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

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

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

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

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

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

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 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 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