The angular width of the central maximum in a single slit diffraction pattern is \(60^\circ\). The width of the slit is \(1~\mu\text{m}\). The slit is illuminated by monochromatic plane waves. If another slit of same width is made near it, Young's fringes can be observed on a screen placed at a distance \(50~\text{cm}\) from the slits. If the observed fringe width is \(1~\text{cm}\), what is the slit separation distance? (i.e. distance between the centers of each slit.)
1. \(25~\mu\text{m}\)
2. \(50~\mu\text{m}\)
3. \(75~\mu\text{m}\)
4. \(100~\mu\text{m}\)

In a double-slit experiment, when a thin film of thickness \(t\) having a refractive index \(\mu\). is introduced in front of one of the slits, the maximum at the centre of the fringe pattern shifts by one fringe width. The value of \(t\) is:
(\(\lambda\) is the wavelength of the light used):
1. \(\frac{\lambda}{2(\mu-1)}\)
2. \(\frac{\lambda}{(2\mu-1)}\)
3. \(\frac{2\lambda}{(\mu-1)}\)
4. \(\frac{\lambda}{(\mu-1)}\)

Orange light of wavelength \(6000 \times 10^{-10} ~\text{m}\) illuminates a single slit of width \(0.6 \times 10^{-4} ~\text{m}\). The maximum possible number of diffraction minima produced on both sides of the central maximum is:
1. \(200\)
2. \(198\)
3. \(400\)
4. \(126\)

Consider the diffraction pattern obtained from the sunlight incident on a pinhole of diameter \(0.1 ~\mathrm{\mu m}\). if the diameter of the pinhole is slightly increased, it will affect the diffraction pattern such that: