A light beam of wavelength 800 nm passes through a single slit and projected on a screen kept at 5m away from the slit. What should be the slit width for the ray optics approximation to be valid ?

Options

A. `0.5mm`
B. `2mm`
C. `1.5 mm`
D. `0.25 mm`

Answer

B

Explanation

Ray optics approximation can be taken upto Fresnels' distance which is given by
`Z _(f) = (a ^(2))/(lamda)`
Given,` Z _(f) = 5m,`
wavelength, `lamda = 800 nm = 800 xx 10 ^(-9) m,`
Slit width `a = ?`
`a = sqrt(Z_(f)lamda)`
`= (sqrt(5xx 800xx10^(-9) xx 10 ^(3) xx 10 ^(3)))mm`
`a =2 mm`