Question

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?

Answer 1

Answer:

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