The angular width of the central maximum in the Fraunhofer diffraction for \(\lambda=6000~\mathrm{\mathring{A}}\) is \(\theta_0\). When the same slit is illuminated by another monochromatic light, the angular width decreases by \(30\%\). The wavelength of this light is:
1. \(1800~\mathrm{\mathring{A}}\)
2. \(4200~\mathrm{\mathring{A}}\)
3. \(420~\mathrm{\mathring{A}}\)
4. \(6000~\mathrm{\mathring{A}}\)
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
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. \(\text{sin}^{-1}\frac{1}{4}\)
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. \(2.4~\text{mm}\)
1. | The angular width of the central maximum of the diffraction pattern will increase. |
2. | The angular width of the central maximum will decrease. |
3. | The angular width of the central maximum will be unaffected. |
4. | A diffraction pattern is not observed on the screen in the case of electrons. |
The interplanar distance in a crystal is \(2.8 \times 10^{-8} \) m. The value of the maximum wavelength which can be diffracted:
1. \(2.8 \times 10^{-8} \)
2. \(5.6 \times 10^{-8} \)
3. \(1.4 \times 10^{-8} \)
4. \(7.6 \times 10^{-8} \)
For a crystal with λ = 1 Å and Bragg's angle θ = 60°, the second-order diffraction, 'd' (distance between two consecutive atomic layers) will be:
1. 1.15 Å
2. 0.75 Å
3. 0.55 Å
4. 2.1 Å