Destructive Interference of a sheet of mica

[conniechiwa]

Homework Statement

A sheet of mica sits on glass (n = 1.8). How thick should the sheet of mica (n = 1.5) be if it is to be as thin as possible and still give rise to destructive interference for reflection of light in the blue part of the spectrum (use l = 420 nm)? (All parts of the mica except the bottom surface are still surrounded by air.)

Homework Equations

1/2 + 2t/(wavelength/n) = m
2t/(wavelength/n) = 1/2
t = (wavelength/n)/4

The Attempt at a Solution

t = (wavelength/n)/4
t = (420nm/1.8/)4
t = 58.3 nm

I'm not sure what I'm doing wrong...

 

[alphysicist]

Hi conniechiwa,

Homework Statement

A sheet of mica sits on glass (n = 1.8). How thick should the sheet of mica (n = 1.5) be if it is to be as thin as possible and still give rise to destructive interference for reflection of light in the blue part of the spectrum (use l = 420 nm)? (All parts of the mica except the bottom surface are still surrounded by air.)

Homework Equations

1/2 + 2t/(wavelength/n) = m
2t/(wavelength/n) = 1/2
t = (wavelength/n)/4

The Attempt at a Solution

t = (wavelength/n)/4
t = (420nm/1.8/)4
t = 58.3 nm

I'm not sure what I'm doing wrong...

The interference comes about from considering two rays of light: one reflects off the air/mica interface (not entering the mica), and the other enters the mica and reflects off the mica/glass interface.

The n in the formula is due to the fact that the wavelength in the mica is smaller than the wavelength in air. Do you see what you did wrong in the above work?

 

[conniechiwa]

Yeah I get it now. Thanks!