Your physics study partner tells you that the width of the central bright band i

Question

Your physics study partner tells you that the width of the central bright band in a single-slit diffraction pattern is inversely proportional to the width of the slit. This means that the width of the central maximum increases when the width of the slit decreases. The claim seems counterintuitive to you, so you make measurements to test it. You shine monochromatic laser light with wavelength ? onto a very narrow slit of width a and measure the width w of the central maximum in the diffraction pattern that is produced on a screen 1.50 m from the slit. (By "width," you mean the distance on the screen between the two minima on either side of the central maximum.) Your measurements are given in the table shown in (Figure 1) . If w is inversely proportional to a, then the product aw is constant, independent of a.

Part A Select the correct plot aw versus a for the data in the table 2.2 2.0 1.9 1.8 1.7 1.6 1.5 a (um) 12 16 0 aw (um-m) 2.2 2.0 1.9 1.8 1.6 1.5 a (um) 12 16 20 0

Explanation / Answer

as a*w is constant, with a slight variation in the beginning, it should settle down to a constant value as eary as possible.

hence plot 2 is the correct option.

part C:

from single slit diffraction principle,

we know that distance of m th order minima from the centrl spot is given by

m*wavelength*distance of the screen/slit width

as here we are measuring distance between minima on each side of the cental spot,

total width w=2*m*wavelength*1.5/a

taking m=1,

a*w=3*wavelength

as per the second plot, value of a*w is 1.55 um.m

hence 3*wavelength=1.55*10^(-6)

==>wavelength=516.67 nm

part D:

tan(theta)=(w/2)/D

given a=0.78 um and a*w=1.55 um.m
==>w=1.9872 m

hence tan(theta)=(1.9878/2)/1.5=0.6626

==>theta=33.53 degrees

part E:

tan(theta)=(w/2)/D

given a=15.6 um and a*w=1.55 um.m
==>w=0.0994 m

hence tan(theta)=(0.0994/2)/1.5=0.0331

==>theta=1.8977 degrees

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