**Examples for optical
instruments**

Example #1

Problem:

a.) Grandpa's far point is
75 *cm*.
What is the prescription (refractive power in diopters) for Grandpa's contact
lenses?

Solution:

A diverging lens will make an image of a far away
object at its focal length. Therefore, the focal length should be
negative 75 *cm*, and the prescription is

-1.33 diopters

b.) What is his prescription (in diopters) for eye glasses?

Solution:

Allowing for 2 *cm* between the eye and the
lens of the glasses, the image must be brought to 73 *cm*. Therefore the
prescription is

-1.37 diopters

c.) Grandma's near
point is 75 *cm*. What is the prescription (in diopters) for Grandma's
contact lenses?

Solution:

Choose the focal length such that an
object at the normal near point of 25 *cm* produces an image where Grandma
can focus on it, at 75 *cm*.
, and the
prescription is

2.67 diopters

d.) What is her prescription for eye glasses?

Solution:

Allowing for 2 *cm* between
the eye and the glasses, the normal near point is 23 *cm* from the glasses
and her near point is 73 *cm* from the lenses,
.

2.81 diopters

Example #2

Problem:

a.) A simple two-lens telescope's
eyepiece has a focal length of 10* cm*. If you want the magnification of
the telescope to be 40, what is the length of the telescope?

Solution:

The second lens must have a focal length 40 times longer,
400 *cm*. The overall length is thus

4.10 *m*