In a Young's double slit experiment, Io is the intensity at the central maximum and β is the fringe width. The intensity at a point P distant x from the centre will be

Question

In a Young's double slit experiment, Io is the intensity at the central maximum and β is the fringe width. The intensity at a point P distant x from the centre will be (A) Io cos (π x/β) (B) 4 Io cos 2 (π x/β) (C) Io cos 2 (π x/β) (D) (Io/4) cos 2 (π x/β)

Tardigrade Admin · Accepted Answer

Path difference at point P=(x d/D) Phase difference at point P=(2 π/λ) (x d/D)=(2 π x/β) I0=4 I1, intensity at point P I=I1+I1+2 I1 cos (2 π x/β)=2 I1[1+ cos (2 π x/β)] =I0 cos 2 (π x/β)

Q. In a Young's double slit experiment, $I_{o}$ is the intensity at the central maximum and $β$ is the fringe width. The intensity at a point $P$ distant $x$ from the centre will be

$I_{o} cos \frac{π x}{β}$

$4 I_{o} cos^{2} \frac{π x}{β}$

$I_{o} cos^{2} \frac{π x}{β}$

$\frac{I _{o}}{4} cos^{2} \frac{π x}{β}$

Path difference at point $P = \frac{x d}{D}$
Phase difference at point $P = \frac{2 π}{λ} \frac{x d}{D} = \frac{2 π x}{β}$
$I_{0} = 4 I_{1}$ , intensity at point $P$
$I = I_{1} + I_{1} + 2 I_{1} cos \frac{2 π x}{β} = 2 I_{1} [1 + cos \frac{2 π x}{β}]$
$= I_{0} cos^{2} \frac{π x}{β}$

Q. In a Young's double slit experiment, Io​ is the intensity at the central maximum and β is the fringe width. The intensity at a point P distant x from the centre will be

Io​cosβπx​

4Io​cos2βπx​

Io​cos2βπx​

4Io​​cos2βπx​