Question

An American standard analog television picture (nonHDTV), also known as NTSC, is composed of approximately 485 visible 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 $5.00mm$ in diameter, and the average wavelength of the light coming from the screen is $550nm.$ 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.

Answer 1

For the limiting angle of resolution between lines we assume
${\theta }_{min}=1.22\frac{\lambda }{D}=1.22\frac{(550\times {10}^{-9}m)}{(5.00\times {10}^{-3}m)}=1.34\times {10}^{-4}rad$
Assuming a picture screen with vertical dimension $\ell$, the minimum viewing distance for no visible lines is found from ${\theta }_{min}=\frac{\ell /485}{L}.$ The desired ratio is then
$\frac{L}{\ell }=\frac{1}{485{\theta }_{min}}=\frac{1}{485(1.34\times {10}^{-4}rad)}=15.4$
When the pupil of a human eye is wide open, its actual resolving power is significantly poorer than Rayleigh's criterion suggests.