$A$ slit of width $a$ is illuminated by red light of wavelength $6500 \, \mathring{A}$. The first minimum will fall at $\theta = 30^{\circ}$ if $a$ is equal to:

In a single slit diffraction pattern,identify the incorrect statement from the following.

In an experiment of single slit diffraction pattern,the first minimum for red light coincides with the first maximum of some other wavelength. If the wavelength of red light is $6600\,\mathring{A}$,then the wavelength of the first maximum will be.....$\mathring{A}$

In the diffraction pattern of a single slit,the width of the secondary maxima compared to the central maximum is:

In a single slit diffraction experiment, the first minimum for red light $(660 \ nm)$ coincides with the first secondary maximum of some other wavelength $\lambda$. The value of $\lambda$ is $..... \mathring{A}$.

The box of a pinhole camera,of length $L$,has a hole of radius $a$. It is assumed that when the hole is illuminated by a parallel beam of light of wavelength $\lambda$,the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size (say $b_{min}$) when