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Wave Optics

Question
CBSEENPH12039478

Assuming human pupil to have a radius of 0.25 cm and a comfortable viewing distance of 25 cm, the minimum separation between two objects that human eye can resolve at 500 nm wavelength is:

  • 1 μm

  • 30 μm

  • 100 μm

  • 300 μm

Solution

B.

30 μm

We can write resolving angle of necked eye as,

Where D is the diameter of the eye lens.
fraction numerator straight Y over denominator 26 space straight X space 10 to the power of negative 2 end exponent end fraction space equals space fraction numerator 122 space straight X space 500 space straight X space 10 to the power of negative 9 end exponent over denominator 0.25 space straight X space 2 straight X space 10 to the power of negative 2 end exponent end fraction
straight Y space equals space 30 space straight x space 10 to the power of negative 6 end exponent space straight m space equals space 30 space μm

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