-> f = 37.5 cm,
and the prescription is 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 cm,
and the prescription is
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 m.
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