Diffraction

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: $\sin(2^\circ)=0.035$]

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 ________.

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.

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 _____.

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]

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.

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 :

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 :

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 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) :

In an experiment of single slit diffraction pattern, first minimum for red light coincides with first maximum of some other wavelength. If wavelength of red light is 6600 Å, then wavelength of first maximum will be :

In a Young's double slit experiment, the distance between the two identical slits is 6.1 times larger than the slit width. Then the number of intensity maxima observed within the central maximum of the single slit diffraction pattern is :