For constructive interference to take place between two monochromatic light waves of wavelength $\lambda$, the path difference should be 

1. $(2\mathrm{n}-1)\frac{\mathrm{\lambda }}{4}$

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

3. $n\lambda$

4. $(2\mathrm{n}+1)\frac{\mathrm{\lambda }}{2}$

For a parallel beam of monochromatic light of wavelength $\text{'}\mathrm{\lambda }\text{'}$, diffraction is produced by a single slit whose width 'a' is of the wavelength of the light. If 'D' is the distance of the screen from the slit, the width of the central maxima will be

1. $\frac{\mathrm{D\lambda }}{\mathrm{a}}$

2. $\frac{\mathrm{D\lambda }}{\mathrm{a}}$

3. $\frac{2\mathrm{Da}}{\mathrm{\lambda }}$

4. $\frac{2\mathrm{D\lambda }}{\mathrm{a}}$

If the ratio of the intensity of two coherent sources is 4 then the visibility $\frac{{\mathrm{I}}_{\max }-{\mathrm{I}}_{\min }}{{\mathrm{I}}_{\max }+{\mathrm{I}}_{\min }}$ of the fringes is -

1. 4

2. 4/5

3. 3/5

4. 9

In Young's experiment, monochromatic light is used to illuminate the two slits A and B. Interference fringes are observed on a screen placed in front of the slits. Now if a thin glass plate is placed nomally in the path of the beam coming from the slit

1. The fringes will disappear

2. The fringe width will increase

3. The fringe width will decrease

4. There will be no change in the fringe width but the pattern shifts

Two light sources are said to be coherent if they are obtained from

1. Two independent point sources emitting light of the same wavelength

2. A single point source

3. A wide source

4. Two ordinary bulbs emitting light of different wavelengths

In a Young's double slit experiment, the fringe width is found to be 0.4 mm. If the whole apparatus is immersed in water of refractive index 4/3 without disturbing the geometrical arrangement, the new fringe width will be 

1. 0.30 mm

2. 0.40 mm

3. 0.53 mm

4. 450 micron

Young's double slit experiment is carried out by using green, red and blue light, one color at a time. The fringe widths recorded are ${\beta }_{\mathrm{G}}, {\beta }_R$ and ${\beta }_B ,$ respectively. Then

1. ${\beta }_G>{\beta }_B>{\beta }_R$

2. ${\beta }_B>{\beta }_C>{\beta }_R$

3. ${\beta }_R>{\beta }_B>{\beta }_G$

4. ${\beta }_R>{\beta }_G>{\beta }_B$

In the Young's double slit experiment using a monochromatic light of wavelength $\lambda$, the path difference (in terms of an integer n) corresponding to any point having half the peak intensity is 

1. $(2n+1)\frac{\lambda }{2}$

2. $(2n+1)\frac{\lambda }{4}$

3. $(2n+1)\frac{\lambda }{8}$

4. $(2n+1)\frac{\lambda }{16}$

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 $\theta$ with the polarivation axis of first polaroid. is placed between these polaroids then the intensity of light emerging from the last polaroid will be 

1. $\left(\frac{I_0}{8}\right){\sin }^{2}2\theta$

2. $\left(\frac{I_0}{4}\right){\sin }^{2}2\theta$

3. $\left(\frac{I_0}{2}\right){\cos }^4\theta$

4. $I_0{\cos }^4\theta$

Intensities of the two waves of light are I and 4I. The maximum intensity of the resultant wave after superposition is 

1. 5I

2. 9I

3. 16I

4. 25I