Multiple reflections and refractions of light in a glass plate When an incident

Question

Multiple reflections and refractions of light in a glass plate When an incident ray of light I strikes the surface of a glass plate, it is divided into a reflected ray R1 and rays labeled R2 . R, R. . and Ti. T:. Ts... that, due to multiple reflections and refractions, are directed away from the top and bottom surfaces of the plate as illustrated in Fig. 4. The following equation can be used to compute the reflectance r, which is the fraction of the incident unpolarized light reflected at each surface dis 2 sin (0,+0,) tan(0,+0 In the above equation, 8, is the angle of illustrated in Fig. 4 Diz Fig. 4 A diagram showing the paths taken by rays of light that experience multiple reflections and refractions at the parallel surfaces of a glass plate. 17. For a glass plate with refractive index n equal to 1.500, the reflectance r is equal to 0.0400 for angles of incidence from zero to about 13 degrees. Assume that the intensity / of the incident ray is 100 W/m, and that the angle of incidence is small enough so that 0.0400. Compute numerical values for the intensities of rays R, through R and Ti through Ts 18. The intensity of ray R, is r/ and the intensity of ray R, is ri (1 -r. Show how to obtain a general expression for the intensity of ray Rn . 19. Rays labeled T. T, T····exit the bottom surface of the glass plate after two or more refractions and after two or more reflections. Show how to obtain a general expression for the intensity of ray T- 20. (a) The perpendicular distance between rays Ri and R: is diz as illustrated in Fig. 4. The distance dz depends on the angle of incidence O,on the thickness h of the plate, and on the refractive index n of the glass Show how to obtain a mathematical expression for diz in terms of O,h and n (b) Show the mathematical details of how to obtain a general expression for the distance du

Explanation / Answer

17. R1 is one reflected and T1 is twice transmitted

for each reflection the intensity falls by 0.04 and for each transmission 0.96

I(r1) = 100*0.04 = 4 W/m2

I(T1) = 100*0.96*0.96 = 92.16 W/m2

R2 is once reflected and twice transmitted where as T2 is twice reflected and twice transmitted

I(R2) = 100*0.04*0.96*0.96 = 3.67 W/m2

I(T2) = 100*0.04*0.96 *0.04 *0.96= 0.147 W/sq.m

R3 has 3-reflections and 1-transmission, T3 has 4 reflections and 2 transmissions

I(R3) = 100*0.043 *0.96 = 0.006 W/sq.m

I(t3) = 100*0.044*0.96 = 0.0003 W/sq.m

R4 has 5 reflections and 1 -transmission, T4 has 6-reflections and 2-transmissions

I(R4) = 100*0.045*0.96 = 9.83e-6 W/sq.m

I(T4) = 3.93e-7 W/sq.m

18)

R1 has one reflection and R2 has one reflection and 2 transmissions. there after every ray will have 2 transmission one at the lower surface and another at the top the exit from the slab , it also has two more reflections from the previous ray

The intensity of Rn can be written as

I(Rn) = rI*(1-r)2 *rn-1 = Irn-1 (1-r)2

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