1/v - 1/5
To isolate 1/v on one side, let's find a common denominator:
8 = (5 - v)/5v
Next, cross-multiply to get rid of the fractions:
8 * 5v = 5 - v
40v = 5 - v
Moving all the terms involving v to one side:
40v + v = 5
Combining like terms:
41v = 5
Finally, solve for v by dividing both sides of the equation by 41:
v = 5/41
Therefore, the distance between the film and the lens to get a properly focused picture is approximately 0.122 m (or 12.2 cm).