A Galilean telescope has an ocular lens with a power of -32.00 D and an objective lens with a power of +8.00 D. What is the magnification provided by the telescope?

To determine the magnification of a Galilean telescope, you can use the formula for magnification, which is the negative ratio of the focal lengths of the ocular and objective lenses.

First, calculate the focal lengths based on their powers. The focal length (f) in meters is the inverse of the power (P) in diopters:

• For the ocular lens with a power of -32.00 D:

[ f_{ocular} = \frac{1}{-32.00} = -0.03125 , \text{meters} , (or , -31.25 , mm) ]

• For the objective lens with a power of +8.00 D:

[ f_{objective} = \frac{1}{8.00} = 0.125 , \text{meters} , (or , 125 , mm) ]

Now, to find the magnification (M) of the telescope, use the following formula:

[ M = -\frac{f_{objective}}{f_{ocular}} ]

Substituting the focal lengths:

[ M = -\frac{0.125}{-0.03125}