Question

A green laser light ( $\lambda$ = 532 ) passes through a diffraction grating (500 lines per millimeter) and creates interference patterns on a viewing screen 0.4 m away. What is the position of the 2nd-order bright fringe on the screen?

Answer 1

The m^th maxima of grating is, d sin theta_m = m lambda: Where m = 0, plusminus 1, plusminus 2, plusminus 3, Here lambda is the wavelength of light used, d is the separation between rulings of the grating, and m is an integer (m = 0, plusminus 1, plusminus 2, plusminus 3,) which corresponds to particular order maxima. Solve the equation for theta_m. d sin theta_m = m lambda sin theta_m = m lambda /d theta_m = sin^-1 (m lambda /d) \r\n The angular deflection of the second order bright band is, theta_2 = sin^-1 (m lambda /d) = sin^-1 ((2) (532 nm)(10^-9 m /1 nm)/20. Times 10^-6 m) = j32.14 degree The separation between the second maximum and zeroth order maximum is, y_2 = L tan theta_2 Here L is the distance from the grating to the screen. So we have, y_2 = l L tan theta_2 = (0.4 m)