question_answer

A telescope has an objective lens of 10 cm diameter and is situated at a distance of one kilometre 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 Å, is of the order of                        [CBSE PMT 2004]

A)            0.5 m                                       

B)            5 m

C)            5 mm                                       

D)            5 cm

Correct Answer: C

Solution :

           \[\theta =\frac{x}{d}=\frac{1.22\,\lambda }{a}\]      \[\Rightarrow x=\frac{1.22\times d}{a}\] \[=\frac{1.22\times 5000\times {{10}^{-10}}\times {{10}^{3}}}{10\times {{10}^{-2}}}\]= 6.1 mm i.e. order will be 5 mm.