In a single slit diffraction pattern,if the first maxima of light of wavelength $\lambda$ coincides with the first minima of yellow light $(540 \ nm)$,then $\lambda$ is ......... $nm$.

Consider diffraction of light through a rectangular slit which is twice as wide as it is high. Which of the following statements is true?

For a parallel beam of monochromatic light of wavelength $\lambda$,diffraction is produced by a single slit whose width $a$ is of the order of the wavelength of the light. If $D$ is the distance of the screen from the slit,the width of the central maxima will be

In a single slit diffraction pattern, the distance between the first minimum on the left and the first minimum on the right is $5 \,mm$. The screen on which the diffraction pattern is obtained is at a distance of $80 \,cm$ from the slit. The wavelength used is $6000 \mathring{A}$. The width of the slit is (in $\,mm$)

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 monochromatic light of wavelength $650 \ nm$. The value of the slit width $a$ when the first minimum is formed at a diffraction angle of $30^\circ$ is: