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 of r3and r4 interfere, and here we consider the type of interference to be either maximum (max) or minimum (min).

For this situation, each problem in the table below refers to the indexes of refraction n1, n2, and n3, the type of interference, the thin-layer thickness L in nanometers, and the wavelength ? in nanometers of the light as measured in air. Where ? is missing, give the wavelength that is in the visible range.

Where L is missing, give the second least thickness or the third least thickness as indicated.

For this problem we are using the values in ROW 60 as shown below.

n1=1.41

n2=1.81

n3=1.43

Type= min

L= thrid thickness

?=421

Explanation / Answer

Now

Apply 2nt=(m+.5)(lambda) m=0,1,2.......

For the third least thickness, m = 2, so...

2(1.81)(t) = (2.5)(421 X 10^-9)

2(1.81)(t)= 1.0525*10^-6

t = 2.90745 X 10^-7 m

which is 290 nm

Related Questions

Navigate

• Browse (All)
• Browse I
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.