Need help with all parts (a-d) Thanks. A laser beam is incident on two slits wit

Question

Need help with all parts (a-d)

Thanks.

A laser beam is incident on two slits with separation d = 0.016 mm. A screen is placed L = 12 m from the slits. The wavelength of the laser light is lambda = 3250 A. theta_1 and theta_2 are the angles to the first and second bright fringes above the center of the screen. Express sin(theta_1) in terms of d and lambda. Express sin(theta_2) in terms of d and A. Express the distance between the two bright fringes on the screen,y, in terms of theta_1,theta_2 and L. Solve for the numcrical value of y in meters.

Explanation / Answer

slit separation, d=0.016 mm

distance between slit and screen, L=1.2 m

wave length, lambda=3250 Ao = 3250*10^-10 m

a)

use,

d*sin(theta1)=n1*lambda

==>

sin(theta1)=n1*lambda/d

sin(theta1)=1*lambda/d

sin(theta1)=lambda/d

b)

d*sin(theta2)=n2*lambda

==>

sin(theta2)=n2*lambda/d

sin(theta2)=2*lambda/d

sin(theta2)=2*lambda/d

c)

here,

sin(theta1)=y1/L

and

sin(theta2)=y2/L

==>

y=y2-y1

y=L*sin(theta2)-L*sin(theta1)

y=L*(sin(theta2)-sin(theta1)) ----->

or

y=L*(2*lambda/d-lambda/d)

y=L*lambda/d --------------->

d)

y=L*lambda/d

=(1.2*3250*10^-10)/(0.016*10^-3)

=0.024375 m

=24.375*10^-3 m

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