Stargazing Understanding the Magnification of a Telescope: Why is M = f_o / f_e?

[quietrain]

hi, i don't understand why the 2 converging lens telescope's magnification is given by M = f_o / f_e

where f_o = focal length of objective, and f_e = focal length of eyepiece...

issn't M = image distance / object distance...

in the case of a infinity object, the image is also infinity for the eye to view it without straining.

so why is there still a magnification ? infinity over infinity?

need help thanks a lot!

 

[jtbell]

the 2 converging lens telescope's magnification is given by M = f_o / f_e

This is angular magnification.

issn't M = image distance / object distance...

This is linear magnification.

They're different things.

 

[quietrain]

oh. i see.

i look up the angular magnification and the formula was

M = tan E / tan E_0 (wikipedia)

where E_0 = the angle subtended by the object at the front focal point of the objective and E =the angle subtended by the image at the rear focal point of the eyepiece.

so how does this become the formula

M = f_o / f_e ?

even with small angle approximation the formula M = tan E / tan E_0 is still not M = f_o / f_e ?

 

[jovial01]

The two formulas for angular magnificaion are equivalent by their very nature and you don't need to prove equality by making arithmetic substitutions
They are both ratios (the focal length equation is simply a ratio of spatial dimensions, where as the angle equations is a ratio of the angles subtended by the magnitude of these dimensions)
Both ratios are in direct proportion.