An American standard analog television picture (non-HDTV), also known as NTSC, is composed of approximately 485 horizontal lines of varying light intensity. Assume your ability to resolve the lines is limited only by the Rayleigh criterion, the pupils of your eyes are 4.80 mm in diameter, and the average wavelength of the light coming from the screen is 570 nm. Calculate the ratio of the minimum viewing distance to the vertical dimension of the picture such that you will not be able to resolve the lines.
To calculate the ratio of the minimum viewing distance to the vertical dimension of the picture, we need to determine the angular resolution of the human eye using the Rayleigh criterion.
The Rayleigh criterion states that two closely spaced objects can be resolved if the center of one diffraction pattern coincides with the first dark fringe of the other diffraction pattern.
The angular resolution (θ) can be calculated using the formula:
θ = 1.22 * (λ / D)
Where:
θ is the angular resolution
λ is the average wavelength of the light (570 nm)
D is the diameter of the pupil (4.80 mm)
Plugging in the values:
θ = 1.22 * (570 nm / 4.80 mm)
Now, we have the angular resolution. This is the smallest angle that the eye can resolve. To determine the minimum viewing distance, we can use the formula:
Tangent of the angular resolution (θ) = vertical dimension of the picture (H) / minimum viewing distance (D')
Tan(θ) = H / D'
Now, we can rearrange the formula to solve for the minimum viewing distance (D'):
D' = H / Tan(θ)
Plugging in the values:
D' = H / Tan(θ)
Finally, we can calculate the ratio of the minimum viewing distance (D') to the vertical dimension of the picture (H):
Ratio = D' / H
1.22*(lambda)/D = (H/480)/L
H is the screen height.
L is the viewing distance for which the line width on the screen equals the eye's limit of resolution.
D = eye pupil diameter.
lambda = avg. wavelength = 570*10^-9 m
Solve for the desired L/H