Correct question is;
To regulate the intensity of light reaching our retinas, our pupils1 change diameter anywhere from 2 mm in bright light to 8 mm in dim light. Find the angular resolution of the eye for 550 nm wavelength light at those extremes. In which light can you see more sharply, dim or bright?
Answer:
We'll see more sharply in dim light
Explanation:
If we consider diffraction through a circular aperture, then angular resolution is given by;
θ = 1.22λ/D
where:
θ is the angular resolution (radians) λ is the wavelength of light
D is the diameter of the lens' aperture.
Thus,
at diameter = 2mm = 2 x 10^(-3) m = 2 x 10^(6) nm
θ = (1.22 * 550)/(2 x 10^(6))
θ = 335.5 x 10^(-6) radians
Now, we need to convert this to arc seconds.
Thus;
1 arc second = 4.85 x 10^(-6) radians
So,θ = 335.5 x 10^(-6) radians = [335.5 x 10^(-6)]/[4.85 x 10^(-6)]
= 69.18 arc seconds
at diameter = 8mm = 8 x 10^(-3) m = 8 x 10^(6) nm
θ = (1.22 * 550)/(8 x 10^(6))
θ = 83.875 x 10^(-6) radians
Now, we need to convert this to arc seconds.
Thus;
1 arc second = 4.85 x 10^(-6) radians
So,θ = 83.875 x 10^(-6) radians = [83.875 x 10^(-6)]/[4.85 x 10^(-6)]
= 17.3 arc seconds
From the values of angular resolution gotten, we see that sharpness of image increases with increasing angular resolution. Thus, objects are sharper in dim light.
