The intensity at the central maxima (0) in a Young's double slit set up is I₀. If the distance OP equals one third of the fringe width of the pattern, show that the intensity, at point P, would equal to I₀/4.

Solution

Intensity at the central maxima = I_oDistance OP is one-third of the fringe width, $x = \frac{1}{3} β$ (given)

Fringe width is given by $\frac{λD}{d}$

$∴$ $x = \frac{λD}{3 d}$

Path difference, $∆_{p} = \frac{xd}{D}$ and,

Phase difference, $ϕ = \frac{2 π}{λ} (∆ P)$

$= 2 π / 3$
Intensity at point P, $I = I_{0} \cos^{2} \frac{ϕ}{2}$

$= I_{0} \cos^{2} (\frac{2 π}{3}) = I_{0 / 4}$
Hence proved.

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Wave Optics

The intensity at the central maxima (0) in a Young's double slit set up is I₀. If the distance OP equals one third of the fringe width of the pattern, show that the intensity, at point P, would equal to I₀/4.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

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Wave Optics

The intensity at the central maxima (0) in a Young's double slit set up is I0. If the distance OP equals one third of the fringe width of the pattern, show that the intensity, at point P, would equal to I0/4.

Some More Questions From Wave Optics Chapter

What is the shape of the wavefront in each of the following cases: Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:The portion of the wavefront of light from a distant star intercepted by the Earth.

Is the speed of light in glass independent of the colour of light? If not, which of the two colours red and violet travels slower in a glass prism?

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

The intensity at the central maxima (0) in a Young's double slit set up is I₀. If the distance OP equals one third of the fringe width of the pattern, show that the intensity, at point P, would equal to I₀/4.

What is the shape of the wavefront in each of the following cases:
Light emerging out of a convex lens when a point source is placed at its focus.

What is the shape of the wavefront in each of the following cases:
The portion of the wavefront of light from a distant star intercepted by the Earth.