# Astronomical telescopes – problems and solutions

1.

Based on the graph above, determine the telescope magnification when the viewing eye is relaxed.

__Known :__

*The lens closest to the object is called the objective lens (focal length f _{o}) and forms a real image. The second lens called the eyepiece (focal length f_{e}) acts as a magnifier.*

The focal length of the objective lens (f_{o}) = 100 cm

The focal length of the eyepiece lens (f_{e}) = 8 cm

__Wanted :__ Telescope magnification when eye is relaxed

__Solution :__

M = -f_{o} / f_{e}

M = -100 cm / 8 cm

M = -12.5 X

Minus sign indicates that the image is inverted.

2.

Based on the figure above, what is the telescope magnification when the eye is relaxed?

__Known :__

The focal length of the objective lens (f_{o}) = 200 cm

The focal length of the eyepiece lens (f_{e}) = 5 cm

__Wanted :__ Total magnification

__Solution :__

When eye is relaxed, the telescope magnification :

M = -f_{o} / f_{e }

M = -200 cm / 5 cm

M = -40 X

Minus sign indicates that the image is inverted.

3.

Based on above figure, if the distance between the eyepiece lens and the objective lens (d) = 11 times the focal length of the eyepiece lens, then what is the total magnification when the eye is relaxed.

__Known :__

The distance between the eyepiece lens and the objective lens = the length of telescope = 11 f_{e}

The focal length of the eyepiece lens (f_{e}) = f_{e}

The focal length of the objective lens (f_{o}) = the length of a telescope – the focal length of the eyepiece lens = 11 f_{e} – f_{e} = 10 f_{e }

__Wanted:__ The telescope magnification

__Solution :__

M = -f_{o} / f_{e }

M = -10 f_{e} / f_{e }

M = -10 X

Minus sign indicates that the image is inverted.

4. What is the total magnification of the astronomical telescope?

__Known :__

The distance between objective and eyepiece lens (l) = 126 cm

The focal length of the eyepiece lens (f_{e}) = 6 cm

The focal length of the objective lens (f_{o}) = 120 cm

__Wanted:__ The total magnification

__Solution :__

Based on the above figure, the final image at infinity, so the eye is relaxed.

The total magnification of the astronomical telescope :