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In a Young’s double slit experiment, an angular width of the fringe is \( 0.35^\circ \) on a screen placed at \( 2 \, \text{m} \) away for particular wavelength of \( 450 \, \text{nm} \). The angular width of the fringe, when whole system is immersed in a medium of refractive index \( 7/5 \), is \( \dfrac{1}{\alpha} \). The value of \( \alpha \) is __________.

A parallel beam of monochromatic light of wavelength \( 600 \, \text{nm} \) passes through single slit of \( 0.4 \, \text{mm} \) width. Angular divergence corresponding to second order minima would be ______ \( \times 10^{-3} \, \text{rad} \).

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

In a Young's double slit experiment, two slits are located \( 1.5 \, \text{mm} \) apart. The distance of screen from slits is \( 2 \, \text{m} \) and the wavelength of the source is \( 400 \, \text{nm} \). If the \( 20 \) maxima of the double slit pattern are contained within the central maximum of the single slit diffraction pattern, then the width of each slit is \( x \times 10^{-3} \) \( \text{cm} \), where x-value is _______.

‘\( n \)’ polarizing sheets are arranged such that each makes an angle \( 45^\circ \) with the proceeding sheet. An unpolarized light of intensity \( I \) is incident into this arrangement. The output intensity is found to be \( \dfrac{I}{64} \). The value of \( n \) will be:

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: The beam of electrons show wave nature and exhibit interference and diffraction.
Reason R: Davisson germer experimentally verified the wave nature of electrons.
In the list of the above statements, choose the most appropriate answer from the options given below:

For a specific wavelength \( 670 \, \text{nm} \) of light coming from a galaxy moving with velocity \( v \), the observed wavelength is \( 670.7 \, \text{nm} \). The value of \( v \) is:

Two loudspeakers ( $L_1$ and $L_2$ ) are placed with a separation of $10\text{ m}$, as shown in figure. Both speakers are fed with an audio input signal of same frequency with constant volume. A voice recorder, initially at point $A$, at equidistance to both loud speakers, is moved by $25\text{ m}$ along the line $AB$ while monitoring the audio signal. The measured signal was found to undergo $10$ cycles of minima and maxima during the movement. The frequency of the input signal is _________ $\text{Hz}$

(Speed of sound in air is $324\text{ m/s}$ and $\sqrt{5} = 2.23$)

An unpolarised light beam of intensity \( 2I_{0} \) is passed through a polaroid \( P \) and then through another polaroid \( Q \) which is oriented in such a way that its passing axis makes an angle of \( 30^\circ \) relative to that of \( P \). The intensity of the emergent light is

In Young’s double slit arrangement, slits are separated by a gap of \( 0.5 \, \text{mm} \), and the screen is placed at a distance of \( 0.5 \, \text{m} \) from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of 5890 Å is:

When a polaroid sheet is rotated between two crossed polaroids then the transmitted light intensity will be maximum for a rotation of:

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are \( 2.8 \) (medium \( -1 \)) and \( 6.8 \) (medium \( -2 \)), respectively. To satisfy the condition, so that the reflected and refracted rays are perpendicular to each other, the angle of incidence should be \( \tan^{-1}\!\left(\left(1+\frac{10}{\theta}\right)^{\frac{1}{2}}\right) \) the value of \( \theta \) is _______. (Given for dielectric media, \( \mu_r=1 \))

In a double slit experiment shown in figure, when light of wavelength \( 400 \, \text{nm} \) is used, dark fringe is observed at \( P \). If \( D = 0.2 \, \text{m} \), the minimum distance between the slits \( S_1 \) and \( S_2 \) is __________ mm.

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.
In the light of the above statements, choose the correct answer from the options given below:

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

Two simple harmonic waves having equal amplitudes of \( 8 \, \text{cm} \) and equal frequency of \( 10 \, \text{Hz} \) are moving along the same direction. The resultant amplitude is also \( 8 \, \text{cm} \). The phase difference between the individual waves is _____ degree.

The light waves from two coherent sources have same intensity \( I_1 = I_2 = I_0 \). In interference pattern the intensity of light at minima is zero. What will be the intensity of light at maxima?

An unpolarized light of intensity \( I_0 \) passes through polarizer and then through a certain optically active solution and finally it goes to analyser. If the angle between analyser and polariser is \( 0^\circ \) and intensity of light emerged from analyser is \( \frac{3}{8} I_0 \), the angle of rotation of the light by the solution with respect to analyser is ______ degrees.

In Young’s double slit experiment, if the source of light changes from orange to blue then:

In a Young's double slit experiment, the slits are separated by \( 0.3 \, \text{mm} \) and the screen is \( 1.5 \, \text{m} \) away from the plane of slits. Distance between fourth bright fringes on both sides of central bright fringe is \( 2.4 \, \text{cm} \). The frequency of light used is ______ \( \times 10^{14} \, \text{Hz} \) .

A parallel beam of monochromatic light of wavelength \( 5000 \, \mathring{A}\) is incident normally on a single narrow slit of width \( 0.001 \, \text{mm} \). The light is focused by convex lens on screen, placed on its focal plane. The first minima will be formed for the angle of diffraction of ________ (degree).

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:

In a Young’s double slit experiment, the slits are separated by \( 0.2 \, \text{mm} \). If the slits separation is increased to \( 0.4 \, \text{mm} \), the percentage change of the fringe width is:

In Young’s double slit experiment, two slits \( S_{1} \) and \( S_{2} \) are \( d \) distance apart and the separation from slits screen is \( D \) (as shown in figure). Now if two transparent slobs of equal thickness \( 0.1 \, \text{mm} \) but index \( 1.51 \) and \( 1.55 \) are introduction in the path of beam \( (\lambda = 4000\ Å\ \) from \( S_{1} \) and \( S_{2} \) respectively. The central bright fringe spot will shift by ________ number of fringes.

As shown in the figure, after passing through the medium \( 1 \). The speed of light \( v_2 \) in medium \( 2 \) will be:
(Given \( c = 3 \times 10^8 \, \text{m s}^{-1} \))

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.)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The phase difference of two light waves change if they travel through different media having same thickness, but different indices of refraction.
Reason R: The wavelengths of waves are different in different media.
In the light of the above statements, choose the most appropriate answer from the options given below

Young's double slit interference apparatus is immersed in a liquid of refractive index \( 1.44 \). It has slit separation of \( 1.5 \,\text{mm} \). The slits are illuminated by a parallel beam of light whose wavelength in air is \( 690 \,\text{nm} \). The fringe-width on a screen placed behind the plane of slits at a distance of \( 0.72 \,\text{m} \), will be:

In free space, an electromagnetic wave of \( 3 \ \text{GHz} \) frequency strikes over the edge of an object of size \( \frac{\lambda}{100} \), where \( \lambda \) is the wavelength of the wave in free space. The phenomenon, which happens there will be:

A beam of unpolarized light of intensity \( I_{0} \) passed through a polaroid \( A \) and then through another polaroid \( B \) which is oriented so that its principal plane makes an angle of \( 45^{\circ} \) relative to that of \( A \). The intensity of emergent light is:

A slit of width \( a \) is illuminated by light of wavelength \( \lambda \). The linear separation between \( 1^\text{st} \) and \( 3^\text{rd} \) minima in the diffraction pattern produced on a screen placed at a distance \( D \) from the slit system is _______.

In a double slit experiment with monochromatic light, fringes are obtained on a screen placed at some distance from the plane of slits. If the screen is moved by \( 5 \times 10^{-2} \, \text{m} \) towards the slits, the change in fringe width is \( 3 \times 10^{-3} \, \text{cm} \). If the distance between the slits is \( 1 \, \text{mm} \), then the wavelength of the light will be _____ \( \text{nm} \).

Red light differs from blue light as they have:

A monochromatic light wave with wavelength \( \lambda_{1} \) and frequency \( v_{1} \) in air enters another medium. If the angle of incidence and angle of refraction at the interface are \( 45^\circ \) and \( 30^\circ \) respectively, then the wavelength \( \lambda_{2} \) and frequency \( v_{2} \) of the refracted wave are:

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion-(A): If Young’s double slit experiment is performed in an optically denser medium than air, then the consecutive fringes come closer.
Reason-(R): The speed of light reduces in an optically denser medium than air while its frequency does not change.
In the light of the above statements, choose the most appropriate answer from the options given below:

A monochromatic light of frequency \( 5 \times 10^{14} \, \text{Hz} \) travelling through air, is incident on a medium of refractive index ‘\( 2 \)’. Wavelength of the refracted light will be:

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 and glass are \( 1.00 \) and \( 1.52 \), respectively.

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

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 ________.

A transparent film of refractive index, \( 2.0 \) is coated on a glass slab of refractive index, \( 1.45 \). What is the minimum thickness of transparent film to be coated for the maximum transmission of Green light of wavelength \( 550 \, \text{nm} \). [Assume that the light is incident nearly perpendicular to the glass surface.]

The width of fringe is \( 2 \, \text{mm} \) on the screen in a double slits experiment for the light of wavelength of \( 400 \, \text{nm} \). The width of the fringe for the light of wavelength \( 600 \, \text{nm} \) will be:

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

The maximum intensity in a Young’s double slit experiment is \( I_0 \). Distance between the slits \( (d) \) is \( 5\lambda \), where \( \lambda \) is the wavelength of light used. The intensity of the fringe, exactly opposite to one of the slits on the screen, placed at \( D = 10d \) is ________________ .

In a double slit experiment the distance between the slits is \( 0.1 \, \text{cm} \) and the screen is placed at \( 50 \, \text{cm} \) from the slits plane. When one slit is covered with a transparent sheet having thickness \( t \) and refractive index n(= 1.5), the central fringe shifts by \( 0.2 \, \text{cm} \). The value of \( t \) is ______________ \( \text{cm} \).

Which of the following are true for a single slit diffraction ?
A. Width of central maxima increases with increase in wavelength keeping slit width constant.
B. Width of central maxima increases with decrease in wavelength keeping slit width constant.
C. Width of central maxima increases with decrease in slit width at constant wavelength.
D. Width of central maxima increases with increase in slit width at constant wavelength.
E. Brightness of central maxima increases for decreases in wavelength at constant slit width.

In the Young's double slit experiment, the distance between the slits varies in time as \( d(t)=d_0+a_0 \sin \omega t \) where \( d_0, \omega \) and \( a_0 \) are constants. The difference between the largest fringe width and the smallest fringe width obtained over time is given as:

When unpolarized light is incident at an angle of \( 60^\circ \) on a transparent medium from air, the reflected ray is completely polarized. The angle of refraction in the medium is:

Which of the following phenomena can not be explained by wave theory of light?

A double slit interference experiment performed with a light of wavelength \( 600 \, \text{nm} \) forms an interference fringe pattern on a screen with \( 10^{\text{th}} \) bright fringe having its centre at a distance of \( 10 \, \text{mm} \) from the central maximum. Distance of the centre of the same \( 10^{\text{th}} \) bright fringe from the central maximum when the source of light is replaced by another source of wavelength \( 660 \, \text{nm} \) would ______ be \( \text{mm} \).

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 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:

The diffraction pattern of a light of wavelength \( 400 \, \text{nm} \) diffracting from a slit of width \( 0.2 \, \text{mm} \) is focused on the focal plane of a convex lens of focal length \( 100 \, \text{cm} \). The width of the \( 1^{\text{st}} \) secondary maxima will be:

White light is passed through a double slit and interference is observed on a screen \( 1.5 \, \text{m} \) away. The separation between the slits is \( 0.3 \, \text{mm} \). The first violet and red fringes are formed \( 2.0 \, \text{mm} \) and \( 3.5 \, \text{mm} \) away from the central white fringes. The difference in wavelengths of red and violet light is ______ \( \text{nm} \).

In Yong’s double slit experiment, monochromatic light of wavelength \( 5000 \, \mathring{A}\) 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 __________ \( \times 10^{-6} \, \text{m} \).

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 \( \dfrac{7\lambda}{4} \). The ratio of intensity of fringe at this point with respect to the maximum intensity of the fringe is:

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

A microwave of wavelength \( 2.0 \, \text{cm} \) falls normally on a slit of width \( 4.0 \, \text{cm} \). The angular spread of the central maxima of the diffraction pattern obtained on a screen \( 1.5 \, \text{m} \) away from the slit, will be:

In a Young’s double slit experiment, a laser light of \( 560 \, \text{nm} \) produces an interference pattern with consecutive bright fringes’ separation of \( 7.2 \, \text{mm} \). Now another light is used to produce an interference pattern with consecutive bright fringes’ separation of \( 8.1 \, \text{mm} \). The wavelength of second light is _______ \( \text{nm} \).

A source of light is placed in front of a screen. Intensity of light on the screen is \( I \). Two Polaroids \( P_1 \) and \( P_2 \) are so placed in between the source of light and screen that the intensity of light on screen is \( \dfrac{I}{2} \). \( P_2 \) should be rotated by an angle of __________ (degrees) so that the intensity of light on the screen becomes \( \dfrac{3I}{8} \).

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 increase when monochromatic source is replaced by another monochromatic source of higher wavelength. In the light of the above statements, choose the correct answer from the options given below:

A linearly polarized electromagnetic wave in vacuum is \( \vec{E}=3.1\cos\!\left[(1.8)z-(5.4\times 10^{6}) t\right]\\,\hat{i}\ \text{N}/\text{C} \) is incident normally on a perfectly reflecting wall at \( z=a \). Choose the correct option

Two plane polarized light waves combine at a certain point whose electric field components are
\( E_1 = E_0 \sin(\omega t) \) 
\( E_2 = E_0 \sin\!\left(\omega t + \frac{\pi}{3}\right) \) 
Find the amplitude of the resultant wave.

Two polaroide A and B are placed in such a way that the pass-axis of polaroids are perpendicular to each other. Now, another polaroid C is placed between A and B bisecting angle between them. If intensity of unpolarized light is \( I_0 \) then intensity of transmitted light after passing through polaroid B will be:

In two separate Young's double-slit experimental set-ups and two monochromatic light sources of different wavelengths are used to get fringes of equal width. The ratios of the slits separations and that of the wavelengths of light used are \( 2:1 \) and \( 1:2 \) respectively. The corresponding ratio of the distances between the slits and the respective screens \( (D1 / D2) \) 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:

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

Given below are two statements :
Statement I : If the Brewster’s angle for the light propagating from air to glass is \( \theta_B \), then the Bresster’s angle for the light propagating from glass to air is \( \frac{\pi}{2} - \theta_B \)
Statement II : The Brewster’s angle for the light propagating from glass to air is \( \tan^{-1}(\mu_g) \) where \( \mu_g \) is the refractive index of glass.
In the light of the above statements, choose the correct answer from the options given below:

An electron (mass \( m \)) with an initial velocity \( \vec{v} = v_{0} \hat{i} \ (v_{0} > 0) \) is moving in an electric field \( \vec{E} = -E_{0} \hat{i} \ (E_{0} > 0) \) where \( E_{0} \) is constant. If at \( t = 0 \) de – Broglie wavelength is \( \lambda_{0} = \dfrac{h}{m v_{0}} \), then its de-Broglie wavelength after time \( t \) is given by:

In single slit diffraction pattern, the wavelength of light used is \( 628 \, \text{nm} \) and slit width is \( 0.2 \, \text{mm} \), the angular width of central maximum is \( \alpha \times 10^{-2} \) degrees. The value of \( \alpha \) is __________.

In a Young's double slit experiment set up, the two slits are kept \( 0.4 \, \text{mm} \) apart and screen is placed at \( 1 \, \text{m} \) from slits. If a thin transparent sheet of thickness \( 20 \, \mu\text{m} \) is introduced in front of one of the slits then center bright fringe shifts by \( 20 \, \text{mm} \) on the screen. The refractive index of transparent sheet is given by \( \dfrac{\alpha}{10} \), where \( \alpha \) is ___________.

A person observes two moving trains, ‘A’ reaching the station and ‘B’ leaving the station with equal speed of \( 30 \, \text{m/s} \). If both trains emit sounds with frequency \( 300 \, \text{Hz} \), (Speed of sound: \( 330 \, \text{m/s} \)) approximate difference of frequencies heard by the person will be:

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 \( \frac{I_1 + I_2}{I_0} = \) ________.

The engine of a train moving with speed \( 10 \, \text{ms}^{-1} \) towards a platform sounds a whistle at frequency \( 400 \, \text{Hz} \). The frequency heard by a passenger inside the train is:
(Neglect air speed. Speed of sound in air \( = 330 \, \text{ms}^{-1} \))

In a double slit experiment, when one of the slits is covered by a transparent mica sheet of refractive index \( 1.56 \), the central fringe shifts to the position of \( 7^{\text{th}} \) bright fringe, obtained with both slits uncovered. If the light source wavelength is \( 450 \, \text{nm} \), the thickness of mica sheet is \( \alpha \times 10^{-9} \, \text{m} \). The value of \( \alpha \) is _______.

In Young’s double slits experiment, the position of \( 5^{\text{th}} \) bright fringe from the central maximum is \( 5 \, \text{cm} \). the distance between slits and screen is \( 1 \, \text{m} \) and wavelength of used monochromatic light is \( 600 \, \text{nm} \). The separation between the slits is:

In a single slit diffraction pattern, a light of wavelength \( 6000 \, \mathring{A} \) is used. The distance between the first and third minima in the diffraction pattern is found to be \( 3 \, \text{mm} \) when the screen in placed \( 50 \, \text{cm} \) away from slits. The width of the slit is __________ \( \times 10^{-4} \, \text{m} \).

The difference in the number of waves when yellow light propagates through air and vacuum columns of the same thickness is one. The thickness of the air column is ______ \( \text{mm} \).
[Refractive index of air = \( 1.0003 \), wavelength of yellow light in vacuum = \( 6000 \, \mathring{A} \)]

If the source of light used in a Young’s double slit experiment is changed from red to violet:

In a Young’s double slit experiment, two slits are illuminated with a light of wavelength \( 800 \, \text{nm} \). The line joining \( A_1P \) is perpendicular to \( A_1A_2 \) as shown in the figure. If the first minimum is detected at \( P \), the value of slits separation \( a \) will be:

Two light waves of wavelengths \( 800 \, \text{nm} \) and \( 600 \, \text{nm} \) are used in Young’s double slit experiment to obtain interference fringes on a screen placed \( 7 \, \text{m} \) away from plane of slits. If the two slits are separated by \( 0.35 \, \text{mm} \), then shortest distance from the central bright maximum to the point where the bright fringes of the two wavelength coincide will be ______ mm.

In Young's double slit experiment, carried out with light of wavelength \( 5000 \,\text{ Å}
 \), the distance between the slits is \( 0.3 \, \text{mm} \) and the screen is at \( 200 \, \text{cm} \) from the slits. The central maximum is at \( x = 0 \, \text{cm} \). The value of \( x \) for third maxima is ________ \( \text{mm} \).

A tunning fork of frequency \( 340\,\text{Hz} \) resonates in the fundamental mode with an air column of length \( 125\,\text{cm} \) in a cylindrical tube closed at one end. When water is slowly poured in it, the minimum height of water required for observing resonance once again is ____________ \( \text{cm} \).
(Velocity of sound in air is \( 340\,\text{ms}^{-1} \))

A thin transparent film with refractive index \( 1.4 \), is held on circular ring of radius \( 1.8 \, \text{cm} \). The fluid in the film evaporates such that transmission through the film at wavelength \( 560 \, \text{nm} \) goes to a minimum every \( 12 \, \text{seconds} \). Assuming that the film is flat on its two sides, the rate of evaporation is __________ \( \pi \times 10^{-13} \, \text{m}^3/\text{s} \).

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 \( \dfrac{I_1}{I_2} = \dfrac{10}{x} \) then \( x = \_\_\_\_\_\_\_\_ \).

Using Young's double slit experiment a monochromatic light of wavelength 5000 Å produces fringes of fringe width \( 0.5 \, \text{mm} \). If another monochromatic light of wavelength 6000 Å is used and the separation between the slits is doubled, then the new fringe width will be:

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:

A single slit of width \( a \) is illuminated by a monochromatic light of wavelength \( 600 \, \text{nm} \). The value of ‘\( a \)’ for which first minimum appears at \( \theta = 30^\circ \) on the screen will be:

The velocity of sound in air is doubled when the temperature is raised from \( 0^{\circ}\mathrm{C} \) to \( \alpha^{\circ}\mathrm{C} \). The value of \( \alpha \) is ______.

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:

Some distant star is to be observed by some telescope of diameter of objective lens \( a \), at an angular resolution of \( 3.0 \times 10^{-7} \) radian. If the wavelength of light from the star reaching the telescope is \( 500 \, \text{nm} \), the minimum diameter of the objective lens of the telescope is ______ \( \text{cm} \). (Nearest integer)

The Young's double slit interference experiment is performed using light consisting of \( 480 \, \text{nm} \) and \( 600 \, \text{nm} \) wavelengths to form interference patterns. The least number of the bright fringes of \( 480 \, \text{nm} \) light that are required for the first coincidence with the bright fringes formed by \( 600 \, \text{nm} \) light 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 :

Sodium light of wavelengths \( 650 \, \text{nm} \) and \( 655 \, \text{nm} \) is used to study diffraction at a single slit of aperture \( 0.5 \, \text{mm} \). The distance between the slit and the screen is \( 2.0 \, \text{m} \). The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is _________ \( \times 10^{-5} \, \text{m} \).

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 __________.

Given below are two statements. One is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): In Young's double slit experiment, the fringes produced by red light are closer as compared to those produced by blue light.
Reason (R): The fringe width is directly proportional to the wavelength of light.
In the light of the above statements, choose the correct answer from the options given below:

If the measured angular separation between the second minimum to the left of the central maximum and the third minimum to the right of the central maximum is \( 30^\circ \) in a single slit diffraction pattern recorded using \( 628 \, \text{nm} \) light, then the width of the slit is \( \underline{\hspace{1cm}} \, \mu\text{m} \).

Two wavelengths \( \lambda_{1} \) and \( \lambda_{2} \) are used in Young’s double slit experiment. \( \lambda_{1} = 450 \, \text{nm} \) and \( \lambda_{2} = 650 \, \text{nm} \). The minimum order of fringe produced by \( \lambda_{2} \) which overlaps with the fringe produced by \( \lambda_{1} \) is \( n \). The value of \( n \) is ________.

Unpolarised light of intensity \( 32 \, \text{W m}^{-2} \) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \( 3 \, \text{W m}^{-2} \), then the angle between pass axis of fist two polaroids is ________ \( ^\circ \).

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

In a Young’s double slit experiment, three polarizers are kept as shown in the figure. The transmission axes of \( P_{1} \) and \( P_{2} \) are orthogonal to each other. The polarizer \( P_{3} \) covers both the slits with its transmission axis at \( 45^{\circ} \) to those of \( P_{1} \) and \( P_{2} \). An unpolarized light of wavelength \( \lambda \) and intensity \( I_{0} \) is incident on \( P_{1} \) and \( P_{2} \). The intensity at a point after \( P_{3} \), where the path difference between the light waves from \( s_{1} \) and \( s_{2} \) is \( \dfrac{\lambda}{3} \), is:

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is \( 2.4 \, \mu \text{m} \). If the experiment is carried out in another medium having refractive index \( 1.2 \), the fringe width will be ___ \( \mu \text{m} \).

A monochromatic light of wavelength \( 6000 \, Å \) is incident on the single slit of width \( 0.01 \, \text{mm} \). If the diffraction pattern is formed at the focus of the convex lens of focal length \( 20 \, \text{cm} \), the linear width of the central maximum is:

Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by \( y=(10 \cos \pi x \sin \frac{2 \pi t}{T}) \, \text{cm} \). The amplitude of the particle at \( x=\frac{4}{3} \, \text{cm} \) will be _______ \( \text{cm} \).

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at \( 30^\circ \) and \( 90^\circ \), respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at \( 60^\circ \) with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer is

An unpolarized light is incident on the plane interface of air–dielectric medium shown in figure. If the incident angle is equal to Brewster angle, identify the expression representing reflected wave.

A travelling wave is described by the equation \( y(x,t) = [0.05 \sin(8x - 4t)] \, \text{m} \). The velocity of the wave is : [all the quantities are in SI unit]

With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength \( 5890 \, \displaystyle \overset{\circ}{\text{A}} \) is observed at \( 5896 \, \displaystyle \overset{\circ}{\text{A}} \) ?

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 of the minimum intensity in the interference pattern is: