Question

A light ray in air (n= 1) is incident on a thin film of oil (noil = 1.60) floating on top of water (nwater = 1.33), as shown below. The wavelength of the incident light in air is Aair = 640 nm. The oil layer has a thickness t = 0.5 um. The ray is assumed to be incident practically along the normal. That is, we won't be worried about angles of reflection or refraction when doing this problem. However, the light rays are drawn at an angle in the figure so we can distinguish the many light-ray segments present in this setup! air n= 1.00 oil n= 1.60 water n= 1.33 The following is a summary of the eight different ray segments shown: Point A is on the air-oil boundary. Ray a is incident from the air. Ray B is the result of Ray a reflecting off the air-oil boundary. Ray y is the result of Ray a refracting into the oil from the air. Point B is on the oil-water boundary. Ray y is incident from the oil. Ray S is the result of Ray y reflecting off the oil-water boundary. Ray e is the result of Ray y refracting into the water from the oil. Point C is on the air-oil boundary. Ray o is incident from the oil. Ray is the result of Ray o reflecting off the air-oil boundary. Ray n is the result of Ray o refracting into the air from the oil Point D is on the oil-water boundary. Ray ^is incident from the oil. Ray 0 is the result of Ray f refracting into the water from the oil Let the phase of Ray a at point A be paA = 0.

Answer 1

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Al reflected 1.6x1028 & 9 640xão 2.5 x x 28 de bransonited (art-anl) x 22 - 2ntx 20 h 640x9 12x1.6 xas x 10 x 20 640x9 (2 2.5x25 - 50 for baht (reflected) to undergo constructive dard winterference for Constructive Interference Preslected needs to be multiple of No Constructive In 49 not add multiple of and aatis (2m-1 for Constructive

x 6 x0 Slà 8 - on 1.68106 ar da de 3.2 x 106 m 3200 nm not visible 2x1.6 x 0.5xiol (2x2- mg 1.6x1662 39. goy da 1.078 106 or de loto nm. 1.6 x 100 = 54 not visit Want an ang dastando 64 x 166 O datieso 640 nm - dan 457 nm. at will be Sbongly, And m s reflected

THURSDAY a 640nm and 457 non will be ti For bransmitted light Six com bransmitted Constructive 2016 2x +33 16 2x 1.6x a salê Or 1.6 16 da 1600 mm net visible for m. 2 for m-3 for m-4 de 800 non = 5 3 3.33 nm d = 400 nm not wisible visible n