An interference experimental setup consists of two slits that are separated by 2

Question

An interference experimental setup consists of two slits that are separated by 2 micro meter. A light beam of 600 nm wavelegnth is incident on the slits and it produces an interference pattern on a screen located 3 m from the slits. What is the angle of diffraction for the second order dark fringe? B. Now if the experiental setup is immersed in water (n=1.33), what would be the new angle for the 3rd order dark fringe in the interference pattern? C. The double slit is removed and a single slit of width 0.8 micrometer is introduced while the setup still remains in water. What is the angle of diffraction for the first order dark fringe on the screen? D. The single slit is now replaced with a 4 mm wide diffraction grating that has 2000 lines and the water is drained out. What is the diffraction angle for the second order bright fringe?

Explanation / Answer

a) (m+1/2) lambda = d sin theta

theta = arcsin(2.5*600.0E-9/2.0E-6)=48.59 degrees

b) now lambda = lambda0/n

theta = arcsin(2.5*600.0E-9/1.33/2.0E-6)=34.33 degrees

c) m lambda = d sin theta

theta = arcsin(1*600.0E-9/1.33/0.8E-6)=34.33 degrees

d) now d = 4.0E-3/2000

so theta = arcsin(2*600.0E-9/(4.0E-3/2000))=36.87 degrees

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