Two coherent narrow slits emitting light of wavelength λ in the same phase are placed parallel to each other at a small separation of 3 λ. The light is collected on a screen S which is placed at a distance D(λ) from the slits. The smallest distance x such that the P is a maxima.

Question

Two coherent narrow slits emitting light of wavelength λ in the same phase are placed parallel to each other at a small separation of 3 λ. The light is collected on a screen S which is placed at a distance D(>>λ) from the slits. The smallest distance x such that the P is a maxima. (A) √3 D (B) √8 D (C) √5 D (D) √5 (D/2)

Tardigrade Admin · Accepted Answer

Δ x=n λ in this case path difference is d cos θ. So n λ=λ=3 λ cos θ ⇒ cos θ=(1/3) ⇒ (D/√D2+y2)=(1/3) ⇒ 3 D=√D2+y2 ⇒ y=√8 D = 2√2 D

$3 D$

$8 D$

$5 D$

$5 \frac{D}{2}$

$Δ x = nλ$
in this case path difference is $d cos θ$ .
So $nλ = λ = 3 λ cos θ$
$\Rightarrow cos θ = \frac{1}{3}$
$\Rightarrow \frac{D}{D ^{2} + y ^{2}} = \frac{1}{3}$
$\Rightarrow 3 D = D^{2} + y^{2}$
$\Rightarrow y = 8 D = 22 D$

Q. Two coherent narrow slits emitting light of wavelength λ in the same phase are placed parallel to each other at a small separation of 3λ. The light is collected on a screen S which is placed at a distance D(>>λ) from the slits. The smallest distance x such that the P is a maxima.

3​D

8​D

5​D

5​2D​

Δx=nλ in this case path difference is dcosθ. So nλ=λ=3λcosθ ⇒cosθ=31​ ⇒D2+y2​D​=31​ ⇒3D=D2+y2​ ⇒y=8​D=22​D

$3 D$

$8 D$

$5 D$

$5 \frac{D}{2}$

$Δ x = nλ$
in this case path difference is $d cos θ$ .
So $nλ = λ = 3 λ cos θ$
$\Rightarrow cos θ = \frac{1}{3}$
$\Rightarrow \frac{D}{D ^{2} + y ^{2}} = \frac{1}{3}$
$\Rightarrow 3 D = D^{2} + y^{2}$
$\Rightarrow y = 8 D = 22 D$