$A$ 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

In Fraunhofer diffraction due to a single slit,the direction of the second secondary maximum is given by ....... ($a$ is the width of the slit).

$A$ screen is placed at $50 \ cm$ from a single slit,which is illuminated with light of wavelength $600 \ nm$. If the separation between the $1^{st}$ and $3^{rd}$ minima in the diffraction pattern is $3 \ mm$,then the slit width is: (in $mm$)

If $\lambda = 6000 \, \mathring{A}$ and $a = 18 \times 10^{-5} \, \text{cm}$,find the angular width of the central maximum in degrees $(^\circ)$.

$A$ light source with a wavelength of $5000 \, \mathring A$ produces a single-slit diffraction pattern. The first minimum in the diffraction pattern is observed at a distance of $5 \, mm$ from the central maximum. The distance between the slit and the screen is $2 \, m$. Find the width of the slit. (in $, mm$)

$A$ diffraction pattern is obtained by making blue light incident on a narrow slit. If blue light is replaced by red light,then: