Question

In: Physics

Below is a diffraction problem. I have the solutions to the problem but I don't know...

Below is a diffraction problem. I have the solutions to the problem but I don't know how to arrive at these solutions.

A) In an experiment two slits are separated by 0.22mm and illuminated by light of wavelength 640nm. How far must a screen be placed in order for the bright fringes to be separated by 5 mm? (1.72 m)

B) A soap film is illuminated by white light normal to its surface. The index of refraction of the film is 1.50. Light corresponding to a wavelength in air of 600 nm is intensified in the reflected beam. The smalled thickness of the film is.. (0.10 micrometers)

C) Unpolarized light of intensity Io passes through a pair of polarizing filters with their axes making an angle of 38 degrees. What fraction of Io passes through? (0.31)

Solutions

Expert Solution

all the formulas

pertain to double slit diffraction
condition for maxima is given by
y=m*lambda*D/d

where y=distance of m th order bright fringe from the center of screen
m=order of the bright fringe
lambda=wavelength of the light
D=distance of the screen
d=slit width


by putting m as any two consecutive integers, we can see that distance between any two bright fringes is given by

lambda*D/d

we are asked to find value of D.

by using all other known values, we get D=1.7188 m


b)in the relfected beam, for maximum reflection, the condition is

2*n*d*cos(theta)=(m-0.5)*lambda

where n=refractive index
d=thickness of film
theta=angle with vertical=0 degree (in this case)
lambda=wavelength

m=any integer, for lowest thickness, we need to take m=1

putting all avaialble values, we get d=1*10^(-7) m=0.1 micrometer


c)when it passes through first polarizing filter, as it is in the begin unpolairized, the light wave intensity will become 50%

so I1=I0/2

now when it passes thorugh second filter, according to Malus' law:

intensity will become I1*cos^2(38)

=(I0/2)*0.62=0.31*I0

so 31% of original intensity will pass through.


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