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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:

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 _______.

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:

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.)

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:

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:

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.]

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 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.

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 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 __________ \( \pi \times 10^{-13} \, \text{m}^3/\text{s} \).

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:

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:

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 \( \underline{\hspace{1cm}} \, \mu\text{m} \).

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:

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JEE MAIN 2025 7th April Morning Shift

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.