The question is not complete.
The complete question is;
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:
A) 16 arc seconds
B) For the 10m telescope, it is 1200 times better.
C) 1.79 arc seconds
Explanation:
A) We are given that ;
lens diameter; D= 0.8 cm = 0.8 x 10^(-2)m
wavelength;λ = 500 nm = 500 x 10^(-9)m
Now the formula for diffraction of human eye is given as;
2.5 x 10^(5) (λ/D) arc seconds
Thus, plugging in the values, we have;
2.5 x 10^(5)•[(500 x 10^(-9)/0.8 x 10^(-2))] = 2.5 x 10^(5)•(625 x 10^(-7))
= 1562.5 x 10^(-2) = 15.625 arc seconds ≈ 16 arc seconds
B) to compare the diffraction of human eye with a 10m telescope, it's the ratio of the the diffraction of the eye to that of the telescope.
Thus,
=[2.5 x 10^(5) (λ/0.8 x 10^(-2))]/[2.5 x 10^(5) (λ/10)]
= some values will cancel out and we are left with;
10/(0.8 x 10^(-2)) = 1250 to 2 significant figures = 1200
For the 10m telescope, it is 1200 times better.
C) now the eyes are 7cm apart, thus D = 7cm = 7 x 10^(-2)m
Thus, diffraction of eye is now ;
2.5 x 10^(5)•[(500 x 10^(-9)/7 x 10^(-2))] = 178.6 x 10^(-2) = 1.79 arc seconds
