How Does Angle of Incidence Affect Color Reflection in Soap Films?

[adc22]

A thin soap film (n=1.318) suspended in air has a uniform thickness. When white light strikes the film at normal incidence, violet light (412 nm) is constructively reflected. At what angle of incidence will green light (564 nm) be most strongly reflected? Assume that the film as the minimum thickness that can produce these reflections.


Snell's Law?
delta = (4*pi*d*nsoap / wavelength) + pi

I am at a real loss here because I just don't know what I should be thinking. I get the difference between constructive and destructive interference, but I have not had to blend wavelengths and indices of refraction using Snell's Law.

Please advise

 

[rl.bhat]

You can rewrite the formula as
2ndcos(beta) = ( m - 1/2 ) lambda. Here beta is the angle of refraction. For brightest reflection m should be 1
Using the values for violet light, find the thickness of the soap film.
Using this thickness find the angle of refraction for green light. Then using Snell's law find the angle of incidence of the green light.

 

[nlightner]

I understand your confusion and I am happy to provide some guidance. Let's break down the problem step by step.

First, we need to understand what is happening in the soap film. When white light strikes the film, it is being reflected off of both the top and bottom surfaces of the film. This creates constructive and destructive interference, resulting in different colors being reflected.

Next, we need to understand the concept of constructive interference. This occurs when the path difference between the two reflected rays is equal to a whole number of wavelengths. In this case, the violet light (412 nm) is being reflected constructively, meaning that the path difference is equal to one wavelength.

Now, let's apply Snell's Law. This law states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the velocities of light in the two mediums. In this case, the two mediums are air and the soap film.

Since we are looking for the angle of incidence at which green light (564 nm) will be most strongly reflected, we can rearrange Snell's Law to solve for the angle of incidence. This gives us the following equation:

sin(theta) = (nair/nsoap) * sin(phi)

Where theta is the angle of incidence, nair is the index of refraction for air (which is approximately 1), nsoap is the index of refraction for the soap film (given as 1.318), and phi is the angle of refraction.

Now, to find the angle of incidence at which green light is most strongly reflected, we need to consider the path difference for the green light. We know that the path difference for violet light is one wavelength, so the path difference for green light must also be one wavelength. This means that the angle of refraction for green light must be equal to the angle of incidence for violet light, which we know is 412 nm.

Using the equation above, we can plug in the values and solve for the angle of incidence:

sin(theta) = (1/1.318) * sin(412 nm)

sin(theta) = 0.758

theta = sin^-1(0.758)

theta = 50.3 degrees

So, at an angle of incidence of 50.3 degrees, green light (564 nm) will be most strongly reflected in the soap film.

I hope this explanation helps clarify