In the visible region of the spectrum the rotation of the place of polarization is given by $\theta =a+\frac{b}{{\lambda }^2}$. The optical rotation produced by a particular material is found to be 30° per mm at $\lambda =5000$Å and 50° per mm at $\lambda =4000\text{Å}$. The value of constant a will be

(1) $+\frac{50°}{9}$per mm

(2) $-\frac{50°}{9}$per mm

(3) $+\frac{9°}{50}$per mm

(4) $-\frac{9°}{50}$per mm

When an unpolarized light of intensity I₀ is incident on a polarizing sheet, the intensity of the light which does not get transmitted is 

(1) Zero

(2) I₀

(3) $\frac{1}{2}{I}_0$

(3) $\frac{1}{4}{I}_0$

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 adjacent diagram, CP represents a wavefront and AO & BP, the corresponding two rays. What would be the condition on θ for constructive interference at P between the ray BP and reflected ray OP?

(1) cosθ = 3λ/2d

(2) cosθ = λ/4d$\theta$

(3) secθ – cosθ = λ/d

(4) secθ – cosθ = 4λ/d

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) $I=A+B\cos \varphi$

When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30^th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20^th bright fringe 

(1) 3.8 mm

(2) 1.6 mm

(3) 7.6 mm

(4) 3.2 mm

In the ideal double-slit experiment, when a glass-plate (refractive index 1.5) of thickness t is introduced in the path of one of the interfering beams (wavelength λ), the intensity at the position where the central maximum occurred previously remains unchanged. The minimum thickness of the glass-plate is 

(1) 2λ

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

(3) $\frac{\lambda }{3}$

(4) λ

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 \(6000 \times10^{-10}\) m, then \(S_1B\) will be equal to:

   
1. \(6\times10^{-6}\) m
2. \(6.6\times10^{-6}\) m
3. \(3.1\times10^{-6}\) m
4. \(3.1\times10^{-7}\) 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 the YDSE apparatus at some angle (say θ) as shown in the 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, the thickness of plate t and refractive index of glass μ