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

A beam with wavelength λ falls on a stack of partially reflecting planes with separation d. The angle θ that the beam should make with the planes so that the beams reflected from successive planes may interfere constructively is (where n =1, 2, ……)

(1) ${\sin }^{-1}\left(\frac{{\displaystyle n\lambda }}{{\displaystyle d}}\right)$

(2) ${\tan }^{-1}\left(\frac{{\displaystyle n\lambda }}{{\displaystyle d}}\right)$

(3) ${\sin }^{-1}\left(\frac{{\displaystyle n\lambda }}{{\displaystyle 2d}}\right)$

(4) ${\cos }^{-1}\left(\frac{{\displaystyle n\lambda }}{{\displaystyle 2d}}\right)$

Two coherent sources separated by distance \(d\) are radiating in a phase having wavelength \(\lambda.\) A detector moves in a big circle around the two sources in the plane of the two sources. The angular position of \(n=4\) interference maxima is given as:

            
1. \(\text{sin}^{-1}\left(\frac{n\lambda}{d}\right )\)
2. \(\text{cos}^{-1}\left(\frac{4\lambda}{d}\right)\)
3. \(\text{tan}^{-1}\left(\frac{d}{4\lambda}\right)\)
4. \(\text{cos}^{-1}\left(\frac{\lambda}{4d}\right)\)

Which of the following property of light is a sure proof of wave nature of light?

1.  Interference 

2.  Diffraction

3.  Photoelectric Effect

4.  Both (1) & (2)

Two slits are made one millimetre apart and the screen is placed one metre away. What should the width of each slit be to obtain \(10\) maxima of the double-slit pattern within the central maximum of the single-slit pattern?
1. \(2~\text{mm}\)
2. \(0.2~\text{mm}\)
3. \(0.02~\text{mm}\)
4. \(20~\text{mm}\)