A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is K units. The intensity of the light at a point where the path difference is $\frac{\lambda}{6}$ is given by $\frac{\mathrm{nK}}{12}$, where 'n' is an integer. The value of 'n' is ____.

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Wave Optics

A Young's double-slit experiment is performed using monochromatic light of wavelength

λ

. The intensity of light at a point on the screen, where the path difference is

λ

, is K units. The intensity of the light at a point where the path difference is

\frac{λ}{6}

is given by

\frac{nK}{12}

, where 'n' is an integer. The value of 'n' is ____.

Answer: 9

Solution

In a two-slit pattern the intensity is

I = 4 I_{0} cos^{2} \frac{ϕ}{2}

, where

ϕ = \frac{2 π}{λ} \times (path difference)

. A path difference of

λ

gives

ϕ = 2 π

and

I = 4 I_{0} = K

, so

I_{0} = K /4

. A path difference of

\frac{λ}{6}

gives

ϕ = \frac{π}{3}

, so

I^{'} = 4 I_{0} cos^{2} \frac{π}{6} = 4 \cdot \frac{K}{4} \cdot \frac{3}{4} = \frac{9 K}{12}

, which means

n = 9

JEE Main · 2020 · 06 Sep 2020 · Shift 2 · Integer answer

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 →