$A$ slit of width $a$ is illuminated by red light of wavelength $6500 Å$. If the first diffraction minimum falls at $30^{\circ}$,then the value of $a$ is

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 the diffraction pattern obtained in the two cases is $x \times 10^{-5}\, m$. Find the value of $x$.

$A$ light wave is incident normally on a slit of width $24 \times 10^{-5} \, cm$. The angular position of the second dark fringe from the central maximum is $30^\circ$. What is the wavelength of light in $\mathring{A}$?

In the far-field diffraction pattern of a single slit under polychromatic illumination,the first minimum with the wavelength ${\lambda _1}$ is found to be coincident with the third maximum at ${\lambda _2}$. So,

In the experiment of diffraction due to a single slit,if the slit width is decreased,the width of the central maximum

The width of the central maximum of a diffraction pattern on a single slit does not depend upon: