Question

A single slit of width W = 0.07 mm is illuminated by light that has a wavelength,  = 680 nm.

a) Calculate the angles at which the first and the second dark fringe appears.

b) Using the small angle approximation (tan θ  sinθ) find the relationship between the size of central maximum and the adjacent bright fringe.

c) Calculate the size of the central bright fringe if the screen is located 2.20 m away from the slit.

d) The single slit is now replaced with a diffraction grating and the second order bright fringe is formed at an angle of 23.0 with respect to the main axis. Find the number of lines per centimeter in the grating.

Answer 1

W = 0.07 mm x = 680 nm Q2 afty Wsinon na for first sin o dark fringe ina sin ma (680X10 sint (oro 0097) त W o = ng o = sint 0:07810 0 5 0:56 dark for in=2 second fring 0, = siul = sint (010194 W o 1:13 4 o at W sin o= na for first minima ; n = Il

sino = w ने Z? 7 W 2 ay 21 D w = central maximum 22D w And Size of two consecutive bright fring AD .

(C) Size of central bright fring 2X 680 X 2.2 -9 Xto MA 0:07 xto? Central Maxima =4.87 cm bright fring e 2.14 um co) asino nd M=2 da 27 sin23 -g = 2x680 Xlo sin (23) m 6 3.48 x 10 ry = 3.48 xlo cm Number of limes / cm = 2873