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) $\sqrt{3\lambda D}$

In a single slit diffraction of light of wavelength λ by a slit of width e, the size of the central maximum on a screen at a distance b is

(1) $2b\lambda +e$

(2) $\frac{2b\lambda }{e}$

(3) $\frac{2b\lambda }{e}+e$

(4) $\frac{2b\lambda }{e}-e$