How to Determine Minimum Thickness for Dark and Bright Spots in Soap Films?

[Motox]

Homework Statement

Light of wavelength 580 nm strikes a soap film (n=1.33), which is surrounded by air. What is the minimum thickness needed to produce
a) dark spot?
b) bright spot?

Homework Equations

n1/n2=wavelength 2 / wavelength 1

2t = m (wavelength) <-- dark
2t = (m + 1/2) (wavelength) <--- bright

 

[ideasrule]

Those equations are right. Just plug in the numbers are you're done.

 

[kerimek]

The minimum thickness needed to produce a dark spot in a soap film is half of the wavelength of the incident light, or 290 nm. This can be calculated using the equation 2t = m (wavelength), where t is the thickness of the film and m is the order of the dark spot (m=0 for the first dark spot). Since the soap film has a refractive index of 1.33, we can use the equation n1/n2=wavelength 2 / wavelength 1 to find the wavelength inside the film, which is 435.7 nm. Plugging this into the equation for the dark spot, we get 2t = 0.5 (435.7 nm), which gives us a minimum thickness of 217.85 nm.

For a bright spot, the minimum thickness needed is half of the wavelength plus half of the wavelength divided by the refractive index of the film, or 362.5 nm. This can be calculated using the equation 2t = (m + 1/2) (wavelength), where m is the order of the bright spot (m=0 for the first bright spot). Plugging in the values, we get 2t = 0.5 (580 nm) + 0.5 (580 nm)/1.33, which gives us a minimum thickness of 362.5 nm.

It is important to note that these calculations are ideal and may vary slightly in real life due to factors such as the thickness and uniformity of the film, as well as the angle of incidence of the light. Additionally, multiple layers of soap film may produce interference patterns, resulting in more complex equations and calculations.