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
B
5 mm
C
5 cm
D
0.5 m

Solution

## The correct option is B 5 mmWe know, Resolving Power = $$\theta = \dfrac{d} {D}$$ but $$\theta \approx \dfrac{\lambda} {a}$$$$\left (Note : exact\ relation, \theta = \dfrac{1.22} {a}\lambda \right )$$$$\dfrac{d} {D} = \dfrac{\lambda} {a} \Rightarrow = d = \dfrac{\lambda D} {a}$$$$\Rightarrow d = \dfrac{5000 \times 10^{-10} \times 10^{3}} {10 \times 10^{-2}} = 5 mm$$Physics

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