Reflected and transmitted colors in thin oil coating on glass

[fredrick08]

[SOLVED] thin layer optical coatings

Homework Statement

a sheet of glass is coated with a 500nm thick layer of oil (n=1.42)
a. for what visible wavelengths of light do the reflected waves interfere constructively?
b. for what visible wavelengths of light do the reflected waves interfere destructively?
c. what is the colour of reflected light? what is the colour of transmitted light?

The Attempt at a Solution

ok a. and b. were straight forward i got 473nm for a. and 406nm,578nm for b.
but how do i do c.? i can't find anything like it in my book, I am pretty sure that the answer to the question in the book is wrong it says (yellow-green)? if the reflected wave act constructively at 473nm which blueish, do that mean that the light reflected is blue, and the light transmitted is not blue?? but what about absorbed light? please some one help

 

[fredrick08]

if anyone would like to know how i got my answers for a. and b. i used the formula
lambda(constructive)=2nd/m and lambda(destructive)=2nd/(m-0.5) where m is an integer

 

[mgb_phys]

For C - assuming the incoming light is white the destrcutively interferred wavelengths will be removed and the remainder reflected, so you have white minus the answer from 'b'

 

[fredrick08]

ok so the light reflected is green and red?

 

[fredrick08]

or all colours except violet and yellow-green?

what about transmitted?

 

[fredrick08]

please anyone??

 

[Redbelly98]

As you said, blue is reflected. Also, there is a reflected peak centered at 710 nm, so deep red wavelengths are reflected as well. The reflected light is stronger at red and blue wavelengths.

Transmitted light is stronger in violet and yellow-green, as you said.

 

[fredrick08]

ok well what about the transmitted light?? its not blue and red, so its yellow greenish?

 

[fredrick08]

omg srry i didnt see that... thankyou heaps, for some reason i got really confused bout this... srry bout that last once again

 

[Redbelly98]

omg srry i didnt see that...

It was an edit, added several minutes after my original response.