Answer to Question #119005 in Optics for Priscilla gyasi

Question

A short sighted person can not see clearly when an object is placed beyond 80.0cm from his eyes.
(a) What type of lens does he have to use?
(b) calculate the focal length of the lens

Answer 1

It's given that a person has shortsightedness and far point is $80cm$ .

We assume here that the person's lens is fitted on the eye.

a).He has to use concave lens.

b).Let $f,u,v$ be the focal length,object distance and image distance respectively.

Now, as the person has shortsightedness so he can'n see distant object clearly and far point is

$v=-80cm$ and $u=-\infty$ (both $v,u$ are negative because lens is concave and both object and image are in same side) ,thus by Len's maker formula we get,

$$\frac{1}{f}=\frac{1}{v}-\frac{1}{u}\\ \implies \frac{1}{f}=\frac{1}{-80}-\frac{1}{-\infty}\implies f=-80cm$$

Hence, we are done.