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

In a YDSE bi-chromatic light of wavelengths, 400 nm and 560 nm are used. The distance between the slits is 0.1 mm and the distance between the plane of the slits and the screen is 1m. The minimum distance between two successive regions of complete darkness is 

(1) 4 mm

(2) 5.6 mm

(3) 14 mm

(4) 28 mm

In Young's double-slit experiment, the intensity at a point is (1/4) of the maximum intensity. Angular position of this point is :

(1) sin^-1(λ/d)

(2) sin^-1(λ/2d)

(3) sin^-1(λ/3d)

(4) sin^-1(λ/4d)

A beam of electron is used in a YDSE experiment. The slit width is d. When the velocity of the electron is increased, then,

(1) No interference is observed

(2) Fringe width increases

(3) Fringe width decreases

(4) Fringe width remains the same