In a Young's double-slit experiment, the wavelength of the light used is 510 nm (in vacuum), and the separatio

Question

In a Young's double-slit experiment, the wavelength of the light used is 510 nm (in vacuum), and the separation between the slits is 2.40 10-6 m. Determine the angle that locates each of the following.
(a) the dark fringe for which m = 0
°
(b) the bright fringe for which m = 1
°
(c) the dark fringe for which m = 1
°
(d) the bright fringe for which m = 2
°

Answer 1

For dark fringe , d sin theta=(2m + 1) wave length /2
where d is separation between the slits
For bright fringe , d sin theta= m x wave length .
(a)For m=0 i.e. first dark fringe, d sin theta=wave length / 2
sin theta= 510 x 10 ( - 9 ) / 2.40 x 10-6/2 = 106.2x 10 ( -3)
angle=6.1 degree
(b)For m=1 i.e. first bright fringe,d sin theta=wave length
angle=12.3 degree
(c)For m=1 i.e second dark fringe ,d sin theta=3wave length / 2
angle=18.6 degree
(d)For m=2 i.e.second bright fringe,d sin theta=2wave length
angle=24.8 degree

Answer 2

(a): d sin theta = wave length / 2
sin theta = (510 x 10^-9 ) / (2.40 x 10-6) / 2 = 0.10625
sin^-1 (0.10625) = θ =6.1°

(b): sin^-1 (2 x 0.10625) = θ = 12.3°

(c): sin^-1 (3 x 0.10625) = θ = 18.6°

(d): sin^-1 (4 x 0.10625) = θ = 25.15°

Answer 3

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