Homework Help: Interference and Diffraction of Light!

1. Mar 17, 2005

cdhotfire

I didnt go to school today, and so missed day of class, now i all lost someone help.

White light is incident normal to the surface of the film as shown below. It is observed that at a point where the light is incident on the film, light reflected from the surface appears green (lamda = 525 nm)

|
|--Light
|Air $n_{a}=1.00$
-------------------------
Film $n_{f}=1.38$
-------------------------

Glass $n_{s}=1.50$
-------------------------
Air $n_{a}=1.00$

i. What is the frequency of the green light in air?
ii. What is the frequency of the green light in the film?
iii. What is the wavelenght of the green light in the film?
iv. Calculate the minimum thickness of film that would produce this green reflection.

I know that the light will reflect off when it hits the film, and again when it hits the glass. Thats about all i can see here. [itex]f=\frac{v}{lamda}[/atex] i have the lamda outside but thats it. Can anyone help i dont want to get behind.

2. Mar 17, 2005

xanthym

ITEM #1:
What is the frequency of the green light in air?
v = f*λ
::: ⇒ f = v/λ
::: ⇒ f = (3*108 m/sec)/(525*10(-9) m)
::: ⇒ f = (5.714*1014 Hz)

ITEM #2:
ii. What is the frequency of the green light in the film?
In the film, velocity & wavelength change. Frequency does not. Frequency is same answer prev item:
::: ⇒ f = (5.714*1014 Hz)

ITEM #3:
iii. What is the wavelength of the green light in the film?
λfilm = λair*nair/nfilm
::: ⇒ λfilm = (525 nm)*(1)/(1.38)
::: ⇒ λfilm = (380.4 nm)

ITEM #4:
Calculate the minimum thickness of film that would produce this green reflection.
The green reflection is caused by CONSTRUCTIVE interference between the ray reflected from the film's top surface with that reflected from the film's bottom surface. Both these rays undergo 180 deg phase shifts from the incident rays at their respective interfaces, so NO net phase shift results from the reflections themselves. However, a phase difference can occur from the added path length traveled by the ray in the film:
{Path Length of Ray in Film} = 2*{Film Thickness}
The minimum film thickness for CONSTRUCTIVE interference occurs when the film ray's path length is exactly {(1.0)*λfilm}. Placing this value into the above equation and solving for minimum film thickness:
{Path Length of Ray in Film} = {(1.0)*λfilm} = 2*{Minimum Film Thickness}
::: ⇒ 2*{Minimum Film Thickness} = (380.4 nm)
::: ⇒ {Minimum Film Thickness} = (190.2 nm) = (0.1902 um) = (1.902*10(-7) m)

~~

3. Mar 18, 2005

cdhotfire

thank you very much, would of helped if it was yesturday, i figured it out later on, but many thanks for helping.