In the figure, light is incident perpendicularly on a thin layer of material 2 t

Question

In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4 (the light reflects twice inside material 2). The waves r3 and r4 interfere. The parameters for this problem are these:n1 = 1.57 , n2 = 1.39 , n3 = 1.77 , wavelength ? in air = 630 nm. What is the second least thickness that gives an interference minimum of rays r3 and r4?

In the figure, light is incident perpendicularly on a thin layer of material 2 that lies between (thicker) materials 1 and 3. (The rays are tilted only for clarity.) Part of the light ends up in material 3 as ray r3 (the light does not reflect inside material 2) and r4 (the light reflects twice inside material 2). The waves r3 and r4 interfere. The parameters for this problem are these:n1 = 1.57 , n2 = 1.39 , n3 = 1.77 , wavelength ? in air = 630 nm. What is the second least thickness that gives an interference minimum of rays r3 and r4?

Explanation / Answer

given refractive indices are n1 = 1.57 , n2 = 1.39 , n3 = 1.77 wavelength ? in air = 600*10-9m the condition for pathdifference under transmitted light to beminimum in this case is 2n2tcosr =(m+1/2)? for normal incidence r= 0 ,so cos0 = 1 for second least thickness m =1 so 2n2t = 3?/2 or t = 3?/4n2 caculate for t we get the second least thickness that gives aninterference minimum of rays r3 andr4 caculate for t we get the second least thickness that gives aninterference minimum of rays r3 andr4

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