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

Two point sources X and Y emit waves of same frequency and speed but Y lags in phase behind X by 2πl radian. If there is a maximum in direction D the distance XO using n as an integer is given by

(1) $\frac{\lambda }{2}(n-l)$

(2) $\lambda (n+l)$

(3) $\frac{\lambda }{2}(n+l)$

(4) $\lambda (n-l)$

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. \(\text{cos}^{-1}\left(\frac{\lambda}{4d}\right)\)

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

The ratio of intensities of consecutive maxima in the diffraction pattern due to a single slit is

(1) 1 : 4 : 9

(2) 1 : 2 : 3

(3) $1:\frac{4}{9{\pi }^2}:\frac{4}{25{\pi }^2}$

(4) $1:\frac{1}{{\pi }^2}:\frac{9}{{\pi }^2}$

A wave is propagating in a medium of electric dielectric constant 2 and relative magnetic permeability 50. The wave impedance of such a medium is

(1) 5 Ω

(2) 376.6 Ω

(3) 1883 Ω

(4) 3776 Ω

A plane electromagnetic wave of wave intensity 6 W/m² strikes a small mirror area 40 cm², held perpendicular to the approaching wave. The momentum transferred by the wave to the mirror each second will be

(1) $6.4\times {10}^{-7}kg-m/s^2$

(2) $4.8\times {10}^{-8}kg-m/s^2$

(3) $3.2\times {10}^{-9}kg-m/s^2$

(4) $1.6\times {10}^{-10}kg-m/s^2$