A thin glass sheet (n = 1.5) is surrounded by air on both sides and is illuminat

Question

A thin glass sheet (n = 1.5) is surrounded by air on both sides and is illuminated by white light. The sheet is 336 nm thick.

Calculate the wavelengths (in nm) of visible light (400 to 700 nm) that will be strongly reflected by this sheet. (There will be more than one wavelength.) HINT: Use the equation for constructive interference, but rewrite it as = ... Then calculate when m = 0, 1, 2, ...Find the wavelengths which are in the range of 400 to 700 nm. These are the wavelengths that will be strongly reflected by the thin glass sheet.

(d) Higher wavelength = ? nm
(e) Lower wavelength = ? nm

Explanation / Answer

The light will have a 1/2 phase change on the top surface reflection but no phase change on the bottom surface reflection

The two reflections from the top and lower surface of the oil layer will be 2 .t out of step plus , because the waves travel more slowly in the oil, an extra factor....

the total path difference will be µ x 2 x t = 1.5 x 2 x 336 = 1008 nm

The number of wavelengths from the range 400 nm to 700 nm would be 1.5 if =1008/1.5=> = 672 nm


2 when =1008/1.5= 504 nm
2.5 when =1008/2.5= 403 nm

These are the only 3 wavelengths that will strongly interfere. The 672 nm will constructively interfere to give a bright red reflection because the two reflection will be 2 out of step ( 1.5 from the oil thickness plus /2 from the first reflection )

The 504 nm will has strong destructive interference because the two reflections are 2.5 out of step

The 403 nm will again be constructively interfering ( blue this time ) with the reflection 3 out of step.

Higher wavelength = 504 nm
Lower wavelength = 403 nm

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