Question

Light of wavelength 720 nm is shone through a double slit. The angle that locates the second dark fringe is 10.3 degrees. Calculate the angle that locates the first dark fringe.
(Give your answer in degrees but don't include the units.)

Answer 1

Condition for n^th order minima (dark fringe) in double slit diffraction pattern : d sin a = ( n + 1/2 ) ,

where = d = distance between slit and screen,

= wavelength used and a = angle of diffraction.

So, sin a / ( n + 1/2 ) = d / = constant.

Now, for n = 2, a = 10.3^o

and, for n = 1, a = x (say).

Hence, sin 10.3^o / ( 2 + 1/2 ) = sin x / ( 1 + 1/2 ) = constant

or, 0.07152 = sin x / (3/2)

or, sin x = 0.10728

or, x = sin^-1 ( 0.10728 )

or, x = 6.16^o

Hence, angle that locates the first dark fringe, in degrees, is : 6.16