Question

Q2. Monochromatic laser light of frequency 5.20 × 10¹⁴ Hz is shown on a pair of thin parallel slits, and the pattern is viewed on a screen 1.20 m away. The 4th bright fringes occur at ±2.12 cm on either side of the central bright fringe. The entire apparatus is now immersed in a transparent liquid. When the experiment is repeated, the 4th bright fringes now occur at ±1.43 cm from the centre.

(a) How far apart are the slits?

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

Answer 1

A)

Wavelength, lambda = c/f = (3 x 10^8)/5.2 x 10^14) = 5.77 x 10^-7 m

Distance, d = m lambda L/y

d = 4 x 5.77 x 10^-7 x 1.20/0.0212 = 1.31 x 10^-4 m

B)

4 x 5.77 x 10^-7/(n x 1.31 x 10^-4) = 1.43 x 10^-2/1.2

n = 1.48

Comment in case any doubt please rate my answer....