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 center of the screen is:
1. \(0.10~\text{cm}\)
2. \(0.25~\text{cm}\)
3. \(0.20~\text{cm}\)
4. \(0.15~\text{cm}\)
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
1. | \(0.2~\text{mm}\) | 2. | \(0.1~\text{mm}\) |
3. | \(0.5~\text{mm}\) | 4. | \(0.02~\text{mm}\) |
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
A parallel beam of fast-moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?
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 main difference between the phenomena of interference and diffraction is that:
1. | diffraction is caused by reflected waves from a source whereas interference is caused due to the refraction of waves from a source. |
2. | diffraction is caused due to the interaction of waves derived from the same source, whereas interference is the bending of light from the same wavefront. |
3. | diffraction is caused due to the interaction of light from the same wavefront, whereas the interference is the interaction of two waves derived from the same source. |
4. | diffraction is caused due to the interaction of light from the same wavefront whereas interference is the interaction of waves from two isolated sources. |
Red light is generally used to observe diffraction patterns from a single slit. If the blue light is used instead of red light, then the diffraction pattern:
1. | will be clearer. |
2. | will contract. |
3. | will expand. |
4. | will not be visible. |
What will be the angular width of central maxima in Fraunhofer diffraction when the light of wavelength \(6000~\mathring {A}\) is used and slit width is \(12\times 10^{-5}~\text{cm}\)?
1. \(2~\text{rad}\)
2. \(3~\text{rad}\)
3. \(1~\text{rad}\)
4. \(8~\text{rad}\)
1. | \(\dfrac{I_0}{4}\) | 2. | \(\dfrac{I_0}{8}\) |
3. | \(\dfrac{I_0}{16}\) | 4. | \(\dfrac{I_0}{2}\) |