Question

For what distance ray optics a good approximation when the aperture is 4 mm wide and the wavelength is 500nm?

• A. $32m$
• B. $69m$
• C. $16m$
• D. $8m$

Answer 1

Answer: (A)

$32m$

The Good approximation distance till ray optics or valid is given by Fresnel distance which is given by

$z_f=\frac{a^2}{\lambda }$

$z_f$ is distance till which diffraction effects of light can be neglected.

$a=$ aperature$=4\times {10}^{-3}m$

$\lambda =$wavelength$=500\times {10}^{-9}$m

$z_f=\frac{(4\times {10}^{-3}{)}^2}{(500\times {10}^{-9})m}$

$=\frac{16\times {10}^{-6}}{500\times {10}^{-9}}$

$=0.032\times {10}^3$m

$\therefore z_f=32m$.