In Young's double slit experiment, the intensity at a point where path difference is (λ/6) is I . If I0 denotes the maximum intensity, (I/I0).

Question

In Young's double slit experiment, the intensity at a point where path difference is (λ/6) is I . If I0 denotes the maximum intensity, (I/I0). (A) (1/√2) (B) (√3/2) (C) (1/2) (D) (3/4)

Tardigrade Admin · Accepted Answer

Where, Δ x=(λ/6) Δ φ=(2 π/λ) Δ x ∴ Δ φ=(π/3) I=I0 cos 2((Δ φ/2)) I=I0 cos 2((π/6)) or I=I0 × (3/4) ∴ (I/I0)=(3/4)

Q. In Young's double slit experiment, the intensity at a point where path difference is $\frac{λ}{6}$ is $I .$ If $I_{0}$ denotes the maximum intensity, $\frac{I}{I _{0}}$ .

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{3}{4}$

Where, $Δ x = \frac{λ}{6}$
$Δ ϕ = \frac{2 π}{λ} Δ x$
$∴ Δ ϕ = \frac{π}{3}$
$I = I_{0} cos^{2} (\frac{Δ ϕ}{2})$
$I = I_{0} cos^{2} (\frac{π}{6})$
or $I = I_{0} \times \frac{3}{4}$
$∴ \frac{I}{I _{0}} = \frac{3}{4}$

Q. In Young's double slit experiment, the intensity at a point where path difference is 6λ​ is I. If I0​ denotes the maximum intensity, I0​I​.

2​1​

23​​

21​

43​

Where, Δx=6λ​ Δϕ=λ2π​Δx ∴Δϕ=3π​ I=I0​cos2(2Δϕ​) I=I0​cos2(6π​) or I=I0​×43​ ∴I0​I​=43​

Q. In Young's double slit experiment, the intensity at a point where path difference is $\frac{λ}{6}$ is $I .$ If $I_{0}$ denotes the maximum intensity, $\frac{I}{I _{0}}$ .

$\frac{1}{2}$

$\frac{3}{2}$

$\frac{1}{2}$

$\frac{3}{4}$

Where, $Δ x = \frac{λ}{6}$
$Δ ϕ = \frac{2 π}{λ} Δ x$
$∴ Δ ϕ = \frac{π}{3}$
$I = I_{0} cos^{2} (\frac{Δ ϕ}{2})$
$I = I_{0} cos^{2} (\frac{π}{6})$
or $I = I_{0} \times \frac{3}{4}$
$∴ \frac{I}{I _{0}} = \frac{3}{4}$