$A$ slit of width $d$ is illuminated by white light. The first minimum for red light $(\lambda = 6500\,\mathring{A})$ will fall at $\theta = 30^\circ$ when $d$ will be

In a single slit diffraction pattern:

$A$ 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 $.....$

Light of wavelength $\lambda$ is incident on a slit of width $a$. The resulting diffraction pattern is observed on a screen placed at a distance $D$. If the linear width of the central maximum is equal to the width of the slit,then $D = $ . . . . . . .

For Bragg's diffraction by a crystal to occur,the $X$-ray of wavelength $\lambda$ and interatomic distance $d$ must satisfy which condition?

$A$ single slit of width $0.20 \, mm$ is illuminated with light of wavelength $500 \, nm$. The observing screen is placed $80 \, cm$ from the slit. The width of the central bright fringe will be ..... $mm$.