The relation between the fringe width for the red light and yellow light is: (all other things being the same.)
1. \(\beta_\text{red} < \beta_\text{yellow}\)
2. \(\beta_\text{red} > \beta_\text{yellow}\)
3. \(\beta_\text{red} = \beta_\text{yellow}\)
4. \(\beta_\text{red} =2 \beta_\text{yellow}\)

Fringe width in a particular Young's double-slit experiment is measured to be \(\beta.\) What will be the fringe width if the wavelength of the light is doubled, the separation between the slits is halved and the separation between the screen and slits is tripled?
1. \(10\) times
2. \(11\) times
3. Same
4. \(12\) times

If the \(5\)th order maxima of wavelength \(4000~\mathring{A}\) in Young's double-slit experiment coincides with the \(n\)th order maxima of wavelength \(5000~\mathring{A},\) then \(n\) is equal to:
1. \(5\)
2. \(8\)
3. \(4\)
4. \(10\)

In Young's double-slit experiment the light emitted from the source has \(\lambda = 6.5\times 10^{-7}~\text{m}\) and the distance between the two slits is \(1\) mm. The distance between the screen and slits is \(1\) metre. Distance between third dark and fifth bright fringe will be:
1. \(3.2\) mm 
2. \(1.63\) mm
3. \(0.585\) mm
4. \(2.31\) mm

In Young's double-slit experiment, the separation \(d\) between the slits is \(2\) mm, the wavelength \(\lambda\) of the light used is \(5896~\mathring{A}\) and distance \(D\) between the screen and slits is \(100\) cm. It is found that the angular width of the fringes is \(0.20^{\circ}\). To increase the fringe angular width to \(0.21^{\circ}\) (with same \(\lambda\) and \(D\)) the separation between the slits needs to be changed to:
1. \(1.8\) mm
2. \(1.9\) mm
3. \(2.1\) mm
4. \(1.7\) mm

In Young's double slit experiment, the angular width of fringe is \(0.20^{\circ}\) for sodium light of wavelength \(5890~\mathring{A}\). The angular width of fringe, if the complete system is dipped in water, will be:
1. \(0.11^{\circ}\)
2. \(0.15^{\circ}\)
3. \(0.22^{\circ}\)
4. \(0.30^{\circ}\)

In Young's experiment, light of wavelength \(4000~\mathring{A}\) is used to produce bright fringes of width \(0.6\) mm, at a distance of \(2\) meters. If the whole apparatus is dipped in a liquid of refractive index \(1.5\), then fringe width will be:
1. \(0.2~\text{mm}\)
2. \(0.3~\text{mm}\)
3. \(0.4~\text{mm}\)
4. \(1.2~\text{mm}\)

Young's double-slit experiment is performed in a liquid. The \(10\)^th bright fringe in the liquid lies where the \(8\)th dark fringe lies in a vacuum. The refractive index of the liquid is approximately:
1. \(1.81\)
2. \(1.67\)
3. \(1.54\)
4. \(1.33\)