The Brewster's angle for an interface should be:
1. \(30^{\circ}<i_b<45^{\circ}\)
2. \(45^{\circ}<i_b<90^{\circ}\)
3. \(i_b=90^{\circ}\)
4. \(0^{\circ}<i_b<30^{\circ}\)

In Young's double-slit experiment, if the separation between coherent sources is halved and the distance of the screen from the coherent sources is doubled, then the fringe width becomes:

Two coherent sources of light interfere and produce fringe patterns on a screen. For the central maximum, the phase difference between the two waves will be: 
1. zero 
2. \(\pi\)
3. \(\frac{3\pi}{2}\)
4. \(\frac{\pi}{2}\)$$

The angular width of the central maximum in the Fraunhofer diffraction for \(\lambda=6000~\mathrm{\mathring{A}}\)  is \(\theta_0\). When the same slit is illuminated by another monochromatic light, the angular width decreases by \(30\%\). The wavelength of this light is:
1. \(1800~\mathrm{\mathring{A}}\)
2. \(4200~\mathrm{\mathring{A}}\)
3. \(420~\mathrm{\mathring{A}}\)
4. \(6000~\mathrm{\mathring{A}}\)

In Young's double-slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has a path difference:
1. \( \frac{5\lambda}{2} \)
2. \( \frac{10\lambda}{2} \)
3. \( \frac{9\lambda}{2} \)
4. \( \frac{11\lambda}{2} \)

In a double-slit experiment, when the light of wavelength \(400~\text{nm}\) was used, the angular width of the first minima formed on a screen placed \(1~\text{m}\) away, was found to be \(0.2^{\circ}\)$$. What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? \(\left(\mu_{\text{water}} = \frac{4}{3}\right)\)
1. \(0.1^{\circ}\)
2. \(0.266^{\circ}\)
3. \(0.15^{\circ}\)
4. \(0.05^{\circ}\)

A linearly polarized monochromatic light of intensity \(10\) lumen is incident on a polarizer. The angle between the direction of polarization of the light and that of the polarizer such that the intensity of output light is \(2.5\) lumen is:

A monochromatic light of frequency \(500\) THz is incident on the slits of a Young's double slit experiment. If the distance between the slits is \(0.2\) mm and the screen is placed at a distance \(1\) m from the slits, the width of \(10\) fringes will be:
1. \(1.5\) mm
2. \(15\) mm
3. \(30\) mm
4. \(3\) mm