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. \(10\)

Two coherent sources are \(0.3~\text{mm}\) apart. They are \(1~\text{m}\) away from the screen. The second dark fringe is at a distance of \(0.3~\text{cm}\)  from the center. The distance of the fourth bright fringe from the centre is:
1. \(0.6~\text{cm}\)
2. \(0.8~\text{cm}\)
3. \(1.2~\text{cm}\)
4. \(0.12~\text{cm}\)

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 \(1~\text{mm}.\) The distance between the screen and slits is \(1~\text m.\) The distance between third dark and fifth bright fringe will be:
1. \(3.2~\text{mm}\) 
2. \(1.63~\text{mm}\) 
3. \(0.585~\text{mm}\) 
4. \(2.31~\text{mm}\) 

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 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 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. \(1.2~\text{mm}\)

In Young's double-slit experiment, the slits are separated by \(0.28\) mm and the screen is placed \(1.4\) m away. The distance between the first dark fringe and the fourth bright fringe is obtained to be \(0.6\) cm. The wavelength of the light used in the experiment is:
1. \(3.4 \times 10^{-7}~\text{m}\)
2. \(4.1 \times 10^{-7}~\text{m}\)
3. \(3.4 \times 10^{-9}~\text{m}\)
4. \(4.1 \times 10^{-9}~\text{m}\)