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Question

A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometer from two objects. The minimum distance between these two objects, which can be resolved by the telescope, when the mean wavelength of light is $$5000 \dot{A}$$, is of the order of :


A
5 m
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B
5 mm
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C
5 cm
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D
0.5 m
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Solution

The correct option is B 5 mm
We know, 

Resolving Power = $$\theta = \dfrac{d} {D}$$ but $$\theta \approx \dfrac{\lambda} {a}$$

$$\left (Note :  exact\ relation,  \theta = \dfrac{1.22} {a}\lambda \right )$$

$$\dfrac{d} {D} = \dfrac{\lambda} {a} \Rightarrow = d = \dfrac{\lambda D} {a}$$

$$\Rightarrow d = \dfrac{5000 \times 10^{-10} \times 10^{3}} {10  \times 10^{-2}} = 5 mm$$

1077680_69537_ans_8075ed08679e451db83ada220feef83d.png

Physics

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