Question

(a) Find the power of the lens necessary to correct an eye with a far point of 23.7 cm


(b) Find the power of the lens necessary to correct an eye with a far point of 45.0 cm.

Answer 1

A person suffering from myopia can not see distant objects distinctly. His far point is limited to some distance as shown in figure. Image of distant objects are formed at a point before retina. In order to correct the myopic eye, a concave lens is used as shown in figure.

We have lens equation :- (1/v) - (1/u) = 1/f

where v is lens to image distance, u is lens to object distance and f is focal length

If a myopic eye has far point 23.7 cm , then we have v = -23.7 cm ( Cartesian sign convention is used ), u is infinity

Hence focal length of lens :- 1/f = -1/23.7 or f = -23.7 cm

power of lens = -100/23.7 = - 4.2 D

Similarly for a myopic eye with far point 45 cm

1/f = -1/45 or focal length of lens = - 45 cm , power of lens = -100/45 = -2.2