In an experiment, electrons are made to pass through a narrow slit of width '$d$' comparable to their de Broglie wavelength. They are detected on a screen at a distance '$D$' from the slit (see figure). Which of the following graphs can be expected to represent the number of electrons '$N$' detected as a function of the detector position '$y$' ($y = 0$ corresponds to the middle of the slit)?

$A$ single slit diffraction experiment is performed to determine the slit width using the equation,$\frac{b d}{D} = m \lambda$,where $b$ is the slit width,$D$ is the distance between the slit and the screen,$d$ is 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 $.....$

The condition for diffraction is

Which of the following statements are correct with reference to single slit diffraction pattern?
$(I)$ The central maxima is twice as wide as the secondary maxima.
$(II)$ The intensity of secondary maxima decreases as we move away from the central maxima.
$(III)$ The width of the central maxima is independent of the slit width.
$(IV)$ The intensity of the central maxima is the same as that of the secondary maxima.

Light of wavelength $6328 \, \mathring{A}$ is incident on a slit of width $0.2 \, mm$. Find the angular width of the central maximum on a screen at a distance of $9 \, m$ in degrees.

$A$ parallel beam of monochromatic light of wavelength $5000 \mathring{A}$ is incident normally on a single narrow slit of width $0.001 \text{ mm}$. The light is focused by a convex lens on a screen placed on its focal plane. The first minima will be formed for the angle of diffraction of . . . . . . (degree).