Superposition, Coherence & Intensity

For obtaining maximum contrast between the bright and dark fringes in an interference pattern, the intensities of the two light coherent sources should be

In interference and diffraction, the light energy is redistributed. If it reduces in one region, producing a dark fringe, it increases in another region, producing a bright fringe.

A. As there is no gain or loss of energy, these phenomena are consistent with the principle of conservation of energy.

B. Diffraction and interference are characteristics exhibited only by light waves. Choose the correct answer from the options given below:

In Young's double slit experiment, for the $n$th dark fringe ($n = 1, 2, 3, \ldots$) the phase difference of the interfering waves in radian will be

In Young's experiment, the intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources is $36 : 1$. The ratio of the amplitudes of the two individual sources will be

Two light waves amplitudes in the ratio $3 : 1$ produce interference. The ratio of the maximum to minimum intensity is

The interference pattern is obtained with two coherent light sources of intensity ($I_1$ and $I_2$) ratio '$\beta$'. In the interference pattern, the ratio $\left(\frac{I_{max} + I_{min}}{I_{max} - I_{min}}\right)$ will be $\left(\beta = \frac{I_2}{I_1}\right)$

At two points $P$ and $Q$ on the screen in Young's double slit experiment, waves from slits $S_1$ and $S_2$ have a path difference of zero and $\frac{\lambda}{4}$ respectively. The ratio of intensities at $P$ and $Q$ will be $\left(\cos 0^\circ = 1,\ \cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

Interference fringes are produced on a screen by using two light sources of intensities I and 9I. The phase difference between the beams is $\frac{\pi}{2}$, at point P and $\pi$ at point Q on the screen. The difference between the resultant intensities at points P and Q is $\left(\cos\frac{\pi}{2} = 0, \cos\pi = -1\right)$

The ratio of intensity at the centre of a bright fringe to the intensity at a point distant $\left(\frac{1}{4}\right)^{th}$ of the distance between two successive bright fringes will be $(\cos 0^\circ = 1, \cos 90^\circ = 0)$

The wavelength of light used in Young's double slit experiment, is $\lambda$. The intensity at a point on the screen is I, where the path difference is $\frac{\lambda}{6}$. If $I_0$ is the maximum intensity then the ratio I to $I_0$ is $\left(\cos 30^\circ = \frac{\sqrt{3}}{2}\right)$

In Young's double slit experiment, the wavelength of light used is $\lambda$. The intensity on the screen at a point for path difference '$\lambda$' is 'X'. The intensity at the point for path difference $\left(\frac{\lambda}{6}\right)$ is ($\cos 180^\circ = -1,\ \cos 30^\circ = \frac{\sqrt{3}}{2}$)

In Young's double slit experiment, width of the second slit is double the width of first slit, consequently the amplitude of the light from two slits. '$I_m$' is the maximum intensity. The resultant intensity '$I$' when they interfere with the phase difference of $\phi$ is given by

The ratio of intensities at two points on the screen in Young's double slit experiment when waves from the two slits have a path difference of zero and $\lambda/4$ is ($\lambda$ is the wavelength of light used) ($\cos 0^\circ = 1,\ \cos\pi/2 = 0$)

In a Young's double slit experiment, the intensities at two points, for the path difference $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ($\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\frac{I_1 + I_2}{I_0} =$

$\left(\cos 45^\circ = \frac{1}{\sqrt{2}}, \cos 60 = \frac{1}{2}\right)$

In Young's double slit experiment, 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 light at a point where the path difference is $\frac{\lambda}{3}$ will be

In interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is ______.

In the Young's double slit experiment the intensity produced by each one of the individual slits is $I_o$. The distance between two slits is 2 mm. The distance of screen from slits is 10 m. The wavelength of light is $6000\ \text{Å}$. The intensity of light on the screen in front of one of the slits is ______

In a Young's double slit experiment, the intensity at some point on the screen is found to be $\frac{3}{4}$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\frac{\lambda}{x}$ where $\lambda$ is wavelength of the incident light. The value of $x$ is _______.

In a Young double slit experiment, the wavelength of incident light is $6000\ \text{Å}$, the separation between slits $S_1$ and $S_2$ is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is ______ Å.

If the two sources of light emit waves of different amplitudes and interfere then

In a Young's double slit experiment, the source is white light. One of the slits is covered by red filter and another by a green filter. In this case:

In Young's double slit experiment, for the $n$th dark fringe ( $n = 1, 2, 3 \ldots$) the phase difference of the interfering waves in radian will be

Two monochromatic light beams have intensities in the ratio 1:9. An interference pattern is obtained by these beams. The ratio of the intensities of maximum to minimum is

Two coherent monochromatic light beams of intensities 4I and 9I are superimposed. The difference between the maximum and minimum intensities in the resulting interference pattern is $xI$. The value of $x$ is___________.

The two coherent sources produce interference with intensity ratio ' $b$ '. In the interference pattern, the ratio $\frac{I_{max} + I_{min}}{I_{max} - I_{min}}$maxmaxminmin will be

In Young's double slit interference experiment, using two coherent sources of different amplitudes, the intensity ratio between bright to dark fringes is $5 : 1$. The value of the ratio of resultant amplitudes of bright fringe to dark fringe is

Width of one of the two slits in a Young's double slit interference experiment is half of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:

The width of one of the two slits in Young's double slit experiment is d while that of the other slit is $x\,d$. If the ratio of the maximum to the minimum intensity in the interference pattern on the screen is $9 : 4$ then what is the value of $x$? (Assume that the field strength varies according to the slit width.)

In Young's double slit experiment, the intensity on screen at a point, where path difference is $\frac{\lambda}{4}$ is $\frac{K}{4}$. The intensity at a point when path difference is ' $\lambda$ ' will be $\left[\cos\frac{\pi}{2} = 0, \cos 2\pi = 1\right]$

In Young's double slit experiment, at two points $P$ and $Q$ on screen, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\frac{\lambda}{4}$ respectively. The ratio of intensities at point $P$ to that at $Q$ will be $\left(\cos 0^\circ = 1, \cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is ' $I$ '. The intensity at a point where the path difference is $\lambda/6$ is $\left[\cos\frac{\pi}{6} = \frac{\sqrt{3}}{2}\right][\lambda =$ wavelength of light $][\cos\pi = -1]$

In Young's double slit experiment, the light of wavelength ' $\lambda$ ' is used. The intensity at a point on the screen is ' I ' where the path difference is $\frac{\lambda}{4}$. If ' $I_0$ ' denotes the maximum intensity then the ratio of ' $I_0$ ' to ' I ' is $\left(\cos 45^\circ = 1/\sqrt{2}\right)$

Interference fringes are produced on the screen by using two light sources of intensities I and 9I. The phase difference between the beams is $\pi/2$ at point P and $\pi$ at point Q on the screen. The difference between the resultant intensities at points P and Q is $(\cos 90^\circ = 0, \cos\pi = -1)$

In Young's double slit experiment, the intensity on screen at a point where path difference is $\frac{\lambda}{4}$ is $\frac{K}{2}$. The intensity at a point when path difference is ' $\lambda$ ' will be

Two sound waves each of wavelength ' $\lambda$ ' and having the same amplitude ' $A$ ' from two source ' $S_1$ ' and ' $S_2$ ' interfere at a point P. If the path difference, $S_2P - S_1P = \lambda/3$ then the amplitude of resultant wave at point ' P ' will be $[\cos(120^\circ) = -0.5]$

In a Young's double slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case

The phase difference between two waves giving rise to dark fringe in Young's double slit experiment is ( n is the integer)

The width of one of the two slits in a Young's double slit experiment is 4 times that of the other slit. The ratio of the maximum to the minimum intensity in the interference pattern is:

Two coherent monochromatic light beams of intensities I and $4I$ are superimposed. The difference between maximum and minimum possible intensities in the resulting beam is $xI$. The value of $x$ is __________.

Two identical light waves having phase difference $\phi$ propagate in same direction. When they superpose, the intensity of resultant wave is proportional to

Interference pattern can be observed due to superposition of the following waves: A. $y = a\sin\omega t$

B. $y = a\sin 2\omega t$

C. $y = a\sin(\omega t - \phi)$

D. $y = a\sin 3\omega t$

Choose the correct answer from the options given below.

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

The intensity ratio of the maxima and minima in an interference pattern produced by two coherent sources of light is $9 : 1$. The intensities of the light sources used are in the ratio

The intensity of light coming from one of the slits in Young's double slit experiment is double the intensity from the other slit. The ratio of the maximum intensity to the minimum intensity in the interference fringe pattern observed is

In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is x units, $\lambda$ being the wavelength of light used. The intensity at a point where the path difference is $\frac{\lambda}{4}$ will be $\left(\cos 2\pi = 1, \cos\frac{\pi}{2} = 0\right)$

In Young's double slit experiment, 'I' is the minimum intensity and ' $I_1$ ' is the intensity at a point where the path difference is $\frac{\lambda}{4}$ where ' $\lambda$ ' is the wavelength of light used. The ratio $\frac{I}{I_1}$ is (Intensities of the two interfering waves are same) $(\cos 0^\circ = 1, \cos 90^\circ = 0)$

Considering interference between two sources of intensities ' I ' and ' 4 I ', the intensity at a point where the phase difference is $\pi$ is $(\cos\pi = -1)$

In the Young's double slit experiment, the intensity at a point on the screen, where the path difference is $\lambda(\lambda =$ wavelength $)$ is $\beta$. The intensity at a point where the path difference is $\lambda/3$, will be $\cos\frac{\pi}{3} = 1/2]$

In Young's double slit experiment using monochromatic light of wavelength ' $\lambda$ ', the maximum intensity of light at a point on the screen is ' K ' units. The intensity of light at a point where the path difference is $\frac{\lambda}{6}$ is $\left(\cos 60^\circ = \sin 30^\circ = 0.5, \sin 60^\circ = \cos 30^\circ = \sqrt{3}/2\right)$

In Young's double slit experiment using monochromatic light of wavelength ' $\lambda$ ', the intensity of light at a point on the screen where path difference ' $\lambda$ ' is K units. The intensity of light at a point where the path difference is $\frac{\lambda}{6}$ is $\left[\cos\frac{\pi}{6} = \sin\frac{\pi}{3} = \frac{\sqrt{3}}{2}\right]$

In Young's double slit experiment, light from two identical sources are superimposing on a screen. The path difference between the two lights reaching at a point on the screen is $7\lambda/4$. The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is:

Two waves of intensity ratio $1 : 9$ cross each other at a point. The resultant intensities at that point, when (a) Waves are incoherent is $I_1$ (b) Waves are coherent is $I_2$ and differ in phase by $60^\circ$. If $\frac{I_1}{I_2} = \frac{10}{x}$ then $x =$ _________.

In Young's double slit experiment, intensity at a point is $\left(\frac{1}{4}\right)$ of the maximum intensity. The angular position of this point is

In a Young's double slit experiment, the intensity at a point is $\left(\frac{1}{4}\right)$th of the maximum intensity, the minimum distance of the point from the central maximum is _________ $\mu\text{m}$. (Given: $\lambda = 600\text{ nm},\ d = 1.0\text{ mm}, D = 1.0\text{ m}$)

In Young's double slit experiment, monochromatic light of wavelength 5000 Å is used. The slits are $1.0\text{ mm}$ apart and screen is placed at $1.0\text{ m}$ away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is _________ $\times 10^{-6}\text{ m}$.

When two light waves each of amplitude '$A$' and having a phase difference of $\frac{\pi}{2}$ superimposed then the amplitude of resultant wave is

In a Young's double slits experiment, the ratio of amplitude of light coming from slits is $2 : 1$. The ratio of the maximum to minimum intensity in the interference pattern is:

Of the two slits producing interference in Young's experiment, one is covered with glass so that light intensity passing is reduced to $50\%$. Which of the following is correct?

$A$ and $B$ are two interfering sources where $A$ is ahead in phase by $54^\circ$ relative to B. The observation is taken from point $P$ such that PB $-$ PA = 2.5 $\lambda$. Then the phase difference between the waves from A and B reaching point P is (in rad)

The ratio of intensities of two points on a screen in Young's double slit experiment when waves from the two slits have a path difference of $\frac{\lambda}{4}$ and $\frac{\lambda}{6}$ is

$(\cos 90^\circ = 0, \cos 60^\circ = 0.5)$

In Young's double slit experiment the intensities at two points, for the path difference $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ($\lambda =$ wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits then $\frac{I_1 + I_2}{I_0}$ is equal to $\left(\cos 60^\circ = 0.5, \cos 45^\circ = \frac{1}{\sqrt{2}}\right)$

Light waves from two coherent sources arrive at two points on a screen with path difference of zero and $\frac{\lambda}{2}$. The ratio of intensities at the points is $(\cos 0^\circ = 1, \cos \pi = -1)$

In Young's double slit experiment, the wavelength of light used is '$\lambda$'. The intensity at a point is '$I$' where path difference is $\left(\frac{\lambda}{4}\right)$. If $I_0$ denotes the maximum intensity, then the ratio $\left(\frac{I}{I_0}\right)$ is $\left(\sin \frac{\pi}{4} = \cos \frac{\pi}{4} = \frac{1}{\sqrt{2}}\right)$

The ratio of intensities at two points $P$ and $Q$ on the screen in a Young's double slit experiment where phase difference between two waves of same amplitude are $\pi/3$ and $\pi/2$, respectively are

In a Young's double slit experiment, the intensities at two points, for the path differences $\frac{\lambda}{4}$ and $\frac{\lambda}{3}$ ( $\lambda$ being the wavelength of light used) are $I_1$ and $I_2$ respectively. If $I_0$ denotes the intensity produced by each one of the individual slits, then $\frac{I_1+I_2}{I_0} =$ __________.

Two light beams of intensities in the ratio of 9: 4 are allowed to interfere. The ratio of the intensity of maxima and minima will be:

Two coherent sources of light interfere. The intensity ratio of two sources is $1 : 4$. For this interference pattern if the value of $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is equal to $\frac{2\alpha + 1}{\beta + 3}$, then $\frac{\alpha}{\beta}$ will be:

Find the ratio of maximum intensity to the minimum intensity in the interference pattern if the widths of the two slits in Young's experiment are in the ratio of 9: 16. (Assuming intensity of light is directly proportional to the width of slits)

The interference pattern is obtained with two coherent light sources of intensity ratio 4: 1. And the ratio $\frac{I_{\max} + I_{\min}}{I_{\max} - I_{\min}}$ is $\frac{5}{x}$. Then, the value of x will be equal to:

The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\pi$/2 at point P and $\pi$ at point Q. Then the difference between the resultant intensities at P and Q will be:

Two light beams of intensities 4I and 9I interfere on a screen. The phase difference between these beams on the screen at point A is zero and at point B is $\pi$. The difference of resultant intensities, at the point A and B, will be _________ I.

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi/2$ and $\pi/3$ at points $A$ and $B$ respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be ________.

In Young's experiment with a monochromatic source and two slits, one of the slits is covered with black opaque paper, the fringes will

If two sources emit light waves of different amplitudes then

Two monochromatic beams of intensities I and 4 I respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern are

The light waves from two coherent sources have same intensity I1 = I2 = I0. In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

Two coherent light sources having intensity in the ratio 2x produce an interference pattern. The ratio $\frac{I_{\max} - I_{\min}}{I_{\max} + I_{\min}}$ will be:

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

The width of one of the two slits in a Young's double slit experiment is three times the other slit. If the amplitude of the light coming from a slit is proportional to the slit-width, the ratio of minimum to maximum intensity in the interference pattern is x: 4 where x is ____________.

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\pi/2$ at point $A$ and $\pi$ at point $B$. Then the difference between the resultant intensities at $A$ and $B$ is

In Young's double slit experiment, the intensity at a point where path difference is $\frac{\lambda}{6}$ ($\lambda$ being the wavelength of light used) is '$I$'. If '$I_0$' denotes the maximum intensity, then $\frac{I}{I_0}$ is equal to $\left(\cos 0^\circ = 1, \cos 60^\circ = \frac{1}{2}\right)$

In Young's double slit experiment using monochromatic light of wavelength '$\lambda$', the maximum intensity of light at a point on the screen is $K$ units. The intensity of light at point where the path difference is $\frac{\lambda}{3}$ is

$\left[\cos 60^\circ = \sin 30^\circ = \frac{1}{2}\right]$

In Young's double slit experiment, the intensity at a point where the path difference is $\frac{\lambda}{4}$ [ $\lambda$ is wavelength of light used] is '$I$'. If '$I_0$' is the maximum intensity then $\frac{I}{I_0}$ is equal to $\left[\cos \frac{\pi}{4} = \sin \frac{\pi}{4} = \frac{1}{\sqrt{2}}\right]$

Two coherent sources of light interfere and produce fringe pattern on a screen. For central maximum, the phase difference between the two waves will be,

In a double slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}$th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is:

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 light at a point where the path difference is $\frac{\lambda}{6}$ is given by $\frac{nK}{12}$, where n is an integer. The value of n is __________.

In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by 90°. A, B and C are three distinct points of observation, each equidistant from the midpoint of PQ. The intensities of radiation at A, B, C will be in the ratio:

The phenomenon of interference is based on

In an interference experiment the ratio of amplitudes of coherent waves is $\frac{a_1}{a_2} = \frac{1}{3}$. The ratio of maximum and minimum intensities of fringes will be:

In a Young's double slit experiment, the ratio of the slit's width is 4: 1. The ratio of the intensity of maxima to minima, close to the central fringe on the screen, will be:

Two coherent sources produce waves of different intensities which interfere. After interference, the ratio of the maximum intensity to the minimum intensity is 16. The intensity of the waves are in the ratio:

In a Young's double slit experiment, the path difference, at a certain point on the screen, between two interfering waves is $\frac{1}{8}$ th of wavelength. The ratio of the intensity at this point to that at the centre of a bright fringe is close to:

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

Two slits in Young's experiment have widths in the ratio 1: 25. The ratio of intensity at the maxima and minima in the interference pattern, $\frac{I_{max}}{I_{min}}$ is