Question

In a Young's double-slit experiment the wavelength of light used is 469 nm (in vacuum), and the separation between the slits is 2.1 × 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.

Answer 1

lamda = 469 nm

= 469*10^-9 m

d = 2.1*10^-6 m

a) for dark fringe m = 0

path difference, d*sin(theta) = lamda/2

sin(theta) = lamda/(2*d)

= 469*10^-9/(2*2.1*10^-6)

= 0.1117

theta = sin^-1(0.1117)

= 6.41 degrees <<<<<<<<<<<-----------------Answer

b) for bright fringe m = 1

path difference, d*sin(theta) = 1*lamda

sin(theta) = lamda/(d)

= 469*10^-9/(2.1*10^-6)

= 0.223

theta = sin^-1(0.223)

= 12.9 degrees <<<<<<<<<<<-----------------Answer

c) for dark fringe m = 1

path difference, d*sin(theta) = 3*lamda/2

sin(theta) = 3*lamda/(2*d)

= 3*469*10^-9/(2*2.1*10^-6)

= 0.335

theta = sin^-1(0.335)

= 19.6 degrees <<<<<<<<<<<-----------------Answer

d) for bright fringe m = 2

path difference, d*sin(theta) = 2*lamda

sin(theta) = 2*lamda/(d)

= 2*469*10^-9/(2.1*10^-6)

= 0.447

theta = sin^-1(0.447)

= 26.6 degrees <<<<<<<<<<<-----------------Answer