In a single slit diffraction experiment,when the distance of separation between the slit and the screen is doubled,the angular separation between the fringes

In a single slit diffraction experiment, for wavelength $\lambda$, the half angular width of the central maximum is $\theta$. For a wavelength $p\lambda$, the half angular width of the central maximum is $q\theta$. What is the ratio of the half angular widths of the first secondary maximum in the first case to the second case?

Ray optics fails when

If a narrow slit of width $2 \, mm$ is illuminated by monochromatic light of wavelength $500 \, nm$,then the distance between the first minima on both sides on a screen at a distance of $1 \, m$ is ....... $mm$.

Light of wavelength $580 \text{ nm}$ is incident normally on a slit of width '$a$'. The distance between the slit and the screen is $2.5 \text{ m}$ and the distance of the second order maximum from the centre of the screen is $14.5 \text{ mm}$ in a diffraction pattern. The value of '$a$' is

The radius $r$ of the $n^{th}$ half-period zone is proportional to: