The figure below gives the parameter of the equation shown below versus the sine

Question

The figure below gives the parameter of the equation shown below versus the sine of the angle in a two-slit interference experiment using light of wavelength 545 nm. (The vertical axis is marked in increments of 10 rad.)

(a) What is the slit separation?

(b) Assume that none of the interference maxima are completely eliminated by a diffraction minimum. What is the total number of interference maxima? (Count them on both sides of the center of the interference pattern.)

(c) What is the smallest (non-negative) angle for a maximum?

(d) What is the largest angle for a minimum?

Explanation / Answer

a) slit seperation,d=(beta/sintheta)*(lambda/pi)=slope(using graph)*(lambda/pi)= (20/0.5)*(545/3.14)=6.94 micrometer

b)d*sin() = m* for interference maxima with slit separation d, maxima are at m = 0, 1, 2, 3 ...
d*sin()/=m

sin()=0, m=0

sin()=0.5, m=6.94 e-6*0.5/545e-9 =6.36=6 approx

sin()=1, m=6.94 e-6/545e-9=12.733=13 approx

c)smallest angle for maxima=0.5 as at zero we have m=0

d) largest angle for a minimum is when sintheta=1 i.e 90 degree

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