$A$ screen is placed $0.5 \,m$ away from a single slit which is illuminated by a monochromatic light of wavelength $6000 \text{ Å}$. If the distance between the first and third minima in the diffraction pattern on the screen is $3 \,mm$, then the slit width is: (in $\,mm$)

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

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 $x$.

$A$ slit of size '$a$' is illuminated by a parallel beam of light of wavelength $\lambda$. The angle at which this light is diffracted is approximately . . . . . . .

$A$ single slit diffraction pattern is formed with light of wavelength $6195 Å$. The second secondary maximum for this wavelength coincides with the third secondary maximum in the pattern for light of wavelength $\lambda_0$. The value of $\lambda_0$ is (in $Å$)

Monochromatic light of wavelength $580 \,nm$ is incident on a slit of width $0.30 \,mm$. The screen is $2 \,m$ from the slit. The width of the central maximum is ........... $\times 10^{-3} \,m$.