In Young's double-slit experiment, the separation \(d\) between the slits is \(2~\text{mm}\), the wavelength \(\lambda\) of the light used is \(5896~\mathring{\text{A}}\) and distance \(D\) between the screen and slits is \(100~\text{cm}\). 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. \(1.8~\text{mm}\)
2. \(1.9~\text{mm}\)
3. \(2.1~\text{mm}\)
4. \(1.7~\text{mm}\)

The intensity at the maximum in Young's double-slit experiment is \(I_0\). The distance between the two slits is  \(d= 5\lambda\)$$,  where \(\lambda \) is the wavelength of light used in the experiment. What will be the intensity in front of one of the slits on the screen placed at a distance \(D = 10 d\)?
1. \(\frac{I_0}{4}\)
2. \(\frac{3}{4}I_0\)
3. \(\frac{I_0}{2}\)
4. \(I_0\)

In a diffraction pattern due to a single slit of width \(a\), the first minimum is observed at an angle of \(30^{\circ}\) when the light of wavelength \(5000~\mathring{\text{A}}\) is incident on the slit. The first secondary maximum is observed at an angle of:
1. \(\text{sin}^{-1}\frac{2}{3}\)
2. \(\text{sin}^{-1}\frac{1}{2}\)
3. \(\text{sin}^{-1}\frac{3}{4}\)
4. \(\text{sin}^{-1}\frac{1}{4}\)

Two slits in Young’s experiment have widths in the ratio of \(1:25\). The ratio of intensity at the maxima and minima in the interference pattern \(\frac{I_{max}}{I_{min}}\) is:
1. \(\frac{9}{4}\)
2. \(\frac{121}{49}\)
3. \(\frac{49}{121}\)
4. \(\frac{4}{9}\)

At the first minimum adjacent to the central maximum of a single slit diffraction pattern, the phase difference between the Huygen’s wavelet from the edge of the slit and the wavelet from the midpoint of the slit is:
1. \(\frac{\pi}{4}\text{radian}\)
2. \(\frac{\pi}{2}\text{radian}\)
3. \({\pi}~\text{radian}\)
4. \(\frac{\pi}{8}\text{radian}\)

For a parallel beam of monochromatic light of wavelength \(\lambda\), diffraction is produced by a single slit whose width \(a\) is much greater than 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. \(\frac{2D\lambda}{a}\)
2. \(\frac{D\lambda}{a}\)
3. \(\frac{Da}{\lambda}\)
4. \(\frac{2Da}{\lambda}\)

A beam of light of \(\lambda = 600~\text{nm}\) from a distant source falls on a single slit \(1~\text{mm}\) wide and the resulting diffraction pattern is observed on a screen \(2~\text{m}\) away. The distance between the first dark fringes on either side of the central bright fringe is:
1. \(1.2~\text{cm}\)
2. \(1.2~\text{mm}\)
3. \(2.4~\text{cm}\)
4. \(2.4~\text{mm}\)

In Young's double-slit experiment, the intensity of light at a point on the screen where the path difference is \(\lambda\) is \(K\), (\(\lambda\) being the wavelength of light used). The intensity at a point where the path difference is \(\frac{\lambda}{4}\) will be:
1. \(K\)
2. \(\frac{K}{4}\)
3. \(\frac{K}{2}\)
4. zero

In Young’s double slit experiment, the slits are \(2~\text{mm}\) apart and are illuminated by photons of two wavelengths \(\lambda_1 = 12000~\mathring{\text{A}}\) and \(\lambda_2 = 10000~\mathring{\text{A}}\). At what minimum distance from the common central bright fringe on the screen, \(2~\text{m}\) from the slit, will a bright fringe from one interference pattern coincide with a bright fringe from the other?
1. \(6~\text{mm}\)
2. \(4~\text{mm}\)
3. \(3~\text{mm}\)
4. \(8~\text{mm}\)