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JEE Mains | PYQ

If a wave gets refracted into a denser medium, then which of the following is true?

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 __________.

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:

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

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

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:

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 _____ \( \text{nm} \).

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:

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:

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:

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 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.

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:

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 \( 340\,\text{ms}^{-1} \))

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:

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 _________ \( \times 10^{-5} \, \text{m} \).

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:

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 _______ \( \text{cm} \).