**1. Attempt any five of the following: [15M]**

**(a) fringes of equal thickness are observed in a thin glass wedge of R.I-1.52. The fringe spacing is 1mm and wavelength of light used is 5893Å. Calculate the angle of the wedge.**

Given,

$latex \begin{array}{l}\mu=1.52,\;\\\\\lambda=5893\;\overset\circ A\\\\\;\;\;=5893\times10^{-10}m,\\\\\beta=0.1mm\end{array}$

$latex \begin{array}{l}\beta=\frac\lambda{2\mu\theta}\\\\\theta=\frac\lambda{2\mu\beta}\\\\\theta=\frac{5893\times10^{-10}m}{2\times1.52\times0.1\times10^{-3}m}\\\\\theta=1.94\times10^{-3}radians\\\\\theta=\frac{1.94\times10^{-3}}\pi\times180\\\\\;\;\;=0.11^\circ\end{array}$

Diffraction: When light passes over a sharp obstacle or through a narrow opening, it bends and enters into the region of its geometrical shadow. This bending of light is called as diffraction. There are two types of diffraction

1. Fraunhoffer Diffraction: when the source and the screen is effectively at infinite distance from each other, the diffraction is termed as Fraunhoffer diffraction. In this case diffraction takes place due to plane wavefront. In order to obtain diffraction on the screen in the laboratory convex lens are used.

2. Fresnel’s Diffraction. When the source and the screen is at finite distance, the diffraction is

termed as Fresnel’s diffraction. In this case the diffraction takes place due to spherical or

cylindrical wavefront.

We have

$latex \begin{array}{l}V=\frac{\pi d}\lambda\left(NA\right)\\\\\;\;\;=\frac{3.14\times50\times10^{-6}}{0.75\times10^{-6}}\left(0.25\right)\\\\\;\;\;=50.34\end{array}$

The number of guided modes,

$latex \begin{array}{l}Nm=\frac12V^2\\\\\;\;\;\;\;\;=\left(50.34\right)^2\div2\\\\\;\;\;\;\;\;=1369.38\\\\1369.38\cong1369\;modes\end{array}$

Spontaneous Emission | Stimulated Emission |

1. Light has high divergence | 1. Light has very low divergence |

2. Emitted light is non – directional | 2. Emitted light is unidirectional |

3. Emitted light is Incoherent | 3. Emitted light is coherent |

4. Emitted light is polychromatic | 4. Emitted light is highly monochromatic |

5 Emitted light is less intense | 5. Emitted light is highly intense |

When two sine waves oscillating in mutually perpendicular direction are of same frequency, the Lissajous pattern takes the form of an ellipse as shown in the figure. This ellipse is used to determine the phase difference between two signals, by using the formula

$latex \phi=\sin^{-1}\left(\frac{AA’}{BB’}\right)$

By measuring the length AA’ and BB’ on the oscillogram and substituting the values in the above formula phase difference can be determined.

We have

$latex \begin{array}{l}\lambda=\frac h{\sqrt{2mev}}\\\\\;\;\;=\frac{12.26}{\sqrt v}\overset\circ{\;A}\\\\\;\;\;=\frac{12.26}{\sqrt{100}}\\\\\;\;\;=1.226\;\overset\circ A\end{array}$

Manglev train do not slide over steel rail but float on a four inch air cushion over a strongly

magnetized track. Superconducting coils produce magnetic repulsion which levitates the coaches of the train. Hence there is no mechanical friction between the steel rail and the coaches due to wich manglev train can achieve very high speed upto 500 km/hr.

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