PHYS 223 Final, Spring 1996

Seeeaianeuned UN Pa 7 ~O ae > J. oO y a ” Physics 223 FINAL EXAM I -- Ina Young’s experiment the incident light is monochromatic and linearly polarized normal to plane of incidence (page), see Fig. 1. 1. a) Give a general expression for the interference intensity 1 in terms of amplitudes a,, a) and phase difference 8. b) Find the conditions for maxima and minima of I. c) Find an expression for the position y of the mth fringe. d) Answer (c) if a glass plate of thickness t and index n covers slil Sj. e) Deduce the lringe spacing i in(c) and (d) . 2. Find the effect on the central fringe and fringe spacing i if : a) glass plate in (d) changes optical path by A/2 b) the whole apparatus is immersed in liquid of index n= 2 ¢) slit S, is covered by a crystalline 2/2-plate whose axes make 45° with page d) the light source is polychromatic. e) the light source is off-axis 3. If slit S, is twice as wide as 5, find : a) Imex 2nd Imin in terms of a; and 6 b) the visibility of the fringes U -- Natural light is incident at angle / on a plane parallel plate of glass of index n= 1.53 (see Fig. 2) 1. If 1 = 52.0°, find the degree of polarization V of the first reflected ray R; 2. If the reflected light is completely linearly polarized find: a) angle of incidence i b) V of Ist transmitted ray T, c) V of 2nd transmitted ray T, III -- Consider a crystalline prism C (ng = 1.544, n.= 1.553) joined along the diagonal to a glass prism G of the same angle 8 and of index n (see Fig. 3). 1. Using Huygens’ construction, trace the path of the refracted rays with vibration direction in prism C, prism G and in air if : a)n=ny b) n<(n = 1.55)cn, 2. Find the angular separation of the emerging rays in (a) and (b) if 8 = 30.0°. n, COSi ~ n, cosr n, COSI — n, Cosr ' 2n, cosi ' 2n, cost r= 1 5 = ; = 1 . > . ofa . ? . n, COSi +n, cosr n n, COSi +n, COsr n,cosi+n, cosr’ 4 n, COSY + Nn, COSI sin(i- 7) tan(i- r) 2 sinr cosi 2 sinr cosi at