Question

A doctor determines that a patient's eye produces an image 20.5 mm from the lens when focusing on very distant objects, and her retina is 21 mm from her eye's lens. What should the focal length of her prescription glasses be?

Answer 1

Given that the eye is viewing distant object,

so, object distance for eyelens is:

u = infinity

Now, lens of eyes form the image at 20.5mm,

so, image distance for eye lens is:

v = 20.5mm = 2.05cm

by thin lens formula, focal length of eyelens fe is given by:

(1/fe) = (1/v) - (1/u)

(1/fe) = (1/2.05) -(1/infinity)

but

(1/infinity) = 0

so,

fe = 2.05cm

Now, for the combination of eyelens and prescription glasses, object distance is same as before:

u' = infinity

Also, retina is 21 mm behind the eyes,

and, the image must be formed at retina, so image distance is:

v' = 21 mm = 2.1 cm

Let the focal length of prescription glasses be fp,

then, by the combination of thin lenses:

(1/fe) + (1/fp) = (1/v') - (1/u')

(1/2.05) + (1/fp) = (1/2.1) - (1/infinity)

again

(1/infinity) = 0

so,

(1/fp) = (1/2.1) - (1/2.05)

(1/fp) = (2.05 - 2.1)/(2.1×2.05)

(1/fp) = -0.05/(2.1×2.05)

fp = -2.1×2.05/0.05

fp = -86.1 cm = -861 mm

This is the focal length of the prescription glasses.

Here - sign shows that the glasses are concave lens.