A standard 14.6-inch or .360 meter computer monitor is 1024 pixels wide and 768 pixels tall. Each pixel is a square approximately 281 micrometers on each side.
If the maximum distance between the screen and your eyes at which you can just barely resolve two adjacent pixels is 1.30 meters, what is the effective diameter of your pupil? Assume that the resolvability is diffraction-limited. Furthermore, use 550 nanometers as a characteristic optical wavelength.
To find the effective diameter of your pupil, we can use the concept of minimum resolvable angle. The minimum resolvable angle is the smallest angle that your eye can distinguish as two separate points.
The formula for the minimum resolvable angle is:
θ = 1.22 * λ / D
Where:
- θ is the minimum resolvable angle
- λ is the wavelength of light
- D is the diameter of your pupil
We are given that the maximum distance between the screen and your eyes is 1.30 meters and the monitor has a resolution of 1024 x 768 pixels. We can calculate the size of each pixel using the screen dimensions:
Pixel width = .360 meters / 1024 = 0.0003515625 meters
Pixel height = .360 meters / 768 = 0.00046875 meters
Next, we need to find the distance between adjacent pixels:
Distance between adjacent pixels = sqrt((Pixel width)^2 + (Pixel height)^2)
Distance between adjacent pixels = sqrt((0.0003515625)^2 + (0.00046875)^2)
Distance between adjacent pixels = 0.0005832986 meters
Now, we can calculate the minimum resolvable angle:
θ = Distance between adjacent pixels / Distance from screen to eyes
θ = 0.0005832986 meters / 1.30 meters
θ = 0.0004486892 radians
Finally, we can solve for the diameter of your pupil:
D = 1.22 * λ / θ
D = 1.22 * 550 nm / 0.0004486892 radians
D ≈ 1496.48 micrometers
Therefore, the effective diameter of your pupil is approximately 1496.48 micrometers.