Light from a sodium lamp passes through a diffraction grating having 1000 slits per millimeter. The interference pattern is viewed on a screen of 1.00m behind the grating. Two bright yellow fringes are visible 72.88cm and 73.00cm from the central maximum.

What are the wavelengths of these two fringes?

The wavelengths of these two fringes is 589.61 x 10∧9

Explanation:

d = slit width = 0.001/1000 = 1 x 10-6 m

X1 = Position of first fringe = 0.7288 m

X2 = Position of second fringe = 0.73 m

D = distance of the screen

tan/theta1 = X1/D / Rightarrow/theta1 = tan-1 (X1/D) = tan-1 (0.7288/1) = 36.085

tan/theta2 = X2/D / Rightarrow/theta2 = tan-1 (X2/D) = tan-1 (0.73/1) = 36.129

position of first bright fringe is given as

d Sin/theta1 = n/lambda1

for bright fringe, n = 1

d Sin/theta1 = / lambda1

/lambda1 = (1 x 10-6) Sin36.085 = 589 x 10-9

position of second bright fringe is given as

d Sin/theta2 = n/lambda2

for bright fringe, n = 1

d Sin/theta2 = / lambda2

/lambda2 = (1 x 10-6) Sin36.129 = 589.61 x 10-9