With the help of a labelled diagram, show that fringe separation β in Young’s double slit experiment is given by:

                               
where the terms have their usual meaning.

(i) What is the difference between polarised light unpolarised light based on the direction of electric vector E?

(ii) What will be the effect on the width of the central bright fringe in the diffraction pattern of a single slit if :

(1)    Monochromatic light of smaller wavelength is used.

(2)    Slit is made narrower.

At what angle, a ray of light should be incident on the first face AB of a regular glass prism ABC so that the emergent ray grazes the adjacent face AC? See Figure 7 below. (Refractive Index of glass = 1.6)

 

37. Show that the axial chromatic aberration (f_r-f_v) for a convex lens is equal to the product of its mean focal length (f) and dispersive power (ω ) of its material i.e. Prove : (f_r-f_v ) = ω f.

Draw a labelled diagram of an image formed by a compound microscope, with the image at least distance of distinct vision. Write any one expression for its magnifying power.

(i) What is meant by ‘Quantization of charge? 

(ii) In Thomson’s experiment, prove that the ratio of charge to the mass (e/m) of an electron is given by :


where the terms have their usual meaning.