Light of wavelength $\lambda$ in air enters a medium of refractive index $\mu$. Two points in this medium, lying along the path of this light, are at a distance x apart. The phase difference between these points is:

1. $\frac{2\mathrm{\pi \mu x}}{\lambda }$

2. $\frac{2\mathrm{\pi x}}{\mu \lambda }$

3. $\frac{2\mathrm{\pi }(\mathrm{\mu }-1)\mathrm{x}}{\lambda }$

4. $\frac{2\mathrm{\pi x}}{(\mu -1)\lambda }$

The ratio of the intensity at the centre of a bright fringe to the intensity at a point one-quarter of the fringe width from the centre is:

1. 2

2. 1/2

3. 4

4. 16

In Young's double-slit interference experiment, if the slit separation is made threefold, the fringe width becomes:

1. sixfold

2. threefold

3. 3/6 fold

4. 1/3 fold

In Young's interference experiment, if the slits are of unequal width, then:

1. no fringes will be formed

2. the positions of minimum intensity will not be completely dark

3. bright fringe as displaced from the original central position

4. distance between two consecutive dark fringes will not be equal to the distance between two consecutive bright fringes

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase between the beams is $\mathrm{\pi }/2$ at point A and $\mathrm{\pi }$ at point B. Then, the difference between the resultant intensities at A and B is:

1. 2I

2. 4I

3. 5I

4. 7I

Two coherent light sources P and Q each of wavelength $\lambda$ are separated by a distance 3$\lambda$. The maximum number of minima formed on line AB, which runs from $-\infty to +\infty$, is

1. 2

2. 4

3. 6

4. 8

The YDSE apparatus is as shown in figure. The condition for point P to be a dark fringe is:

($\lambda$=wavelength of light waves)

1. $(l_1-l_3)+(l_2-l_4)=n\lambda$

2. $(l_1-l_2)+(l_3-l_4)=\frac{(2n-1)\lambda }{2}$

3. $(l_1+l_3)+(l_2+l_4)=\frac{(2n-1)\lambda }{2}$

4. $(l_1-l_2)+(l_4-l_3)=\frac{(2n-1)\lambda }{2}$

In a double-slit experiment, two parallel slits are illuminated first by light of wavelength 400 nm and then by the light of unknown wavelength. The fourth-order dark fringe resulting from the known wavelength of light falls in the same place on the screen as the second-order bright fringe from the unknown wavelength. The value of the unknown wavelength of the light is:

1. 900 nm

2. 700 nm

3. 300 nm

4. none of these

In Young's double-slit experiment d/D=10^-4(d=distance between slits, D=distance of screen from the slits). At point P on the screen, the resulting intensity is equal to the intensity due to the individual slit $I_0$. Then, then the distance of point P from the central maximum is $(\lambda =6000 \stackrel{0}{A})$

1. 2 mm

2. 1 mm

3. 0.5 mm

4. 4 mm

In Young's double-slit experiment, the y-coordinates of central maximum and 10th maximum are 2 cm and 5 cm, respectively. When the YDSE apparatus is immersed in a liquid of refractive index 1.5, the corresponding y-coordinates will be:

1. 2 cm, 7.5 cm

2. 3 cm, 6 cm

3. 2 cm, 4 cm

4. 4/3 cm, 103 cm