Wave Optics

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are $\pi/2$ and $\pi/3$ at points A and B respectively. The difference between the resultant intensities at the two points is $xI$. The value of $x$ will be ______.

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 :

In a Young's double slit experiment, a laser light of 560 nm produces an interference pattern with consecutive bright fringes' separation of 7.2 mm. Now another light is used to produce an interference pattern with consecutive bright fringes' separation of 8.1 mm. The wavelength of second light is ______ nm.

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 π. The difference of resultant intensities, at the point A and B, will be _______ I.

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° relative to that of P. The intensity of the emergent light is

Two poloroids P$_1$ and P$_2$ are placed parallel to each other with common axis. The light of intensity I$_0$ passes through a polaroid sheet P$_1$ and then passes through polaroid P$_2$. If P$_2$ is now rotated by 60°, then the intensity of the output light from P$_2$ will be:

In a Young's double slit experiment, the width of the one of the slit is three times the other slit. The amplitude of the light coming from a slit is proportional to the slit-width. Find the ratio of the maximum to the minimum intensity in the interference pattern.

An unpolarized light beam is incident on the polarizer of a polarization experiment and the intensity of light beam emerging from the analyzer is measured as 100 Lumens. Now, if the analyzer is rotated around the horizontal axis (direction of light) by 30° in clockwise direction, the intensity of emerging light will be _______ Lumens.

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)

In a Young's double slit experiment, the slit separation $d$ is 0.3 mm and the screen distance $D$ is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point $O$ is equidistant from the slits and distance $PO$ is 11.0 mm. Which of the following statement(s) is/are correct?

Two coherent monochromatic point sources $S_1$ and $S_2$ of wavelength $\lambda = 600$ nm are placed symmetrically on either side of the center of the circle as shown. The sources are separated by a distance $d = 1.8$ mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $\Delta\theta$. Which of the following options is/are correct?

In a Young's double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is :

Let the refractive index of a denser medium with respect to a rarer medium be $n_{12}$ and its critical angle be $\theta_C$. At an angle of incidence A when light is travelling from denser medium to rarer medium, a part of the light is reflected and the rest is refracted and the angle between reflected and refracted rays is 90°. Angle A is given by :

A single slit of width b is illuminated by a coherent monochromatic light of wavelength λ. If the second and fourth minima in the diffraction pattern at a distance 1 m from the slit are at 3 cm and 6 cm respectively from the central maximum, what is the width of the central maximum ? (i.e. distance between first minimum on either side of the central maximum)

A single slit of width 0.1 mm is illuminated by a parallel beam of light of wavelength 6000 Å and diffraction bands are observed on a screen 0.5 m from the slit. The distance of the third dark band from the central bright band is :

While conducting the Young's double slit experiment, a student replaced the two slits with a large opaque plate in the $x$-$y$ plane containing two small holes that act as two coherent point sources $(S_1,S_2)$ emitting light of wavelength 600 nm. The student mistakenly placed the screen parallel to the $x$-$z$ plane (for $z>0$) at a distance $D=3$ m from the mid-point of $S_1S_2$, as shown schematically in the figure. The distance between the sources $d=0.6003$ mm. The origin O is at the intersection of the screen and the line joining $S_1S_2$. Which of the following is(are) true of the intensity pattern on the screen?

The box of a pin hole camera, of length L, has a hole of radius $a$. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength λ the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{min}$) when :

A Young's double slit interference arrangement with slits $S_1$ and $S_2$ is immersed in water (refractive index = 4/3) as shown in the figure. The positions of maxima on the surface of water are given by $x^2=p^2m^2\lambda^2-d^2$, where $\lambda$ is the wavelength of light in air (refractive index = 1), $2d$ is the separation between the slits and $m$ is an integer. The value of $p$ is

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

A parallel beam of electrons travelling in $x$-direction falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum $p_y$ in the $y$-direction then for a majority of electrons passing through the slit (h is Planck's constant) :