Question #162536

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.


1
Expert's answer
2021-02-25T11:38:15-0500

Answer

a)

λ=587.5×109m\lambda=587.5\times10^{-9}m

a=0.75×109m0.75\times10^{-9}m

y1=0.85×103my_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=y1aλL=y_1\frac{a}{\lambda}

=0.85×103×0.75×109587.5×109\frac{0.85\times10^{-3}\times0.75\times10^{-9}}{587.5\times10^{-9}}

=1.1m


b) the width of the central maximum.

X=2DλdX=\frac{2D\lambda}{d}

=2×1.1×587.5×1090.85×103=1.5mm=\frac{2\times1.1\times587.5\times10^{-9}}{0.85\times10^{-3}}\\=1.5mm


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