Two light waves given below superimpose at a point.

$y_1=a\sin \left(2\mathrm{\pi t}\right)$
${\mathrm{y}}_2=2\mathrm{asin}\left(2\mathrm{\pi t}+\frac{\mathrm{\pi }}{3}\right)$.

The resultant amplitude of the waves is

1.  $a\sqrt{6}$

2.  $a\sqrt{5}$

3.  $a\sqrt{3}$

4.  $a\sqrt{7}$

When a transparent sheet of thickness t and refractive index $\mu$ is introduced in one of the paths in YDSE having slit width d and distance between slits and screen is D, then the fringe pattern shifts by

1.  $\frac{d}{D}\left(\mu -1\right)t$

2.  $\frac{d}{D\left(\mu -1\right)t}$

3.  $\frac{D}{d}\left(\mu -1\right)t$

4.  $\frac{dt}{\left(\mu -1\right)D}$

Which statement is not true for the polarization of light?

1. Light vibrations are restrained only in one plane.
2. Establishes the longitudinal nature of light.
3. The intensity of light decreases.
4. Both (2) & (3)

The intensity of the polarized light becomes $\frac{1}{a}$ times its initial intensity. The angle between the axis of analyzer and polarizer is

1.  $\theta <mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\tan }^{-1}\sqrt{a-1}$

2.  $\theta <mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\tan }^{-1}\left(\frac{1}{\sqrt{a}}\right)$

3.  $\mathrm{\theta }<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\sin }^{-1}\sqrt{\mathrm{a}-1}$

4.  $\mathrm{\theta }<mspace\; width="1em"></mspace>=<mspace\; width="1em"></mspace>{\sin }^{-1}\left(\frac{1}{\sqrt{\mathrm{a}}}\right)$

Which statement is true for interference?

In Y.D.S.E., if the intensity ratio of bright and dark fringes is 81: 25. The ratio intensity of two waves is

1.  1: 49

2.  49: 4

3.  1: 4

4.  4: 40

Two monochromatic waves each of amplitude A have a phase difference $\frac{\mathrm{\pi }}{2}$ between them. When they superimpose, the amplitude of the resultant wave is

1.  2A

2.  Zero

3.  4A

4.  $A\sqrt{2}$

A screen is placed 100 cm from a single slit which is illuminated with 5000 $\stackrel{\mathrm{o}}{\mathrm{A}}$ light. If the distance between the first and third minima in the diffraction pattern is 5 mm. The width of the slit is

1.  2 mm

2.  0.2 $\mu$m

3.  $2<mspace\; width="1em"></mspace>\times {10}^{-4}<mspace\; width="1em"></mspace>\mathrm{m}$

4.  $4<mspace\; width="1em"></mspace>\times {10}^{-5}<mspace\; width="1em"></mspace>\mathrm{m}$

When the light of a certain wavelength is incident on a plane surface of a material of a glancing angle $30°$, the reflected light is polarised. The angle of refraction is

1.  $60°$

2.  $30°$

3.  $45°$

4.  $40°$

In a double-slit experiment, the distance between the slit is d. The screen is at a distance D from the slits and $\lambda$ is the wavelength of light used. If a dark fringe is formed opposite to a slit on the screen, the order of fringe is

1.  $\frac{{\mathrm{d}}^2+\mathrm{\lambda D}}{2\mathrm{\lambda D}}$

2.  $-\frac{\left(\mathrm{D}+\mathrm{d}\right)}{2\mathrm{\lambda }}$

3.  $\frac{\mathrm{D\lambda }+\mathrm{d}}{2\mathrm{D}}$

4.  $\frac{{\mathrm{D}}^2+\mathrm{d\lambda }}{2\mathrm{\lambda }}$