JEE MAIN - Physics (2005 - No. 20)
Two point white dots are $$1$$ $$mm$$ apart on a black paper. They are viewed by eye of pupil diameter $$3$$ $$mm.$$ Approximately, what is the maximum distance at which these dots can be resolved by the eye? [ Take wavelength of light $$=500$$ $$nm$$ ]
$$1m$$
$$5m$$
$$3m$$
$$6m$$
Explanation
$${y \over D} \ge 1.22{\lambda \over d}$$
$$ \Rightarrow D \le {{yd} \over {\left( {1.22} \right)\lambda }}$$
$$ = {{{{10}^{ - 3}} \times 3 \times {{10}^{ - 3}}} \over {\left( {1.22} \right) \times 5 \times {{10}^{ - 7}}}}$$
$$ = {{30} \over {61}} \approx 5m$$
$$\therefore$$ $${D_{\max }} = 5m$$
$$ \Rightarrow D \le {{yd} \over {\left( {1.22} \right)\lambda }}$$
$$ = {{{{10}^{ - 3}} \times 3 \times {{10}^{ - 3}}} \over {\left( {1.22} \right) \times 5 \times {{10}^{ - 7}}}}$$
$$ = {{30} \over {61}} \approx 5m$$
$$\therefore$$ $${D_{\max }} = 5m$$
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