On superposition of two waves \(y_{1}=3sin\left ( \omega t-kx \right )\) and \(y_{2}=4sin\left ( \omega t-kx+\frac{\pi }{2} \right )\) at a point, the amplitude of the resulting wave will be:

1.  7

2.  5

3.  $\sqrt{7}$

4.  6.5

If the polarising angle for a material is $60°$, then the refractive index of the material will be:

1.  $\frac{1}{\sqrt{3}}$

2.  $\frac{3}{2}$

3.  $\sqrt{3}$

4.  $\frac{\sqrt{3}}{2}$

Five identical polaroids are placed coaxially with \(45^{\circ}\) angular separation between pass axes of adjacent polaroids as shown in the figure. (I₀: Intensity of unpolarized light)
          
The intensity of light, I, emerging out of the 5^th polaroid is:

1.  $\frac{{\mathrm{I}}_0}{4}$

2.  $\frac{{\mathrm{I}}_0}{8}$

3.  $\frac{{\mathrm{I}}_0}{16}$

4.  $\frac{{\mathrm{I}}_0}{32}$

Two light sources are said to be coherent when their:

Light waves of intensities \(I\) and \(9I\) interfere to produce a fringe pattern on a screen. The phase difference between the waves at point P is $\frac{3\mathrm{\pi }}{2}$ and 2$\mathrm{\pi }$ at other point Q. The ratio of intensities at P and Q is:

1.  8: 5

2.  5: 8

3.  1: 4

4.  9: 1

Two coherent sources are 0.3 mm apart. They are 1 m away from the screen. The second dark fringe is at a distance of 0.3 cm from the center. The distance of the fourth bright fringe from the centre is:

1.  0.6 cm

2.  0.8 cm

3.  1.2 cm

4.  0.12 cm

Huygens' wave theory allows us to know the:

Unpolarized light of intensity 32 Wm^–2 passes through three polarizers such that the transmission axes of the first and second polarizer make an angle of 30° with each other and the transmission axis of the last polarizer is crossed with that of the first. The intensity of the final emerging light will be:

1. 32 Wm^–2

2. 3 Wm^–2

3. 8 Wm^–2

4. 4 Wm^–2

If we observe the single slit Fraunhofer diffraction with wavelength $\mathrm{\lambda }$ and slit width d, the width of the central maxima is 2$\mathrm{\theta }$. On decreasing the slit width for the same wavelength $\mathrm{\lambda }$:

Two polaroids P₁ and P₂ are placed with their axis perpendicular to each other. Unpolarised light of intensity I_o is incident on P₁. A third polaroid P₃ is kept in between P₁ and P₂ such that its axis makes an angle 45° 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. $\frac{I_0}{2}$