The maximum intensity in Young's double slit experiment is \${I}_{0}\$. Distance between the slits is \$d=5\lambda\$, where \$\lambda\$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance \$D=10d\$?

Path difference \$=\Delta x=\dfrac{xd}{D}\$-------(i)In front of one of the slits,\$x=\dfrac{d}{2}\$ but \$d=5\lambda\$\$x=\dfrac{5\lambda}{2}\$ and \$D=10d=50\lambda\$Now, from equation (i), we have:\$\Delta x=\dfrac{5\lambda}{2}\times\dfrac{5\lambda}{50\lambda}=\dfrac{\lambda}{4}\$So, corresponding phas defference:\$\phi=\dfrac{2\pi}{\lambda}.(\Delta x)=\dfrac{2\pi}{\lambda}\times\dfrac{\lambda}{4}=\dfrac{\pi}{2}\$As, \$I=I_0\cos^2(\dfrac{\phi}{2})\$So, \$I=I_0\cos^2(\dfrac{\pi}{4})=\dfrac{I_0}{2}\$

In Young's double slit experiment, the slits are 2mm apart are illuminated by photons of two wavelengths \${ I }_{ 1 }=12000\mathring { A } \$ and \${ I }_{ 2 }=10000\mathring { A } \$. at what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Now, from the question we can infer that\$n_1\lambda_1 = n_2\lambda_2\$so,\$\frac{n_1}{n_2} = \frac{\lambda_2}{\lambda_1}\$or \$\frac{n_1}{n_2} = \frac{10000A}{12000A}\$thus,we have\$\frac{n_1}{n_2} = \frac{5}{6}\$5th and 6th fringes will coincide respectively.the minimum distance is given as\$X_{min} =\frac{ n_1\lambda_1D}{d}\$here,\$n_1 = 5\$D = 2md = 2mm = 2\$\times10^{-3}m\$so,\$X_{min} = \frac{[5\times12000\times10^{-10}\times2]}{2\times10^{-3}}\$thus, we get\$X_{min}\$ = 6mm hence B option is the correct answer

Solve Study Textbooks Guides

Use app

>>Class 12
>>Physics
>>Wave Optics
>>Young's Double Slit Experiment
>> $Coherent and Incoherent Sou...$

Coherent and Incoherent Source

Q: In a double slit experiment, the two slits are 1 mm apart and the screen is place 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

\$d = 10^{-3}\:m\$\$D=1\:m\$\$ \lambda = 500 \times 10^{-9}\:m\$The width of central maxima in a single slit diffraction: \$\dfrac{2 \lambda D}{a}\$Fringe width in double slit pattern: \$\beta = \dfrac{\lambda D}{d}\$Given,\$10 \beta = \dfrac{2 \lambda D}{a}\$\$ \Rightarrow 10 \dfrac{\lambda D}{d} = \dfrac{2 \lambda D}{a}\$\$ \Rightarrow a =\dfrac{d}{5}\:mm= 0.2\:mm\$

Q: A beam of light consisting of two wavelengths, \$650 nm\$ and \$520 nm\$, is used to obtain interference fringes in a Young's double-slit experiment.(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength \$650 nm\$.(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide? The distance between the two slits is \$0.28mm\$ and the screen is at a distance of \$1.4m\$ from the slits.

GivenThe wavelength of the light is \$ \lambda_1 = 650 nm\$The wavelength of seond light,\$ \lambda_2 = 520 nm\$Distance between the slit and the screen is \$1.4m\$.Distance between the slits is \$0.28mm\$.\$(a)\$The relation between the \$n^{th}\$ bright fringe and the width of fringe is:\$x = n\lambda_1\dfrac Dd\$For third bright fringe, \$n = 3\$\$ x = 3 \times 650\dfrac {1.4}{0.28\times10^{-3}}= 1950 \times5\times10^3 nm\$\$x=9.75\times10^{-3} m\$\$=9.75mm\$\$(b)\$We can consider that \$n^{th}\$ bright frind of \$\lambda_2\$ and the \$(n-1)^{th}\$ bright fringe of wavelength \$\lambda_1\$ coincide with each other.\$n\lambda_2 = (n - 1) \lambda_1\$\$520n = 650n - 650\$\$650 = 130n\$\$ n = 5\$therefore, the least distance from the central maximum can be obtained as:\$x' = n\lambda_2 \dfrac Dd \$\$x'= 5 \times 520 \dfrac Dd = 2600 \dfrac {1.4}{0.28\times10^{-3}} nm\$\$x'=1.30\times10^{-2}m=1.3cm\$

Q: Two coherent monochromatic light beams of intensities \$I\$ and \$4I\$ are superposed. The maximum and minimum possible resulting intensities are :

Maximum intensity, \$I_{max} = (\sqrt {I_{1}} + \sqrt {I_{2}})^{2}\$\$= (\sqrt {I} + \sqrt {4I})^{2}\$\$= 9I\$Minimum intensity \$I_{min} = (\sqrt {I_{1}} - \sqrt {I_{2}})^{2}\$\$(\sqrt {I} - \sqrt {4I})^{2}\$\$= I\$

Q: In a Youngs double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Distance between the slits, \$d=0.28\times10^{-3}\ m\$Distance between the slits and the screen, \$D = 1.4 m\$Distance between the central fringe and the fourth \$(n = 4)\$ fringe, \$u=1.2\times10^{-2}\ m\$In case of a constructive interference, we have the relation for the distance between the two fringes as:\$u=n\lambda D/d\$\$\Rightarrow \lambda=ud/nD=6\times10^{-7}m=600nm\$

Q: The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio \$\dfrac{I_{max}-I_{min}}{I_{max}+I_{min}}\$ will be

Given : \$I_2 = n I_1\$Maximum intensity of interference \$I_{max} = (\sqrt{I_1} + \sqrt{I_2})^2\$\$\therefore\$ \$I_{max} = (\sqrt{I_1} + \sqrt{nI_1})^2 = (1+\sqrt{n})^2 I_1 = (1+ n +2\sqrt{n } ) I_1\$Minimum intensity of interference \$I_{min} = (\sqrt{I_1} - \sqrt{I_2})^2\$\$\therefore\$ \$I_{min} = (\sqrt{I_1} - \sqrt{nI_1})^2 = (1-\sqrt{n})^2 I_1 = (1+ n - 2\sqrt{n})I_1\$\$\therefore\$ \$\dfrac{I_{max} -I_{min}}{I_{max} + I_{min}} = \dfrac{2\sqrt{n} - (-2\sqrt{n})}{2(1+n) } = \dfrac{2\sqrt{n}}{1+n}\$

Q: Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for the maximum and zero intensity.

Let \$y_1\$ and \$y_2\$ be displacement of two waves having same amplitude a and phase difference \$\phi\$ between them. \$y_1=a\sin\omega t\$\$y_2=a\sin(\omega t+\phi)\$Resultant displacement is: \$y=y_1+y_2\$\$y=a\sin\omega t+a\sin(\omega t+\phi)=a\sin\omega t(1+\cos\phi)+\cos\omega t(a\sin\phi) \$\$R\cos \theta=a(1+\cos\phi)\$\$R\sin \theta=a\sin\phi\$\$y=R\sin(\omega t +\theta)\$Where, \$R\$ is resultant amplitude at \$P\$, \$I\$ is intensity, squaring the equations we get,\$I=R^2=a^2(1+\cos\phi)^2+a^2(\sin\phi)^2=2a^2(1+\cos\phi)=4a^2\cos^2\dfrac{\phi}{2}\$Maximum intensity:\$\cos^2\dfrac{\phi}{2}=1\$\$\phi=2n\pi\$ where \$n=0,1,2,3,\$....Therefore, \$I_{max}=4a^2\$Minmum intensity:\$\cos^2\dfrac{\phi}{2}=0\$\$\phi=(2n+1)\pi\$ where \$n=0,1,2,3,\$....Therefore, \$I_{max}=0\$

Physics

definition

Coherent and Incoherent Sources

In coherent light the photons are all in 'step' other words the change of phase within the beam occurs for all the photons at the same time. There are no abrupt phase changes inside the beam. Light produced by lasers is both coherent and monochromatic (of one 'colour').

Incoherent source emits light with frequent and random change of phase between the photons. (Tungsten filament lamps and 'ordinary' fluorescent tubes emit incoherent light).

REVISE WITH CONCEPTS

Superposition of Light Rays

ExampleDefinitionsFormulaes

Positions of Fringes in Double Slit Experiment, Fringe Width

ExampleDefinitionsFormulaes

Interference and Coherent Sources

ExampleDefinitionsFormulaes

Young's Double Slit Experiment

ExampleDefinitionsFormulaes

Important Quantities Derivation from YDSE

ExampleDefinitionsFormulaes

Interference with Polychromatic Light

ExampleDefinitionsFormulaes

LEARN WITH VIDEOS

Introduction to Interference of Light

12 mins

Introduction to Coherent and Incoherent Sources

5 mins

Quick Summary With Stories

Introduction to Coherent and Incoherent Sources

2 mins

Problems on Intensity of Coherent Source

2 mins

Important Questions

In a double slit experiment, the two slits are 1 mm apart and the screen is place 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

Medium

NEET

View solution

A beam of light consisting of two wavelengths, $650 n m$ and $520 n m$ , is used to obtain interference fringes in a Young's double-slit experiment.(a) Find the distance of the third bright fringe on the screen from the central maximum for wavelength $650 n m$ .(b) What is the least distance from the central maximum where the bright fringes due to both the wavelengths coincide? The distance between the two slits is $0.28 m m$ and the screen is at a distance of $1.4 m$ from the slits.

Medium

View solution

The maximum intensity in Young's double slit experiment is $I_{0}$ . Distance between the slits is $d = 5 λ$ , where $λ$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance $D = 10 d$ ?

Medium

View solution

Two coherent monochromatic light beams of intensities $I$ and $4 I$ are superposed. The maximum and minimum possible resulting intensities are :

Medium

View solution

Derive the expression for the fringe width in a Young's double slit experiment. How will the fringe width change if (i) separation between the slits is increased (ii) screen is moved away from the plane of the slits.

Easy

View solution

In a Youngs double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

Medium

View solution

The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio $\frac{I _{m a x} - I _{m i n}}{I _{m a x} + I _{m i n}}$ will be

Hard

NEET

View solution

In Young's double slit experiment, the fringe width is found to be $0.4$ mm. If the whole apparatus is immersed in water of refractive index $(4 / 3)$ , without disturbing the geometrical arrangement, what is the new fringe width?

Hard

View solution

Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for the maximum and zero intensity.

Medium

View solution

In Young's double slit experiment, the slits are 2mm apart are illuminated by photons of two wavelengths $I_{1} = 12000 \overset{˚}{A}$ and $I_{2} = 10000 \overset{˚}{A}$ . at what minimum distance from the common central bright fringe on the screen 2m from the slit will a bright fringe from one interference pattern coincide with a bright fringe from the other?

Hard

View solution

definition

Coherent and Incoherent Sources

REVISE WITH CONCEPTS

Superposition of Light Rays

Positions of Fringes in Double Slit Experiment, Fringe Width

Interference and Coherent Sources

Young's Double Slit Experiment

Important Quantities Derivation from YDSE

Interference with Polychromatic Light

Quick Summary With Stories

Introduction to Coherent and Incoherent Sources

Problems on Intensity of Coherent Source

In a double slit experiment, the two slits are 1 mm apart and the screen is place 1 m away. A monochromatic light of wavelength 500 nm is used. What will be the width of each slit for obtaining ten maxima of double slit within the central maxima of single slit pattern?

The maximum intensity in Young's double slit experiment is I0​. Distance between the slits is d=5λ, where λ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance D=10d?

Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible resulting intensities are :

Derive the expression for the fringe width in a Young's double slit experiment. How will the fringe width change if (i) separation between the slits is increased (ii) screen is moved away from the plane of the slits.

In a Youngs double-slit experiment, the slits are separated by 0.28 mm and the screen is placed 1.4 m away. The distance between the central bright fringe and the fourth bright fringe is measured to be 1.2 cm. Determine the wavelength of light used in the experiment.

The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio Imax​+Imin​Imax​−Imin​​ will be

In Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in water of refractive index (4/3), without disturbing the geometrical arrangement, what is the new fringe width?

Derive the expression for the intensity at a point where interference of light occurs. Arrive at the conditions for the maximum and zero intensity.

The maximum intensity in Young's double slit experiment is $I_{0}$ . Distance between the slits is $d = 5 λ$ , where $λ$ is the wavelength of monochromatic light used in the experiment. What will be the intensity of light in front of one of the slits on a screen at a distance $D = 10 d$ ?

Two coherent monochromatic light beams of intensities $I$ and $4 I$ are superposed. The maximum and minimum possible resulting intensities are :

The interference pattern is obtained with two coherent light source of intensity ratio n. In the interference pattern, the ratio $\frac{I _{m a x} - I _{m i n}}{I _{m a x} + I _{m i n}}$ will be

In Young's double slit experiment, the fringe width is found to be $0.4$ mm. If the whole apparatus is immersed in water of refractive index $(4 / 3)$ , without disturbing the geometrical arrangement, what is the new fringe width?