Wave Optics

In the List-I, four optical effects are mentioned. The physical phenomena of light which are essential to describe these optical effects are given in List-II. Choose the option which describes the correct match between the entries in List-I to those in List-II.

In a single slit diffraction experiment, a slit of width $(0.016\pm0.002)$ mm is used to measure the wavelength of a monochromatic light source. In the diffraction pattern, the angular distance between the central maximum and first minimum is measured to be $(2^\circ\pm40')$. The value of the fractional error in the measurement of wavelength is:
[Given: $\sin(2^\circ)=0.035$]

As shown in the figure, a ray $AB$ of unpolarized light enters from water of refractive index $n_w=4/3$ into a medium of refractive index $n_p=4/\sqrt3$ after passing through a glass plate of refractive index $n_g=1.5$ and a layer of water. At a particular incident angle $i$ the reflected ray $CD$ is polarized in the direction as shown in the figure. The value of $i$ (in degrees) is:

In single slit diffraction pattern, the wavelength of light used is 628 nm and slit width is 0.2 mm, the angular width of central maximum is $\alpha\times10^{-2}$ degrees. The value of $\alpha$ is ________.

In a Young's double slit experiment, the intensity at some point on the screen is found to be $\dfrac34$ times of the maximum of the interference pattern. The path difference between the interfering waves at this point is $\dfrac\lambda x$ where $\lambda$ is wavelength of the incident light. The value of $x$ is ________.

A slit of width $a$ is illuminated by light of wavelength $\lambda$. The linear separation between 1st and 3rd minima in the diffraction pattern produced on a screen placed at a distance $D$ from the slit system is ________.

A telescope with objective diameter $R$ is used to observe a distant star emitting light of wavelength 500 nm, at a resolution of $5\times10^{-7}$ radian. The value of $R$ is ________ cm.

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.

An unpolarized light of certain intensity passes through a combination of two polarizers whose transmission axes are at 30° and 90°, respectively, with respect to the horizontal axis. A third polarizer with its transmission axis at 60° with the horizontal axis is placed between the two existing polarizers. The ratio of the output intensities with and without the third polarizer 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 7th bright fringe, obtained with both slits uncovered. If the light source wavelength is 450 nm, the thickness of mica sheet is $\alpha\times10^{-9}$ m. The value of $\alpha$ is ________.

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is 2.4 μm. If the experiment is carried out in another medium having refractive index 1.2, the fringe width will be ________ μm.

The maximum intensity in a Young's double slit experiment is $I_o$. 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 interference experiment the path difference between two interfering waves at a point $A$ on the screen is $\lambda/3$, where $\lambda$ is the wavelength of these waves, and at another point $B$ the path difference is $\lambda/6$. The ratio of intensities at points $A$ and $B$ is ________.

An unpolarized light of intensity $I_o$ 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° and intensity of light emerged from analyser is $\dfrac38I_o$, the angle of rotation of the light by the solution with respect to analyser is ________ degrees.

In a Young double slit experiment, the wavelength of incident light is 6000 Å, the separation between slits $S_1$ and $S_2$ is 5 cm and the distance between slits plane and screen is 50 cm, as shown in the figure below. If the resultant intensity at $P$ is equal to the intensity due to individual slits, the path difference between interfering waves is ________ Å.

A solid glass sphere of refractive index $n = \sqrt3$ and radius $R$ contains a spherical air cavity of radius $\dfrac{R}{2}$, as shown in the figure. A very thin glass layer is present at the point O so that the air cavity (refractive index $n = 1$) remains inside the glass sphere. An unpolarized, unidirectional and monochromatic light source $S$ emits a light ray from a point inside the glass sphere towards the periphery of the glass sphere. If the light is reflected from the point O and is fully polarized, then the angle of incidence at the inner surface of the glass sphere is $\theta$. The value of $\sin\theta$ is _____.

A single slit diffraction experiment is performed to determine the slit width using the equation, $\dfrac{bd}{D} = m\lambda$, where $b$ is the slit width, $D$ the shortest distance between the slit and the screen, $d$ the distance between the $m^{\text{th}}$ diffraction maximum and the central maximum, and $\lambda$ is the wavelength. $D$ and $d$ are measured with scales of least count of 1 cm and 1 mm, respectively. The values of $\lambda$ and $m$ are known precisely to be 600 nm and 3, respectively. The absolute error (in $\mu$m) in the value of $b$ estimated using the diffraction maximum that occurs for $m = 3$ with $d = 5$ mm and $D = 1$ m is _____.

In a Young's double slit experiment, a combination of two glass wedges $A$ and $B$, having refractive indices 1.7 and 1.5, respectively, are placed in front of the slits, as shown in the figure. The separation between the slits is $d = 2$ mm and the shortest distance between the slits and the screen is $D = 2$ m. Thickness of the combination of the wedges is $t = 12\ \mu$m. The value of $l$ as shown in the figure is 1 mm. Neglect any refraction effect at the slanted interface of the wedges. Due to the combination of the wedges, the central maximum shifts (in mm) with respect to O by _____.

A point source S emits unpolarized light uniformly in all directions. At two points A and B, the ratio $r = I_A/I_B$ of the intensities of light is 2. If a set of two polaroids having $45^{\circ}$ angle between their pass-axes is placed just before point B, then the new value of $r$ will be _____.

The $8^{\text{th}}$ bright fringe above the point O oscillates with time between two extreme positions. The separation between these two extreme positions, in micrometer ($\mu$m), is _____.