A beam of light \(AO\) is incident on a glass slab \((\mu= 1.54)\) in a direction as shown in the figure. The reflected ray \(OB\) is passed through a Nicol prism. On viewing through a Nicole prism, we find on rotating the prism that:

        

1.	the intensity is reduced down to zero and remains zero.
2.	the intensity reduces down somewhat and rises again.
3.	there is no change in intensity.
4.	the intensity gradually reduces to zero and then again increases.

Unpolarized light falls on two polarizing sheets placed one on top of the other. What must be the angle between the characteristic directions of the sheets if the intensity of the final transmitted light is one-third the maximum intensity of the first transmitted beam?

$Given:$
$\cos {75}^0 =0.26$
$\cos {57}^0 =0.57$
$\cos {35}^0 =0.82$
$\cos {15}^0 =0.96$
$$

(1) 75°

(2) 55°

(3) 35°

(4) 15°

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 \(30^{\circ}\) 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

When an unpolarized light of intensity \(I_0\) is incident on a polarizing sheet, the intensity of the light which does not get transmitted is:

When the angle of incidence on a material is 60°, the reflected light is completely polarized. The velocity of the refracted ray inside the material is (in ms^–1)

1. 3 × 10⁸

2. $\left(\frac{{\displaystyle 3}}{{\displaystyle \sqrt{2}}}\right)\times {10}^8$

3. $\sqrt{3}\times {10}^8$

4. 0.5 × 10⁸

Two polaroids are placed in the path of unpolarized beam of intensity I₀ such that no light is emitted from the second polaroid. If a third polaroid whose polarization axis makes an angle θ with the polarization axis of first polaroid, is placed between these polaroids then the intensity of light emerging from the last polaroid will be 

(1) $\left(\frac{{\displaystyle I_0}}{{\displaystyle 8}}\right){\sin }^{2}2\theta$

(2) $\left(\frac{{\displaystyle I_0}}{{\displaystyle 4}}\right){\sin }^{2}2\theta$

(3) $\left(\frac{{\displaystyle I_0}}{{\displaystyle 2}}\right){\cos }^4\theta$

(4) $I_0{\cos }^4\theta$

In the Young's double slit experiment, if the phase difference between the two waves interfering at a point is ϕ, the intensity at that point can be expressed by the expression-
(where A and B depend upon the amplitudes of the two waves)
(1) $I=\sqrt{A^2+B^2{\cos }^2\varphi }$
(2) $I=\frac{A}{B}\cos \varphi$
(3) $I=A+B\cos \frac{\varphi }{2}$
(4) $I=A+B\cos \varphi$

In the figure is shown Young’s double-slit experiment, Q is the position of the first bright fringe on the right side of O. P is the 11^th bright fringe on the other side, as measured from Q. If the wavelength of the light used is 6000 × 10^–10 m, then S₁B will be equal to 

(1) 6 × 10^–6 m

(2) 6. 6 × 10^–6 m

(3) 3.138 × 10^–7 m

(4) 3.144 × 10^–7 m

In Young’s double slit experiment, the two slits act as coherent sources of equal amplitude A and wavelength λ. In another experiment with the same set up the two slits are of equal amplitude A and wavelength λ but are incoherent. The ratio of the intensity of light at the mid-point of the screen in the first case to that in the second case is 

(1) 1 : 2

(2) 2 : 1

(3) 4 : 1

(4) 1 : 1