Unpolarised light is incident from the air on a plane surface of a material of refractive index \(\mu\). At a particular angle of incidence \(i\), it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

1.	the reflected light is polarised with its electric vector parallel to the plane of incidence.
2.	the reflected light is polarised with its electric vector perpendicular to the plane of incidence.
3.	$\mathrm{}$\(i = \text{sin}^{-1}\frac{1}{\mu}\)
4.	\(i = \text{tan}^{-1}\frac{1}{\mu}\)$\mathrm{}$

In Young's double-slit experiment, the separation \(d\) between the slits is \(2~\text{mm}\), the wavelength \(\lambda\) of the light used is \(5896~\mathring{A}\) and distance \(D\) between the screen and slits is \(100~\text{cm}\). It is found that the angular width of the fringes is \(0.20^{\circ}\). To increase the fringe angular width to \(0.21^{\circ}\) (with same \(\lambda\) and \(D\)) the separation between the slits needs to be changed to:
1. \(1.8~\text{mm}\)
2. \(1.9~\text{mm}\)
3. \(2.1~\text{mm}\)
4. \(1.7~\text{mm}\)

The intensity at the maximum in Young's double-slit experiment is \(I_0\). The distance between the two slits is  \(d= 5\lambda\)$$,  where \(\lambda \) is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance \(D = 10 d\)?
1. \(\dfrac{I_0}{4}\)

2. \(\dfrac{3}{4}I_0\)

3. \(\dfrac{I_0}{2}\)

4. \(I_0\)

Two slits in Young’s experiment have widths in the ratio of \(1:25.\) The ratio of intensity at the maxima and minima in the interference pattern \(\dfrac{I_{max}}{I_{min}}\) is:

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is:
1. \(\dfrac{\pi}{4}~\text{radian}\)
2. \(\dfrac{\pi}{2}~\text{radian}\)
3. \({\pi}~\text{radian}\)
4. \(\dfrac{\pi}{8}~\text{radian}\)

For a parallel beam of monochromatic light of wavelength \(\lambda\), diffraction is produced by a single slit whose width \(a\) is much greater than the wavelength of the light. If \(D\) is the distance of the screen from the slit, the width of the central maxima will be:

In Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is \(\lambda\) is \(K\), (\(\lambda\) being the wavelength of light used). The intensity at a point where the path difference is \(\frac{\lambda}{4}\) will be:
1. \(K\)
2. \(\frac{K}{4}\)
3. \(\frac{K}{2}\)
4. zero

Two periodic waves of intensities I₁ and I₂ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:

1.  $2\left({\mathrm{l}}_1+{\mathrm{l}}_2\right)$

2.  ${\left({\sqrt{\mathrm{I}}}_1+{\sqrt{\mathrm{l}}}_2\right)}^2$

3.  ${\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)}^2$

4.  $2\left({\sqrt{\mathrm{I}}}_1-{\sqrt{\mathrm{l}}}_2\right)$