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

$A$ parallel beam of monochromatic light of wavelength $5000 \; \mathring{A}$ is incident normally on a single narrow slit of width $0.001 \; mm$. The light is focused by a convex lens on a screen placed on the focal plane. The first minimum will be formed for the angle of diffraction equal to ........$^o$.

The angular width of the central maximum in a single-slit diffraction pattern does not depend on .........

$A$ slit of width $a$ is illuminated by white light. For red light $(\lambda = 6500 \; \mathring{A})$,the first minima is obtained at $\theta = 30^\circ$. Then the value of $a$ will be

$A$ parallel beam of fast-moving electrons is incident normally on a narrow slit. $A$ screen is placed at a large distance from the slit. If the speed of the electrons is increased,which of the following statements is $CORRECT$?

$A$ linear aperture whose width is $0.02\, cm$ is placed immediately in front of a lens of focal length $60\, cm.$ The aperture is illuminated normally by a parallel beam of wavelength $5 \times 10^{-5}\, cm.$ The distance of the first dark band of the diffraction pattern from the centre of the screen is .....$cm$