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Chapter 36: Q80P (page 1114)

The pupil of a person鈥檚 eye has a diameter of 5.00 mm. According to Rayleigh鈥檚 criterion, what distance apart must two small objects be if their images are just barely resolved when they are 250 mm from the eye? Assume they are illuminated with light of wavelength 500 nm

Short Answer

Expert verified

The distance between two small objects is 3.05脳10-5m

Step by step solution

01

Identification of given data

The given data can be listed below,

  • The diameter of the eye is,d=5.00mm
  • The wavelength of the light is,位=500nm
  • The distance of image from eye is,L=250mm
02

Concept/Significance of Rayleigh criterion

According to the Rayleigh criterion, there must be a minimum distance between two light sources in order for them to be resolved into separate objects.

03

Determination of the distance that two small objects must be apart

The Rayleigh angle is given by,

胃R=1.22位d=DLD=1.22位Ld

Here,位 is the wavelength of the light, dis the diameter of eye.

Substitute all the values for distance between two objects,

D=1.22500脳10-9m250脳10-3m5脳10-3m=3.05脳10-5m

Thus, the distance between two small objects is 3.05脳10-5m.

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