Light with a wavelength of 400 nm passes through a double slit experiment and pr

Question

Light with a wavelength of 400 nm passes through a double slit experiment and projected onto a screen 10m away. The 4^th bright fringe is 5mm away from the center of the central bright fringe. What is the frequency of this light? Express your answer in gigahertz. How far apart are the two slits? Express your answer in millimeters. What is the path length difference from the nearer slit to the 4^th bright fringe compared to the distance to this fringe from the other slit? Express your answer in micrometers. How far from the central fringe is the first dark fringe? Express your answer in micrometers. Light with a wavelength of 400 nm is violet. If red light (wavelength ~ 700mm) had been used instead, would the fringes have been closer together or further apart? Justify your answer.

Explanation / Answer

part a:

speed of a wave=wavelength*frequency

==>freqency=speed/wavelength

=3*10^8/(400*10^(-9))

=7.5*10^14 Hz

=7.5*10^5 GHz

part b:

m th order bright fringe is given at a distance of y=m*lambda*D/d

where lambda=wavelength

D=distance of the screen from the slit

d=slit width

given, form m=4, y=0.005 m, D=10 m, lambda=400 nm

then d=m*lambda*D/y

=4*400*10^(-9)*10/0.005

=3.2 mm

so slit width is 3.2 mm.

part C:

path difference=m*lambda=4*400*10^(-9)=1.6 micrometer

part d

firt dark fringe distance=0.5*lambda*D/d

=0.5*400*10^(-9)*10/0.0032

=625 micrometer

part e:

distance between successive bright fringe=lambda*D/d

so higher the lambda, higher is the gap between fringes

hence if red light had been used, fringes would have been farther apart.

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