Question

a)How many bright interference fringes appear between the first diffraction minima to either side of the central maximum if the light is 550 nm, d = 0.15 mm, and a = 0.003 mm?

b)What is the ratio of the intensity of the 3rd bright interference fringe to the intensity of the central fringe? Answer: 0.255

Please carefully write all steps in a clear manner.

Answer 1

Solution:-

? = 550 nm,d = 0.15 mm, and a =0.003 mm

a)

the numbers of fringes appears, n = d/a

==> n = 0.15mm/0.003?m

         = 50 frings

b )

   Intensity

I = I_m cos² ?( sin? /? )²

    But ? = ?a / ?sin?    ? = ?d / ? sin?

for third brigth interference fringe dsin? =3?

     ?? /? =3? =>?=3?

   cos² ? =1

    ? = ??3? /?d

        = 3?a/d

    ? = 3? ( 0.003* 10^-3m) / 0.15 * 10^-3 m

        = 3?* 220*10^-3 m

        = 0.06?rad

    (sin?/? )² = [ sin0.06? / 0.06? ]²

                  = -----

Intensity ratio I / I_m = ----

Solve it