A hyperopic eye has a near point at 2 m Determine the power

A hyperopic eye has a near point at 2 m. Determine the power of the corrective lens for reading (book at 25 cm from the eyes). Assuming that the focal length for the reduced eye focused at its near point is 2.098 cm, estimate the size of the eyeball (distance to the retina).

Solution

A) here convex lense will have to be used in order to fix the reduced converging power of eye. The image formed from first lense will act as object for eye, i.e, we need to produce the image of book at near point using additional lense.

using lense formula 1/v-1/u=1/f,

1/-200 - 1/-25 =1/f

=>1/f=7/200 cm^-1 =+3.5 dioptre

B) again using 1/v-1/u=1/f,

1/v - 1/-200 =1/2.098

=> v= 2.120 cm

size of eyeball =2.12cm