Wave Optics · JEE Advanced previous year questions

A single slit diffraction experiment is performed to determine the slit width using the equation, $\frac{bd}{D}=m\lambda$, 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 ____

A point source $\mathrm{S}$ emits unpolarized light uniformly in all directions. At two points $\mathrm{A}$ and $\mathrm{B}$, the ratio $r=I_{\mathrm{A}}/I_{\mathrm{B}}$ 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 $\mathrm{B}$, then the new value of $r$ will be _____.

PARAGRAPH I In a Young’s double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time $t$ is given by $d=(0.8+0.04\sin \omega t)\mathrm{mm}$, where $\omega =0.08\mathrm{rad}{\mathrm{s}}^{-1}$. The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 Å. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O. 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 ____.

PARAGRAPH I In a Young’s double slit experiment, each of the two slits A and B, as shown in the figure, are oscillating about their fixed center and with a mean separation of 0.8 mm. The distance between the slits at time $t$ is given by $d=(0.8+0.04\sin \omega t)\mathrm{mm}$, where $\omega =0.08\mathrm{rad}{\mathrm{s}}^{-1}$. The distance of the screen from the slits is 1 m and the wavelength of the light used to illuminate the slits is 6000 Å. The interference pattern on the screen changes with time, while the central bright fringe (zeroth fringe) remains fixed at point O. The maximum speed in $\mu$m/s at which the $8^{\text{th}}$ bright fringe will move is ____.