A linear aperture whose width is \(0.02\) cm is placed immediately in front of a lens of focal length \(60\) cm. The aperture is illuminated normally by a parallel beam of wavelength \(5\times 10^{-5}\) cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is:
1. \( 0.10 \) cm
2. \( 0.25 \) cm
3. \( 0.20 \) cm
4. \( 0.15\) cm

Unpolarised light is incident from the air on a plane surface of a material of refractive index \(\mu\). At a particular angle of incidence \(i\), it is found that the reflected and refracted rays are perpendicular to each other. Which of the following options is correct for this situation?

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. \(2.4~\text{mm}\)