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