r_0 coefficient at the air side, which means Er0/E = r0; r_1 represents the reflection coefficient at the coating side; t_0 represents the transmission coefficient from air into coating; t1 rep- resents the transmission coefficient from coating into air. At the coating/glass interface, r_2 represents the reflection coefficient at the coating side.

EE, E,E,2 E,3 E,4 ..... Air 1 Coating d n Glass ng (a) Show that EL E * toratie2ikd, and E2/E1 = E3/E2 = E4/EX = ... = rirzelikd = a, where k is the wavevector in the coating. The total reflected wave is simply the sum of all the reflected waves: Er = E + E + E- + E + E + = E. + E. +aE. +aE+aE- + .... = E + E1(1+ a + a + a2 + ....) - (b) Find the ratio Er/E expressed in terms of the reflection and transmission coefficients defined above. (Apply the knowledge for the sum of an infinite geometric series.) (c) Find the expressions for ro, r1, r2, to, and t1, in terms of the refractive indices, and show that r = -ro and toti = 1-r. (d) Anti reflective coating simply requires Er = 0. Typically, d is chosen to be a quarter of the wavelength in the coating. Find the expression of n that satisfies this condition. EE, E,E,2 E,3 E,4 ..... Air 1 Coating d n Glass ng (a) Show that EL E * toratie2ikd, and E2/E1 = E3/E2 = E4/EX = ... = rirzelikd = a, where k is the wavevector in the coating. The total reflected wave is simply the sum of all the reflected waves: Er = E + E + E- + E + E + = E. + E. +aE. +aE+aE- + .... = E + E1(1+ a + a + a2 + ....) - (b) Find the ratio Er/E expressed in terms of the reflection and transmission coefficients defined above. (Apply the knowledge for the sum of an infinite geometric series.) (c) Find the expressions for ro, r1, r2, to, and t1, in terms of the refractive indices, and show that r = -ro and toti = 1-r. (d) Anti reflective coating simply requires Er = 0. Typically, d is chosen to be a quarter of the wavelength in the coating. Find the expression of n that satisfies this condition