Unpolarised light is incident from the air on a plane surface of a material of refractive index 'μ'. 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?

In Young's double-slit experiment, the separation d between the slits is 2 mm, the wavelength $\lambda$ of the light used is 5896 Å and distance D between the screen and slits is 100 cm. It is found that the angular width of the fringes is 0.20°. To increase the fringe angular width to 0.21° (with same $\lambda$ and D) the separation between the slits needs to be changed to:-

1. 1.8 mm

2. 1.9 mm

3. 2.1 mm

3. 1.7 mm

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light of intensity \(I_0\) is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle \(45^\circ\) with that of P₁. The intensity of transmitted light through P₂ is:
1. $\frac{I_0}{4}$

2. $\frac{I_0}{8}$

3. $\frac{I_0}{16}$

4. $\frac{I_0}{2}$

An interference pattern is obtained with two coherent light sources of intensity ratio \(n.\) In the interference pattern, the ratio \(\frac{I_{max}-I_{min}}{I_{max}+I_{min}}\) will be:
1. \(\frac{\sqrt{n}}{n+1}\)
2. \(\frac{2\sqrt{n}}{n+1}\)
3. \(\frac{\sqrt{n}}{(n+1)^2}\)
4. \(\frac{2\sqrt{n}}{(n+1)^2}\)

A linear aperture whose width is \(0.02\) cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times 10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is:
1. \( 0.10 \) cm
2. \( 0.25 \) cm
3. \( 0.20 \) cm
4. \( 0.15\) cm

The intensity at the maximum in Young's double-slit experiment is I_o. 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 = 10d?

1. $\frac{I_0}{4}$

2. $\frac{3}{4}{I}_0$

3. $\frac{I_0}{2}$

4. $I_0$

In a diffraction pattern due to a single slit of width a, the first minimum is observed at an angle of 30^o when the light of wavelength 5000 Å is incident on the slit. The first secondary maximum is observed at an angle of:

$1.$ ${\sin }^{-1}\left(\frac{2}{3}\right)$

$2.$ ${\sin }^{-1}\left(\frac{1}{2}\right)$

$3.$ ${\sin }^{-1}\left(\frac{3}{4}\right)$

$4.$ ${\sin }^{-1}\left(\frac{1}{4}\right)$