How Does Glass Thickness Affect Color Interference?

[jjg]

A thin piece of glass with an index of refraction of n2 = 1.50 is placed on top of a medium that has an index of refraction n3 = 2.00. A beam of light traveling in air (n1 = 1.00) shines perpendicularly down on the glass. The beam contains light of only two colors, blue light with a wavelength in air of 456 nm and orange light with a wavelength in air of 608 nm.
(a) What is the minimum non-zero thickness of the glass that gives completely constructive interference for the orange light reflecting from the film?
nm

(b) What is the minimum non-zero thickness of the glass that gives completely constructive interference for BOTH the blue and orange light simultaneously?
nm

For (a)
I tried using t= ((m+.5) *wavelength(film)) /2, using m =1, and wavelength(film)= 608/1.5 = 405

I got 304 nm , but that isn't right...

 

[jjg]

Please Help!

 

[alphysicist]

Hi jjg,

What was your reasoning for choosing that particular equation? You have to take into account the effect of reflection on both waves, and that will tell you what relationship to use for constructive and destructive interference.