Question

Soap films and bubbles are colorful because the interference conditions depend on the angle of illumination (which we aren't covering in 126) and the variable thickness. If a soap film (n = 1.33) has its longest constructive reflection at the red end of the visible spectrum (700 nm), by how much must it thin (in nm) to shift the longest constructive reflection to the blue end of the spectrum (400 nm). Note that we are asking for the difference in thickness, and answer with a positive number.

Answer 1

Answer:

56.39 nm

Step-by-step explanation:

In order to have constructive interference total optical path difference should be an integral number of wavelengths (crest and crest should be interfered). Therefore the constructive interference condition for soap film can be written as,

$2t=(m+\frac{1}{2} ).\frac{\lambda}{n}$

where λ is the wavelength of light and n is the refractive index of soap film, t is the thickness of the film, and m=0,1,2 ...

Please note that here we include an additional 1/2λ phase shift due to reflection from air-soap interface, because refractive index of latter is higher.

In order to have its longest constructive reflection at the red end (700 nm)

$t_1=(m+\frac{1}{2} ).\frac{\lambda}{2.n}\\ \\ t_1=\frac{1}{2} .\frac{700}{(2)*(1.33)}\\ \\ t_1=131.58\ nm$

Here we take m=0.

Similarly for the constructive reflection at the blue end (400 nm)

$t_2=(m+\frac{1}{2} ).\frac{\lambda}{2.n}\\ \\ t_2=\frac{1}{2} .\frac{400}{(2)*(1.33)}\\ \\ t_2=75.19\ nm$

Hence the thickness difference should be

$t_1-t_2=131.58-75.19=56.39 \ nm$