In a Young's double slit experiment the intensity at a point where the path difference is $\frac{\lambda}{6}$ ($\lambda$ being the wavelength of the light used) is I. If $\mathrm{I}_{0}$ denotes the maximum intensity, $\frac{\mathrm{I}}{\mathrm{I}_{0}}$ is equal to

JEE Main · 2007 · 29 Apr 2007 · Offline · Wave Optics

In a Young's double slit experiment the intensity at a point where the path difference is

\frac{λ}{6}

(

λ

being the wavelength of the light used) is I. If

I_{0}

denotes the maximum intensity,

\frac{I}{I _{0}}

is equal to

(A) $\frac{1}{2}$
(B) $\frac{3}{2}$
(C) $1/2$
(D) $3/4$ ✓ Correct

Answer: (D)

Solution

In two-slit interference the intensity is

I = I_{0} cos^{2} \frac{ϕ}{2}

, where the phase difference is tied to the path difference by

ϕ = \frac{2 π}{λ} Δ

. With a path difference of

\frac{λ}{6}

the phase difference is

\frac{π}{3}

, so

\frac{I}{I _{0}} = cos^{2} \frac{π}{6} = (\frac{3}{2})^{2} = \frac{3}{4}

JEE Main · 2007 · 29 Apr 2007 · Offline · Single correct option

Practise more: all JEE Main PYQs on Wave Optics →

More JEE Main questions on Wave Optics

Given below are two statements:
Statement I: In a Young's double slit experiment, the angular separation of fringes will increase as the screen is moved away from the plane of the slits
Statement II : In a Young's double slit experiment, the angular separation of fringes will inc …
JEE Main 2026View solution →
In a Young's double slit experiment set up, the two slits are kept 0.4 mm apart and screen is placed at 1 m from slits. If a thin transparent sheet of thickness $20 μ m$ is introduced in front of one of the slits then centre bring fringe shifts by 20 mm on the screen …
JEE Main 2026View solution →
In two separate Young's double-slit experimental set-ups, two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slit separations and that of the wavelengths of light used are $2 : 1$ and $1 : 2$ respectively. The correspo …
JEE Main 2026View solution →
When an unpolarized light falls at a particular angle on a glass plate (placed in air), it is observed that the reflected beam is linearly polarized. The angle of refracted beam with respect to the normal is $____$ .
( $tan^{- 1} (1.52) = 57. 7^{\circ}$ , refractive indices of air a …
JEE Main 2026View solution →
Given below are two statements:

Statement-I: A plane wave after passing through prism remains as plane wave but passing through small pin hole may become spherical wave.
Statement-II: The curvature of a spherical wave emerging from a slit will increase for increasing slit width. …
JEE Main 2026View solution →
In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_{0}$ . The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is $6000 \overset{˚}{A}$ . The intensity of light on the screen in front of …
JEE Main 2026View solution →