Question

In a Young's double-slit experiment the wavelength of light used is 481 nm (in vacuum), and the separation between the slits is 1.9 × 10^-6 m. Determine the angle that locates (a) the dark fringe for which m = 0, (b) the bright fringe for which m = 1, (c) the dark fringe for which m = 1, and (d) the bright fringe for which m = 2. To 3 significant figures.

Answer 1

X Let central maxima is at O. and post maxima line formed at point P. The path difference betuleen two rays S.P mat SzP is Al(say) Q o 11 a MU - Aliz S incident wave slit screen = di = s,p-sal Dareco a perpendicular on sip from Sad Let angle CPMO for small angle approximations ZPS_A = 0 Then By geomentory Z S, SQN E O triangle S, S, N, Then In sino = - S, M SA S, Sż. S, N = Sisa sino path difference - SN = Als Sise sind het separation between slits is Sysx=d se = dsinio path difference's dsino

for bright fringe, path clifference a mi where m= order of fringe mis 1,2,3,- Wavelength of light used Thus, d sino mi sinos for mi d angle appooximation Smallo sino = o a = md d (6) for mal O, = 2 4010m 109x16 d D 481X60-90 1.9x10 cm or 253-157 X 16-3 O, 0.253

(d) for m=2, Oz 20 alto Oz_3 = 2 x 421469m 109x10m = 2X O. 253 og 0.506 Now for dank fringe, fath difference (2m+ dsino = (2mul) sino = amid 2 2 2d for small angles, sind=0 famt d o 2 d (a) for mo o Indo 2. d *0-253 1 2 = 0.1265 0.127 o

(6) for m= - ALL 4 1 다 on gro.253 1 03715 Q 0-30 0 수
Summary: first I derived expression for the position of mth bright fringe and dark fringe then I calculated various parts of question.