# Optical instrument telescopes – problems and solution

1. The focal length of the objective lens is 400 cm and the focal length of the ocular lens is 20 cm. If the eye is relaxed, determine :

a) The overall magnification of telescope (M)

b) the image distance from the objective lens (d_{ob}’),

c) the image distance from the ocular lens (d_{oc})

d) the distance between the lenses

__Known :__

The focal length of objective lens (f_{ob}) = 400 cm

The focal length of ocular lens (f_{oc}) = 20 cm

*The eye is relaxed so that the real image generated by the objective lens is at the focal point of the objective lens and the first focal point of the ocular lens.*

__Solution :__

__a) ____The overall magnification ____(M)__

M = f_{ob} / f_{oc}

M = 400 cm / 20 cm = 20X

The image is virtual and inverted.

__b) ____The image distance from objective lens ____(____d___{ob}__’)__

If the eye is relaxed, the image distance from objective lens (d_{ob}’) = the focal length of objective lens (f_{ob}) = 400 cm = 4 m.

__c) ____The distance of real image from the ocular lens ____(____d___{oc}__)__

If the eye is relaxed, the distance of real image and ocular lens (s_{oc}) = the focal length of ocular lens (f_{oc}) = 20 cm = 0.2 m.

__d) ____The distance between the lenses__

The distance between the lenses = the telescope length (l) = the focal length of objective lens (f_{ob}) + the focal length of ocular lens (f_{oc}) = 400 cm + 20 cm = 420 cm.

2. The distance between objective lens and ocular lens is 20 cm. The overall magnification of telescope when the eye is relaxed is 40X. Calculate the focal length of ocular lens (f_{oc}) and the focal length of objective lens (f_{ob})

__Known :__

the telescopes length (l) = 20 cm

the overall magnification of telescope (M) = 40X

__Solution :__

If the eye is relaxed, the focal length of ocular lens (f_{oc}) + the focal length of objective lens (f_{ob}) = the telescope length (l)

f_{oc} + f_{ob} = l

f_{ob} = l – f_{oc}

f_{ob} = 20 – f_{o}_{c} —–> equation 1

__The overall magnification of telescope ____(M) :__

M = f_{ob} / f_{oc}

f_{ob} = M f_{oc}

f_{ob} = 40 f_{oc }—–> equation 2

__The focal length of ocular lens ____:__

Subtitute f_{ob} in equation 1 with f_{ob} in equation 2 :

f_{ob} = 20 – f_{oc}

40 f_{oc} = 20 – f_{oc}

40 f_{oc} + f_{oc} = 20

41 f_{oc} = 20

f_{oc} = 20 cm / 41

f_{oc} = 0.5 cm

The focal length of ocular lens = 0.5 cm.

__The focal length of the objective lens ____:__

f_{ob} = 20 – f_{oc}

f_{ob} = 20 – 0.5

f_{ob} = 19.5 cm

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