$A$ parallel beam of light of wavelength $6000 \text{ Å}$ is diffracted by a single slit of width $0.3 \text{ mm}$. The angular position of the first minima of the diffracted light is

Assertion : Standard optical diffraction gratings cannot be used for discriminating between $X-$ray wavelengths.
Reason : The grating spacing is not of the order of $X-$ray wavelengths.

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

$A$ 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

$A$ single slit of width $a$ is illuminated by a monochromatic light of wavelength $600 \, nm$. The value of $a$ for which the first minimum appears at $\theta = 30^{\circ}$ on the screen will be ........... $\mu m$.

Through a narrow slit of width $2 \,mm$, a diffraction pattern is formed on a screen kept at a distance $2 \,m$ from the slit. The wavelength of the light used is $6330 \mathring{A}$ and it falls normal to the slit and screen. Then, the distance between the two minima on either side of the central maximum is (in $\,mm$)