# Int Physics Olympiad Questions 1_2_3 - Q1 A plane...

This preview shows pages 1–3. Sign up to view the full content.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Q1 A plane monochromatic light wave, wavelength Î» and frequency f , is incident normally on two identical narrow slits, separated by a distance d , as indicated in Figure 1.1. The light wave emerging at each slit is given, at a distance x in a direction Î¸ at time t , by )] / ( 2 cos[ Î» Ï€ x ft a y- = where the amplitude a is the same for both waves. (Assume x is much larger than d ). (i) Show that the two waves observed at an angle Î¸ to a normal to the slits, have a resultant amplitude A which can be obtained by adding two vectors, each having magnitude a , and each with an associated direction determined by the phase of the light wave. Verify geometrically, from the vector diagram, that Î¸ cos 2 a A = where Î¸ Î» Ï€ Î² sin d = (ii) The double slit is replaced by a diffraction grating with N equally spaced slits, adjacent slits being separated by a distance d . Use the vector method of adding amplitudes to show that the vector amplitudes, each of magnitude a , form a part of a regular polygon with vertices on a circle of radius R given by , sin 2 Î² a R = Deduce that the resultant amplitude is Î² Î² sin sin N a 1 Î¸ Î¸ Figure 1.1 d and obtain the resultant phase difference relative to that of the light from the slit at the edge of the grating. (iii) Sketch, in the same graph, sin NÎ² and (1/sin Î² ) as a function of Î² . On a separate graph show how the intensity of the resultant wave varies as a function of Î². (iv) Determine the intensities of the principal intensity maxima....
View Full Document

## This note was uploaded on 11/08/2011 for the course PHYS 0000 taught by Professor Na during the Spring '11 term at Rensselaer Polytechnic Institute.

### Page1 / 6

Int Physics Olympiad Questions 1_2_3 - Q1 A plane...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online