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

A monochromatic beam of light falls on YDSE apparatus at some angle (say θ) as shown in figure. A thin sheet of glass is inserted in front of the lower slit S₂. The central bright fringe (path difference = 0) will be obtained

(1) At O

(2) Above O

(3) Below O

(4) Anywhere depending on angle θ, thickness of plate t and refractive index of glass μ

Two ideal slits S₁ and S₂ are at a distance d apart, and illuminated by light of wavelength λ passing through an ideal source slit S placed on the line through S₂ as shown. The distance between the planes of slits and the source slit is D. A screen is held at a distance D from the plane of the slits. The minimum value of d for which there is darkness at O is

(1) $\sqrt{\frac{3\lambda D}{2}}$

(2) $\sqrt{\lambda D}$

(3) $\sqrt{\frac{\lambda D}{2}}$

(4) $\sqrt{3\lambda D}$