Look at the following diagram. The lens of a normal eye has a focal point that l

Question

Look at the following diagram. The lens of a normal eye has a focal point that lies on the retina, so that images can form there. However, if the lens is misshaped, then the focal point moves. To correct this, we use corrective glasses. If a person has a lens with focal length f = 1.2cm, and a corrective lens is placed 2 cm in front of the eye. what focal length should the corrective lens be to focus the image of an object 500m (50,000cm) in front of the eye onto the retina (1.7cm behind the eye's lens)?

Explanation / Answer

For the corrective lens,

focal length,F = -f

object distance, u = 50000 cm

So, using the equation,

1/u +1/v = 1/F

v = image distance

So, 1/50000 + 1/v = 1/(-f)

So, So, v = 1/(1/50000 - 1/f) <------ image will be formed at focal length

-ve sign for image formed at 'f' cm to the left of corrective lens

So, for the eyelens,

object distance, u = 2cm - v

focal length, F = 1.2 cm

v = image distance = 1.7 cm

So, using the same equation,

1/u + 1/v = 1/f

So, 1/(2-(1/(1/50000 - 1/f))) + 1/1.7 = 1/1.2

So, f = 2.08 cm

So, focal length of the corrective lens = -f = -2.08 cm <----------answer

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