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.  $a\sqrt{7}$

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.  $\theta = {\tan }^{-1}\sqrt{a-1}$

2.  $\theta = {\tan }^{-1}\left(\frac{1}{\sqrt{a}}\right)$

3.  $\mathrm{\theta } = {\sin }^{-1}\sqrt{\mathrm{a}-1}$

4.  $\mathrm{\theta } = {\sin }^{-1}\left(\frac{1}{\sqrt{\mathrm{a}}}\right)$

Which statement is true for interference?

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.  $2 \times {10}^{-4} \mathrm{m}$

4.  $4 \times {10}^{-5} \mathrm{m}$

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.  $40°$

The angular width of the principal maximum in Fraunhofer single slit diffraction is 0.1 radian. The angular width of second-order secondary maxima is

1.  0.05 radian

2.  0.1 radian

3.  0.5 radian

4.  0.25 radian

The resolving power of a microscope can be increased by using:

1.  red light.
2.  blue light.
3.  oil between objective lens and object.
4.  both (2) and (3).

Assume that light of wavelength 7000 $\stackrel{\mathrm{o}}{\mathrm{A}}$ is coming from a star. The limit of resolution (in radian) of a telescope whose objective has a diameter of 244 cm, will be

1.  $2.5 \times {10}^{-7}$

2.  $5.0 \times {10}^{-7}$

3.  $3.5 \times {10}^{-7}$

4.  $4.5 \times {10}^{-7}$