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 mm]

  • Option 1)

    6 \: mm

  • Option 2)

    3 \: mm

  • Option 3)

    5 \: mm

  • Option 4)

    1 \: mm

 

Answers (1)

As we learnt in

Radius of diffraction disc -

R=1.22\frac{\lambda D}{b}
 

- wherein

D= Distance of screen from hole

b= slit width

 

 

 

Resolution limit  = \frac{1.22\lambda }{d}

Again resolution limit = \sin \Theta = \Theta = \frac{y}{D}

\therefore \; \; \; \; \frac{y}{D}= \frac{1.22\lambda }{d}

or\; \; \; \; \; \; D= \frac{\lambda d}{1.22\lambda }

or\; \; \; \; \; \; D= \frac{\left ( 10^{3} \right )\times \left ( 3\times 10^{-3} \right )}{\left ( 1.22 \right )\times \left ( 5\times 10^{-7} \right )}= \frac{30}{6.1}\approx 5mm

Correct option is 3.

 


Option 1)

6 \: mm

This is an incorrect option.

Option 2)

3 \: mm

This is an incorrect option.

Option 3)

5 \: mm

This is the correct option.

Option 4)

1 \: mm

This is an incorrect option.

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