Due to which optical phenomenon do we not see the shadow of an opaque object clearly?

When the frequency of the light used is changed from $4 \times 10^{14} \ s^{-1}$ to $5 \times 10^{14} \ s^{-1}$, the angular width of the principal (central) maximum in a single slit Fraunhofer diffraction pattern changes by $0.6 \ \text{radian}$. What is the width of the slit? (Assume that the experiment is performed in vacuum.)

In a Fraunhofer diffraction experiment, a single slit of width $0.5 ~mm$ is illuminated by a monochromatic light of wavelength $600 ~nm$. The diffraction pattern is observed on a screen at a distance of $50 ~cm$ from the slit. What will be the linear separation of the first order minima (in $~mm$)?

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 $..... \mathring{A}$.

Angular width $(\beta)$ of the central maximum of a diffraction pattern on a single slit does not depend upon

The distance between the first and the sixth minima in the diffraction pattern of a single slit is $0.5 \, mm$. The screen is $0.5 \, m$ away from the slit. If the wavelength of light used is $5000 \, \mathring{A}$,then the slit width will be ....... $mm$.