Answer to Question #162536 in Optics for Novella

Question

Light of wavelength 587.5 nm illuminates a slit of width 0.75 mm.

(a) At what distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85mm from the central maximum?

(b) Calculate the width of the central maximum.

Answer 1

Answer

a)

$\lambda=587.5\times10^{-9}m$

a=$0.75\times10^{-9}m$

$y_1=0.85\times10^{-3}m$

distance from the slit should a screen be placed if the first minimum in the diffraction pattern is to be 0.85mm from the central maximum

$L=y_1\frac{a}{\lambda}$

=$\frac{0.85\times10^{-3}\times0.75\times10^{-9}}{587.5\times10^{-9}}$

=1.1m

b) the width of the central maximum.

$X=\frac{2D\lambda}{d}$

$=\frac{2\times1.1\times587.5\times10^{-9}}{0.85\times10^{-3}}\\=1.5mm$