Question

Light from a helium-neon laser (λ = 633 nm) is used to illuminate two narrow slits. The interference pattern is observed on a screen 3.00 m behind the slits. Eleven bright fringes are seen, spanning a distance of 52.0 mm. What is the spacing (in mm) between the slits?

Answer 1

Answer:

The spacing between the slits is 0.40233 mm

Explanation:

Let 'd' be the distance between the slits and 'D' be the distance of the screen from the plane of slits.

We know that , in an interference pattern the fringe(dark or bright) width is given by -

f = $\dfrac{Dλ}{d}$

For 11 bright fringes , if its total spanning distance is 52.0 mm , then for one bright fringe , the fringe width(f) would be -

f = $\dfrac{52}{11}$ = 4.72 mm

∴ From above equations ,

$\dfrac{Dλ}{d}$ = 4.72 mm = (4.72 × $10^{-3}[/teλx]) mHere, D = 3 m λ = 633 nm =(633 × [tex]10^{-9}$) m

Substituting the values in above equation -

$\dfrac{3×633×10^{-9} }{d}$ = 4.72 ×$10^{-3}$

∴ d = 0.0004023 m =0.4023 mm