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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 __________.

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 $\sqrt{5} = 2.23$)

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:

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.

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 _______.

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.

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 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 ______.

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:

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 ______.

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 ___________.

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 _______.

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 ______.

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)

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 ___ \( \mu \text{m} \).

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.