In a double-slit diffraction set-up, the screen is 1.7 m away from the slits having width 0.08 mm & they are 0.4 mm apart. Calculate$ \lambda$ if fringe separation is 0.25 cm. Also find the missing orders.

Subject: Applied Physics 2

Topic: Interference And Diffraction

Difficulty: Medium

a=0.08 mm, b= 0.4 mm

Condition for absent spectra

$ m= \frac{(a+b)n}{a} = \frac{(0.08+0.4) n}{0.08} =6n $

So the orders 6,12,18……..will be missing.

Wavelength λ =?, (a+b) = (0.08+0.4) = 0.48 mm= 0.048 cm , Distance D = 1.7 x10$^{-2}$ cm, fringe separation X is 0.25 cm

$ \frac{λ}{(a+b)} = \frac{X}{D} $

Therefore,

$ λ = \frac{X(a+b)}{D} = \frac{0.25 \times 0.048}{1.7 \times 10^{-2}} = 7058 AU$