A short sighted person's range of vision is between 12 cm and 35 cm from the eye.What focal length lens is needed to allow her to see distant objects clearly?
A)35 cm
B)-12 cm
C)-23 cm
D)12 cm
E)-35 cm

Question

Quizplus · Accepted Answer

Since the person is short-sighted, they can see objects only within a range of 12 cm to 35 cm. To allow the person to see distant objects clearly, we need to use a concave lens, which will diverge the incoming light rays and make them appear to be coming from a farther distance. The focal length of the lens can be calculated using the formula:
1/f = 1/di + 1/do
where f is the focal length of the lens, di is the distance at which the person can see clearly (12 cm in this case), and do is the distance of the object from the lens (which we want to be at infinity).
Substituting di = -12 cm (since the person is short-sighted and can see only nearby objects), and do = infinity, we get:
1/f = 0 - 1/infinity
1/f = 0
Therefore, f has to be infinity, which means we need a lens that is as close to a flat glass plate as possible. However, since no lens is perfectly flat and has some thickness, we use a lens with the smallest possible negative focal length, which is -35 cm (the maximum distance at which the person can see clearly). Therefore, the correct choice is (E) -35 cm.

A Short Sighted Person's Range of Vision Is Between 12