First slide

Coherent sources and their importance in interference

Question

In young double slit experiment $λ = 500 nm, d = 1 mm and D = 1 m$ .The minimum distance from the central maximum where intensity is half of the maximum intensity is (assume intensity from each slit is same)

Moderate

A

$2 \times 10^{- 4} m$
B

$1.25 \times 10^{- 4} m$
C

$4 \times 10^{- 4} m$
D

$2.5 \times 10^{- 4} m$

Solution

Given Wavelength $λ = 500 nm = 5 \times 10^{- 7} m$
Distance between two slits $d = 1 {mm=10}^{- 3} m$
Distance between slits and screen $D = 1 m$
Maximum intensity $= 4 I_{0}$
$I = 4 I_{o} \cos^{2} \frac{ϕ}{2}$
$\Rightarrow 2 I_{o} = 4 I_{o} \cos^{2} \frac{ϕ}{2}$
$\Rightarrow \cos \frac{ϕ}{2} = \frac{1}{\sqrt{2}}$
$∴ ϕ = \frac{π}{2}$
Path difference $Δ ϕ = \frac{2 π}{λ} Δ x$
$\Rightarrow Δ x = \frac{λ}{4}$
$∴ y = \frac{Δ x . D}{d} = \frac{λ D}{4 d} = \frac{5 \times 10^{- 7} \times 1}{4 \times 10^{- 3}} = 1.25 \times 10^{- 4} m$

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