CBSE Class 12 · 2011 · Geometrical OpticsLong Answer

A giant refracting telescope at an observatory has an objective lens of focal length

15 m

. If an eyepiece lens of focal length

1.0 cm

is used, find the angular magnification of the telescope. If this telescope is used to view the Moon, what is the diameter of the image of the Moon formed by the objective lens? The diameter of the Moon is

3.42 \times 1 0^{6} m

and the radius of the lunar orbit is

3.8 \times 1 0^{8} m

Answer: Angular magnification $= 1500$ ; diameter of the Moon's image $\approx 13.5 cm$ .

Solution

Angular magnification (normal adjustment):

m = \frac{f _{o}}{f _{e}} = \frac{1500 cm}{1 cm} = 1500

.
Image diameter

d = α f_{o}

, with

α = \frac{3.42 \times 1 0 ^{6}}{3.8 \times 1 0 ^{8}} = 9.0 \times 1 0^{- 3} rad

d = 9.0 \times 1 0^{- 3} \times 1500 cm = 13.5 cm

CBSE Class 12 Board · 2011 · Subjective

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