Question

A. Calculate the diffraction limit of the human eye, assuming a wide-open pupil so that your eye acts like a lens with diameter 0.8 centimeter, for visible light of 500-nanometer wavelength.

Express your answer using two significant figures.

B. How does this compare to the diffraction limit of a 10-meter telescope?
Express your answer using two significant figures.

C. Now remember that humans have two eyes that are approximately 7 centimeters apart. Estimate the diffraction limit for human vision, assuming that your "optical interferometer" is just as good as one eyeball as large as the separation of two regular eyeballs.
Express your answer using two significant figures.

Answer 1

a) 16 arc seconds

b) 1250

c)1.785 arc seconds

Step-by-step explanation:

Given data:

lens diameter = 0.8 cm

wavelength 500 nm

a) the diffraction of the eye is given as

`= 2.5* 10^5 (\lmbda)/(D)` arc seconds

`= 2.5* 10^5 (5* 10^(-7))/(8* 10^(-3))` arc seconds

= 16 arc seconds

b) we know that

`(DIffraction\ limit\ of\ eye)/(diffraction\ limit\ of\telescope)`

`= \frac{2.5* 10^5((\lambda)/(D_(eye)))}\frac{2.5* 10^5((\lambda)/(D_(telescope)))}`

`(\theta_(eye))/(\theta_(telescope)) = (10)/(8* 10^(-3)) = 1250`

c)
`\theta_(eye) = 2.5* 10^(5) (5* 10^(-7))/(7* 10^(-2))`
`\theta_(eye) = 1.78\ arc\ second`