Wave Optics

The maximum speed in $\mu$m/s at which the $8^{\text{th}}$ bright fringe will move is _____.

A plane polarized blue light ray is incident on a prism such that there is no reflection from the surface of the prism. The angle of deviation of the emergent ray is $\delta = 60^\circ$ (see Figure-1). The angle of minimum deviation for red light from the same prism is $\delta_{\min} = 30^\circ$ (see Figure-2). The refractive index of the prism material for blue light is $\sqrt3$. Which of the following statement(s) is(are) correct?

Match the temperature of a black body given in List-I with an appropriate statement in List-II, and choose the correct option.

[Given: Wien's constant as $2.9\times10^{-3}$ m-K and $\dfrac{hc}{e} = 1.24\times10^{-6}$ V-m]

A monochromatic light wave is incident normally on a glass slab of thickness $d$, as shown in the figure. The refractive index of the slab increases linearly from $n_1$ to $n_2$ over the height $h$. Which of the following statement(s) is(are) true about the light wave emerging out of the slab?

The electric field associated with an electromagnetic wave propagating in a dielectric medium is given by $\vec E = 30(2\hat x + \hat y)\sin\left[2\pi\left(5\times10^{14}\,t - \frac{10^7}{3}z\right)\right]\ \mathrm{V\,m^{-1}}$. Which of the following option(s) is(are) correct?

[Given: The speed of light in vacuum, $c = 3\times10^8\ \mathrm{m\,s^{-1}}$]

A double slit setup is shown in the figure. One of the slits is in medium 2 of refractive index $n_2$. The other slit is at the interface of this medium with another medium 1 of refractive index $n_1\ (\neq n_2)$. The line joining the slits is perpendicular to the interface and the distance between the slits is $d$. The slit widths are much smaller than $d$. A monochromatic parallel beam of light is incident on the slits from medium 1. A detector is placed in medium 2 at a large distance from the slits, and at an angle $\theta$ from the line joining them, so that $\theta$ equals the angle of refraction of the beam. Consider two approximately parallel rays from the slits received by the detector.

Which of the following statement(s) is(are) correct?

Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ______ $\times10^{-5}$ m.

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 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 :

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 $\dfrac5x$. Then, the value of $x$ will be equal to :

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.

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

For a specific wavelength 670 nm of light coming from a galaxy moving with velocity $v$, the observed wavelength is 670.7 nm. The value of $v$ is :

In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ______ nm.

In young's double slit experiment performed using a monochromatic light of wavelength $\lambda$, when a glass plate ($\mu=1.5$) of thickness $x\lambda$ is introduced in the path of the one of the interfering beams, the intensity at the position where the central maximum occurred previously remains unchanged. The value of $x$ will be :

In a Young's double slit experiment, an angular width of the fringe is 0.35° on a screen placed at 2 m away for particular wavelength of 450 nm. The angular width of the fringe, when whole system is immersed in a medium of refractive index 7/5, is $\dfrac1\alpha$. The value of $\alpha$ is ______.

Using Young's double slit experiment, a monochromatic light of wavelength 5000 Å produces fringes of fringe width 0.5 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 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 $5\times10^{-2}$ m towards the slits, the change in fringe width is $3\times10^{-3}$ cm. If the distance between the slits is 1 mm, then the wavelength of the light will be ______ nm.

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)

In Young's double slit experiment, the fringe width is 12 mm. If the entire arrangement is placed in water of refractive index $\dfrac43$, then the fringe width becomes (in mm) :