Question

Problem 35.54

In your research lab, a very thin, flat piece of glass with refractive index 1.90 and uniform thickness covers the opening of a chamber that holds a gas sample. The refractive indexes of the gases on either side of the glass are very close to unity. To determine the thickness of the glass, you shine coherent light of wavelength λ0 in vacuum at normal incidence onto the surface of the glass. When λ0= 496 nm, constructive interference occurs for light that is reflected at the two surfaces of the glass. You find that the next shorter wavelength in vacuum for which there is constructive interference is 386 nm.

Part A

Use these measurements to calculate the thickness of the glass.

Express your answer with the appropriate units.

h =

5.87•10−7m

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Part B

What is the longest wavelength in vacuum for which there is constructive interference for the reflected light?

Express your answer with the appropriate units.

λ =

Answer 1

For Constructive interference

use the equation 2nt = (m + 1/2) ?--------------------1

t is thickness

so in 1st Case,

2nt = (m + 1/2) 496 nm

For 2nd Case,

2nt = (m +1+ 1/2) * 386

2nt = (m+3/2) * 386

(m + 1/2) 496 = (m+3/2) * 386

m = 3

Putting value of m in 1

2nt = (m + 1/2) 496

2*1.5t = (3 + 1/2) * 496

t = ((3 + 1/2) * 496 nm)/ 3

t = 578.6 nm is the thickness of the glass.

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b)

Again for constructive interfernce

2nt = (m + 1/2) ?

? = 2nt / ((m + 1/2))

here m = 0 for longest Wavelength

then

? = 2*1.5*578.6/ (1/2)

? = 3472 nm