Question

# A astronomical telescope has objective and eyepiece of focal lengths $$40\ cm$$ and $$4\ cm$$ respectively. To view an object $$200\ cm$$ away from the objective, the lenses must be separated by a distance:

A
54.0 cm
B
37.3 cm
C
46.0 cm
D
50.0 cm

Solution

## The correct option is A $$54.0$$ cmOn applying the lens formula for the objective lens:$$\dfrac{1}{f_0}=\dfrac{1}{v_0}-\dfrac{1}{u_0}$$$$\dfrac{1}{v_0}=\dfrac{1}{f_0}+\dfrac{1}{u_0}$$$$\dfrac{1}{v_0}=\dfrac{1}{40}+\dfrac{1}{-200}$$$$v_0=50\ cm$$Therefore, tube length $$=v_0+f_e=50+4=54\ cm$$Physics

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