Assignment-II

      Detailed Answer:

     

1.Derive equations for the path difference for bright and dark fringes in the case of  Interference in thin films due to reflected light

   In an air-wedge experiment, for a given thin wire, fringe width of 40 µm is obtained. Calculate the expected fringe width if the air-wedge is filled with water of refractive index 1.333.

         Ans: β = 30 µm

2.       In Michelson interferometer arrangement, if one of the mirrors is moved by 0.04 nm, 125 fringes cross the field of view. Calculate the wavelength of light used.

      Ans: λ = 640 nm

3.         A thin plate of refractive index 1.5 displaces 10 fringes when it is introduced in one of the arms of Michelson interferometer. Calculate the thickness of the plate if  λ = 600 nm.

Ans: t = 6 µm

4.       Find the energy and momentum of an X-ray photon whose wavelength is 2 x 10^-11m.

Ans : E= 9.95 x 10^-15 J, P = 3.32 x 10^-23 kg m/s

5.       X-rays of wavelength 0.112 nm is scattered from a carbon target. Calculate the wavelength of X-rays scattered at an angle of 90º with respect to the original direction and the energy of the recoil electron after collision.

      Ans : l¢ =0.1144nm,Energy of the recoil electron = 235.27eV

6.         Calculate the de-Broglie wavelength associated with a proton moving with a velocity of 1/10^th of

velocity of light (mass of proton = 1.67 x 10^-27kg; h = 6.626 x 10^-34Js).

Ans : λ= 1.323 x 10^-14m.

7.         Calculate the minimum energy an electron can posses in an infinitely deep potential well of width 4 nm.

Ans : E = 3.7639 x 10^-21 J (or) 0.0235eV.