Interference and Young's Double-Slit Experiment

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JEE Advanced 1998

LEVELJEE Advanced

A coherent parallel beam of microwaves of wavelength $λ = 0.5 mm$ falls on a Young's double slit apparatus. The separation between the slits is $1.0 mm$ . The intensity of microwaves is measured on a screen placed parallel to the plane of the slits at a distance of $1.0 m$ from it as shown in the figure. (a) If the incident beam falls normally on the double slit apparatus, find the $y$ -coordinates of all the interference minima on the screen. (b) If the incident beam makes an angle of $3 0^{\circ}$ with the $x$ -axis (as in the dotted arrow shown in figure), find the $y$ -coordinates of the first minima on either side of the central maximum.

JEE Advanced 1999

LEVELJEE Advanced

The Young's double slit experiment is done in a medium of refractive index $4/3$ . A light of $600 nm$ wavelength is falling on the slits having $0.45 mm$ separation. The lower slit $S_{2}$ is covered by a thin glass sheet of thickness $10.4 \mu m$ and refractive index $1.5$ . The interference pattern is observed on a screen placed $1.5 m$ from the slits as shown in the figure. (a) Find the location of central maximum (bright fringe with zero path difference) on the $y$ -axis. (b) Find the light intensity of point $O$ relative to the maximum fringe intensity. (c) Now, if $600 nm$ light is replaced by white light of range $400$ to $700 nm$ , find the wavelengths of the light that form maxima exactly at point $O$ . (All wavelengths in the problem are for the given medium of refractive index $4/3$ . Ignore dispersion)

JEE Advanced 2001

LEVELJEE Advanced

A vessel $A B C D$ of 10 cm width has two small slits $S_{1}$ and $S_{2}$ sealed with identical glass plates of equal thickness. The distance between the slits is 0.8 mm. $P O Q$ is the line perpendicular to the plane $A B$ and passing through $O$ , the middle point of $S_{1}$ and $S_{2}$ . A monochromatic light source is kept at $S$ , 40 cm below $P$ and 2 m from the vessel, to illuminate the slits as shown in the figure alongside. Calculate the position of the central bright fringe on the other wall $C D$ with respect to the line $O Q$ . Now, a liquid is poured into the vessel and filled upto $O Q$ . The central bright fringe is found to be at $Q$ . Calculate the refractive index of the liquid.

LEVELJEE Main

In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other, then in the interference pattern

(A)

the intensities of both the maxima and the minima increases

(B)

the intensity of the maxima increases and the minima has zero intensity

(C)

the intensity of maxima decreases and that of minima increases

(D)

the intensity of maxima decreases and the minima has zero intensity

JEE Advanced 2002

LEVELJEE Main

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness $t$ is introduced in the path of one of the interfering beams (wavelength $λ$ ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is

(A)

2 λ

(B)

\frac{2 λ}{3}

(C)

\frac{λ}{3}

(D)

λ

JEE Advanced 2017

LEVELJEE Advanced

Two coherent monochromatic point sources $S_{1}$ and $S_{2}$ of wavelength $λ = 600 nm$ are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d = 1.8 mm$ . This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $Δ θ$ . Which of the following options is/are correct?

* Multiple Correct Options

(A)

The angular separation between two consecutive bright spots decreases as we move from

P_{1}

P_{2}

along the first quadrant

(B)

A dark spot will be formed at the point

P_{2}

(C)

The total number of fringes produced between

P_{1}

and

P_{2}

in the first quadrant is close to 3000

(D)

P_{2}

the order of the fringe will be maximum

JEE Advanced 1997

LEVELJEE Advanced

In a Young's experiment, the upper slit is covered by a thin glass plate of refractive index 1.4, while the lower slit is covered by another glass plate, having the same thickness as the first one but having refractive index 1.7. Interference pattern is observed using light of wavelength $5400 \overset{˚}{A}$ . It is found that the point $P$ on the screen, where the central maximum ( $n = 0$ ) fall before the glass plates were inserted, now has $3/4$ the original intensity. It is further observed that what used to be the fifth maximum earlier lies below the point $P$ while the sixth minima lies above $P$ . Calculate the thickness of glass plate. (Absorption of light by glass plate may be neglected).

LEVELJEE Main

Young's double slit experiment is carried out by using green, red and blue light, one colour at one time. The fringe widths recorded are $β_{G}, β_{R}$ and $β_{B}$ respectively. Then,

(A)

β_{G} > β_{B} > β_{R}

(B)

β_{B} > β_{G} > β_{R}

(C)

β_{R} > β_{B} > β_{G}

(D)

β_{R} > β_{G} > β_{B}

JEE Advanced 1997

LEVELJEE Advanced

In Young's experiment, the source is red light of wavelength $7 \times 1 0^{- 7} m$ . When a thin glass plate of refractive index $1.5$ at this wavelength is put in the path of one of the interfering beams, the central bright fringe shifts by $1 0^{- 3} m$ to the position previously occupied by the 5th bright fringe. Find the thickness of the plate. When the source is now changed to green light of wavelength $5 \times 1 0^{- 7} m$ , the central fringe shifts to a position initially occupied by the 6th bright fringe due to red light. Find the refractive index of glass for green light. Also estimate the change in fringe width due to the change in wavelength.

JEE Advanced 2016

LEVELJEE Advanced

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x$ - $y$ plane containing two small holes that act as two coherent point sources ( $S_{1}, S_{2}$ ) emitting light of wavelength $600 nm$ . The student mistakenly placed the screen parallel to the $x$ - $z$ plane (for $z > 0$ ) at a distance $D = 3 m$ from the mid-point of $S_{1} S_{2}$ , as shown schematically in the figure. The distance between the sources $d = 0.6003 mm$ . The origin $O$ is at the intersection of the screen and the line joining $S_{1} S_{2}$ .

* Multiple Correct Options

(A)

Semi circular bright and dark bands centered at point

O

(B)

The region very close to the point

O

will be dark

(C)

Straight bright and dark bands parallel to the

x

-axis

(D)

Hyperbolic bright and dark bands with foci symmetrically placed about

O

in the

x

-direction

JEE Advanced 2000

LEVELJEE Advanced

A glass plate of refractive index 1.5 is coated with a thin layer of thickness $t$ and refractive index 1.8. Light of wavelength $λ$ travelling in air is incident normally on the layer. It is partly reflected at the upper and the lower surfaces of the layer and the two reflected rays interfere. Write the condition for their constructive interference. If $λ = 648 nm$ , obtain the least value of $t$ for which the rays interfere constructively.

JEE Advanced 1982

LEVELJEE Main

In the Young's double slit experiment, the interference pattern is found to have an intensity ratio between the bright and dark fringes as 9. This implies that

* Multiple Correct Options

(A)

the intensities at the screen due to the two slits are 5 units and 4 units respectively

(B)

the intensities at the screen due to the two slits are 4 units and 1 unit respectively

(C)

the amplitude ratio is 3

(D)

the amplitude ratio is 2

JEE Advanced 1993

LEVELJEE Advanced

In given figure, $S$ is a monochromatic point source emitting light of wavelength $λ = 500 nm$ . A thin lens of circular shape and focal length $0.10 m$ is cut into two identical halves $L_{1}$ and $L_{2}$ by a plane passing through a diameter. The two halves are placed symmetrically about the central axis $S O$ with a gap of $0.5 mm$ . The distance along the axis from $S$ to $L_{1}$ and $L_{2}$ is $0.15 m$ while that from $L_{1}$ and $L_{2}$ to $O$ is $1.30 m$ . The screen at $O$ is normal to $S O$ . (a) If the third intensity maximum occurs at the point $A$ on the screen, find the distance $O A$ . (b) If the gap between $L_{1}$ and $L_{2}$ is reduced from its original value of $0.5 mm$ , will the distance $O A$ increase, decrease, or remain the same.

JEE Main 2005

LEVELJEE Main

In Young's double slit experiment, the intensity at a point is (1/4) of the maximum intensity. Angular position of this point is

(A)

sin^{- 1} (\frac{λ}{d})

(B)

sin^{- 1} (\frac{λ}{2 d})

(C)

sin^{- 1} (\frac{λ}{3 d})

(D)

sin^{- 1} (\frac{λ}{4 d})

LEVELBoard

In Young's double slit experiment, the separation between the slits is halved and the distance between the slits and the screen is doubled. The fringe width is

A light source, which emits two wavelengths $λ_{1} = 400 nm$ and $λ_{2} = 600 nm$ , is used in a Young's double-slit experiment. If recorded fringe widths for $λ_{1}$ and $λ_{2}$ are $β_{1}$ and $β_{2}$ and the number of fringes for them within a distance $y$ on one side of the central maximum are $m_{1}$ and $m_{2}$ , respectively, then

* Multiple Correct Options

(A)

β_{2} > β_{1}

(B)

m_{1} > m_{2}

(C)

from the central maximum, 3rd maximum of

λ_{2}

overlaps with 5th minimum of

λ_{1}

(D)

the angular separation of fringes of

λ_{1}

is greater than

λ_{2}

JEE Main 2004

LEVELJEE Advanced

In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum distance between two successive regions of complete darkness is

In a Young's double slit experiment, the separation between the two slits is $d$ and the wavelength of the light is $λ$ . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice (s).

* Multiple Correct Options

(A)

d = λ

, the screen will contain only one maximum

(B)

λ < d < 2 λ

, then at least one more maximum (besides the central maximum) will be observed on the screen

(C)

If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase

(D)

If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase

JEE Advanced 1984

LEVELJEE Advanced

White light is used to illuminate the two slits in a Young's double slit experiment. The separation between the slits is $b$ and the screen is at a distance $d$ ( $>> b$ ) from the slits. At a point on the screen directly in front of one of the slits, certain wavelengths are missing. Some of these missing wavelengths are

* Multiple Correct Options

(A)

λ = \frac{b ^{2}}{d}

(B)

λ = \frac{2 b ^{2}}{d}

(C)

λ = \frac{b ^{2}}{3 d}

(D)

λ = \frac{2 b ^{2}}{3 d}

JEE Advanced 1983

LEVELJEE Advanced

In Young's double slit experiment using monochromatic light the fringe pattern shifts by a certain distance on the screen when a mica sheet of refractive index $1.6$ and thickness $1.964$ microns is introduced in the path of one of the interfering waves. The mica sheet is then removed and the distance between the slits and the screen is doubled. It is found that the distance between successive maxima (or minima) now is the same as the observed fringe shift upon the introduction of the mica sheet. Calculate the wavelength of the monochromatic light used in the experiment (in $\overset{˚}{A}$ ).

JEE Advanced 2002

LEVELJEE Advanced

A point source $S$ emitting light of wavelength $600 nm$ is placed at a very small height $h$ above a flat reflecting surface $A B$ (see figure). The intensity of the reflected light is $36%$ of the incident intensity. Interference fringes are observed on a screen placed parallel to the reflecting surface at a very large distance $D$ from it. (a) What is the shape of the interference fringes on the screen? (b) Calculate the ratio of the minimum to the maximum intensities in the interference fringes formed near the point $P$ (shown in the figure). (c) If the intensity at point $P$ corresponds to a maximum, calculate the minimum distance through which the reflecting surface $A B$ should be shifted so that the intensity at $P$ again becomes maximum.

LEVELJEE Main

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

(A)

5 I

and

I

(B)

5 I

and

3 I

(C)

9 I

and

I

(D)

9 I

and

3 I

JEE Advanced 2015

LEVELJEE Advanced

A Young's double slit interference arrangement with slits $S_{1}$ in air and $S_{2}$ is immersed in water (refractive index = $4/3$ ) as shown in the figure. The positions of maxima on the surface of water are given by $x^{2} = p^{2} m^{2} λ^{2} - d^{2}$ , where $λ$ is the wavelength of light in air (refractive index = $1$ ), $2 d$ is the separation between the slits and $m$ is an integer. The value of $p$ is

JEE Advanced 1990

LEVELJEE Advanced

A narrow monochromatic beam of light of intensity $I$ is incident on a glass plate as shown in figure. Another identical glass plate is kept close to the first one-and parallel to it. Each glass plate reflects 25 per cent of the light incident on it and transmits the remaining. Find the ratio of the minimum and maximum intensities in the interference pattern formed by the two beams obtained after one reflection at each plate.

JEE Advanced 2004

LEVELJEE Main

In a Young's double slit experiment, two wavelengths of $500 nm$ and $700 nm$ were used. What is the minimum distance from the central maximum where their maximas coincide again? Take $D / d = 1 0^{3}$ . Symbols have their usual meanings.

In a double slit experiment instead of taking slits of equal widths, one slit is made twice as wide as the other, then in the interference pattern

In the Young's double slit experiment, the interference pattern is found to have an intensity ratio between the bright and dark fringes as 9. This implies that

In Young's double slit experiment, the intensity at a point is (1/4) of the maximum intensity. Angular position of this point is

In Young's double slit experiment, the separation between the slits is halved and the distance between the slits and the screen is doubled. The fringe width is

In a YDSE bi-chromatic light of wavelengths 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1 m. The minimum distance between two successive regions of complete darkness is

.math-text-wrapper .katex { font-size: 1.05em !important; } .math-text-wrapper .katex-display { margin: 1rem 0 !important; } Two coherent monochromatic light beams of intensities I and 4I are superposed. The maximum and minimum possible intensities in the resulting beam are

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