The separation between successive fringes in a double-slit arrangement is x. If the whole arrangement is dipped underwater, what will be the new fringe separation? [The wavelength of light being used is 5000 $\stackrel{0}{A}$]

1. 1.5 x

2. x

3. 0.75 x

4. 2 x

If the intensities of the two interfering beams in Young's double-slit experiment be ${\mathrm{I}}_1 \mathrm{and} {\mathrm{I}}_2$, then the contrast between the maximum and minimum intensity is good when

1. ${\mathrm{l}}_1$ is much greater than ${\mathrm{I}}_2$

2. ${\mathrm{l}}_1$ is much smaller than ${\mathrm{I}}_2$

3. ${\mathrm{I}}_1={\mathrm{I}}_2$

4. Either ${\mathrm{I}}_1=0 \mathrm{or} {\mathrm{I}}_2=0$

The fringe width at a distance of 50 cm from the slits in Young's experiment for light of wavelength 6000 $\stackrel{0}{A}$ is 0.048 cm. The fringe width at the same distance for $\lambda =5000 \stackrel{0}{A}$, will be:

1. 0.04 cm

2. 0.4 cm

3. 0.14 cm

4. 0.45 cm

In an experiment, the two slits are 0.5 mm apart and the fringes are observed from a distance of 100 cm from the plane of the slits. The distance of the 11th bright fringe from the 1st bright fringe is 9.72 mm. The wavelength is: 

1. $4.86\times {10}^{-5} cm$

2. $5.72\times {10}^{-4} cm$

3. $5.87\times {10}^{-4} cm$

4. $3.25\times {10}^{-4} cm$

Two light rays having the same wavelength $\lambda$ in vacuum are in phase initially. Then the first ray travels a path $L_1$ through a medium of refractive index $n_1$, while the second ray travels a path of length $L_2$ through a medium of refractive index $n_2$. The two waves are then combined to observe interference. The phase difference between the two waves is:

1. $\frac{2\mathrm{\pi }}{\lambda }(L_1-L_1)$

2. $\frac{2\mathrm{\pi }}{\lambda }(n_1{L}_1-n_2{L}_2)$

3. $\frac{2\mathrm{\pi }}{\lambda }(n_2{L}_1-n_1{L}_2)$

4. $\frac{2\mathrm{\pi }}{\lambda }\left(\frac{L_1}{n_1}-\frac{L_2}{n_2}\right)$

The equations of two interfering waves are $y_1=b \cos \omega t and y_2=b \cos (\omega t+\varphi )$. For destructive interference, the phase difference $\varphi$ is :

1. $0°$

2. $360°$

3. $180°$

4. $720°$

When two coherent monochromatic light beams of intestines I and 4I are superimposed, what are the maximum and minimum possible intensities in the resulting beams?

1. 5l and l

2. 5l and 3l

3. 9l and l

4. 9l and 3l

In a Young's double-slit experiment, the source is white light. One of the holes is covered by a red filter and another by a blue filter. In this case:

1. there shall be alternate interference patterns of red and blue

2. there shall be an interference pattern for red distinct from that for blue

3. there shall be no interference fringes

4. there shall be an interference pattern for red mixing with one for blue

Two non-coherent sources emit a light beam of intensities I and 4I. The maximum and minimum intensities in the resulting beam are: 

1. 9l and l

2. 9l and 3l

3. 5l and l

4. there is no interference, the intensity is 5I everywhere

In Young's double-slit experiment, the distance of the nth dark fringe from the centre is:

1. $n\left(\frac{\lambda D}{2d}\right)$

2. $n\left(\frac{2d}{\lambda D}\right)$

3. $(2n-1)\frac{\lambda D}{2d}$

4. $(2n-1)\frac{4d}{\lambda D}$