In Young's double-slit experiment, if there is no initial phase difference between the light from the two slits, a point on the screen corresponding to the fifth minimum has a path difference:
1. \( \dfrac{5\lambda}{2} \)
2. \( \dfrac{10\lambda}{2} \)
3. \( \dfrac{9\lambda}{2} \)
4. \( \dfrac{11\lambda}{2} \)
The angular width of the central maximum in the Fraunhofer diffraction for \(\lambda=6000~{\mathring{A}}\) 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. \(1800~{\mathring{A}}\)
2. \(4200~{\mathring{A}}\)
3. \(420~{\mathring{A}}\)
4. \(6000~{\mathring{A}}\)
In a double-slit experiment, when the light of wavelength \(400~\text{nm}\) was used, the angular width of the first minima formed on a screen placed \(1~\text{m}\) away, was found to be \(0.2^{\circ}.\) What will be the angular width of the first minima, if the entire experimental apparatus is immersed in water? \(\left(\mu_{\text{water}} = \dfrac{4}{3}\right)\)
1. \(0.1^{\circ}\)
2. \(0.266^{\circ}\)
3. \(0.15^{\circ}\)
4. \(0.05^{\circ}\)
Two periodic waves of intensities I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is:
1.
2.
3.
4.
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. |
In Young’s double slit experiment, the slits are \(2~\text{mm}\) apart and are illuminated by photons of two wavelengths \(\lambda_1 = 12000~\mathring{A}\) and \(\lambda_2 = 10000~\mathring{A}\). 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. \(8~\text{mm}\)
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 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. \(2.4~\text{mm}\)
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. | \(\dfrac{2D\lambda}{a}\) | 2. | \(\dfrac{D\lambda}{a}\) |
3. | \(\dfrac{Da}{\lambda}\) | 4. | \(\dfrac{2Da}{\lambda}\) |