**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 is negative 75 *cm*, and the prescription is

-1.33 diopters

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

Solution:

The image must be brought to 74 *cm*.
Therefore the prescription is

-1.35 diopters

c.)
Grandma's near point is 75 *cm*. What is the prescription
(in diopters) for Grandpa'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 see it, at 75 *cm*.
-> * f* = 37.5

2.33 diopters

d.) What is her prescription for eye glasses?

Solution:

The same as above,
only the normal near point is 24 *cm* from the glasses and
her near point is 74 *cm* from the lenses,
-> * f* = 35.5

2.81 diopters

Example #2

Problem:

a.) A simple
two-lens telescope's eyepiece has a focal length of 10* cm*.
If one wishes the magnification of the telescope to by a factor
of 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*