Assume that the maximum aperture of the human eye, D, is approximately 8 mm and the average wavelength of visible light, λ, is 5.5 x 10-4 mm.
a. Calculate the diffraction limit of the human eye in visible light.
D = 8 mm = 0.008 m
λ = 5.5 x 10-4 mm = 5.5 x10-7 m
θ = (2.06 x 105) . ( (5.5 x 10-7) / (0.008) ) = 14.1625 arcseconds
b. How does the diffraction limit compare with the actual resolution of 1-2 arcminutes (60- 120 arcseconds)?
c. To what do you attribute the difference?
I know the answer for part a but i didn't understand b and c
To answer part b, we need to compare the diffraction limit calculated in part a (14.1625 arcseconds) with the actual resolution of the human eye, which is stated to be 1-2 arcminutes (60-120 arcseconds).
The diffraction limit of the human eye in this case refers to the smallest angle at which two closely spaced objects can be distinguished. It is a measure of the eye's ability to resolve fine details.
Comparing the diffraction limit (14.1625 arcseconds) with the actual resolution of the human eye (1-2 arcminutes or 60-120 arcseconds), we can observe that the diffraction limit is significantly smaller than the actual resolution.
This means that the human eye has the potential to resolve finer details than the diffraction limit would suggest. In other words, our eyes can see details that are smaller than what is theoretically limited by diffraction.
However, part c asks us to consider the reason for this difference. The difference between the diffraction limit and the actual resolution of the human eye is attributed to various factors such as the optics of the eye, the sensitivity of the photoreceptor cells in the retina, and the neural processing that occurs in the visual system.
The eye's optics, including the shape and clarity of the lens, affect the quality of the image formed on the retina. Additionally, the retina contains two types of photoreceptor cells - rods and cones. Cones are responsible for color vision and detailed visual acuity, while rods are more sensitive to low light levels but have lower spatial acuity.
Furthermore, the brain plays a crucial role in processing visual information received from the eyes. The visual cortex processes and interprets incoming signals, allowing us to perceive and recognize objects. This neural processing helps to enhance our ability to discern fine details and resolve greater levels of visual acuity compared to the theoretical diffraction limit.
In summary, while the diffraction limit provides a theoretical limit to the eye's ability to resolve details, the actual resolution of the human eye is better due to a combination of factors including the optics of the eye, the sensitivity of the photoreceptor cells, and the neural processing that occurs in the brain.