Monochromatic laser light of frequency 5.20×10^14 Hz is shown on a pair of thin

Question

Monochromatic laser light of frequency 5.20×10^14 Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20m away. The fifth bright fringes (not counting the central fringe) occur at ± 2.12cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the fifth bright fringes now occur at ±1.43 cm from the central bright fringe. (c = 3.00×108 m/s)

(a) How far apart are the slits?

(b) What is the index of refraction of the liquid?

Explanation / Answer

dsintheta = n*lambda

tan theta = y/D

here angle is small so

tan theta = sin theta

y = m*lambda*D/d

lambda = c/f

lambda = 576 nm

D = 1.2 m

n = 5

y = 2.12 cm = 2.12 x 10^-2 m

d = m*lambda*D/y

d = 1.630 x 10^-4 m = 0.163 mm

part b )

lambda in liquid = y*d/m*D

lambda = 388 nm

by using snell law

n1sintheta1 = n2sintheta2

n1*lambda1 = n2*lambda2

n2 = lambda1/lambd2

n2 = 576/388

n2 = 1.48

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