# Formula for maximum interference for reflected light (thin - film)

Homework Statement:
For case where light comes from the glass and reflects off a soap film with vacuum on the other side, what is the formula used to give an interference maximum for reflected light?
Relevant Equations:
Thin - film interference
The light comes from glass to boundary of glass and soap film, then there will be light which is reflected and transmitted. The reflected light has no phase shift and the transmitted light will hit the boundary of soap film and vacuum and the reflected light from this boundary will also has no phase shift.

Because the two reflected light has no phase shift, the path difference (2d, where d is the thickness of the soap film) should be mλ (m is integer and λ is the wavelength of the light), so the formula used to give an interference maximum for reflected light will be: 2d = mλ

But the answer key is: 2d = (m + 1/2)λ

Where is my mistake? Thanks

kuruman
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How many wavelengths can you fit in soapy water of length ##2d## when the wavelength in vacuum is ##\lambda##? Anti-hint: The answer is not ##2d/\lambda##. Also, when is there a phase shift upon reflection and when is there not?

ehild
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Homework Statement:: For case where light comes from the glass and reflects off a soap film with vacuum on the other side, what is the formula used to give an interference maximum for reflected light?
Relevant Equations:: Thin - film interference

The light comes from glass to boundary of glass and soap film, then there will be light which is reflected and transmitted. The reflected light has no phase shift and the transmitted light will hit the boundary of soap film and vacuum and the reflected light from this boundary will also has no phase shift.

Because the two reflected light has no phase shift, the path difference (2d, where d is the thickness of the soap film) should be mλ (m is integer and λ is the wavelength of the light), so the formula used to give an interference maximum for reflected light will be: 2d = mλ

But the answer key is: 2d = (m + 1/2)λ

Where is my mistake? Thanks
You are right, there are no phase shifts at the boundaries, so maximum reflectance occurs when the phase shift inside the layer is integer times 2pi. Your formula is correct, but you need to clarify what lambda you use in the formula: it is not the vacuum wavelength.

How many wavelengths can you fit in soapy water of length ##2d## when the wavelength in vacuum is ##\lambda##? Anti-hint: The answer is not ##2d/\lambda##.
You mean the number of wavelengths should be ##2dn/\lambda## where n is refractive index of soapy water and λ is wavelength of light in vacuum?

Also, when is there a phase shift upon reflection and when is there not?
When the light travels from denser to less dense medium, no phase shift upon reflection and when the light travels from less dense medium to denser medium there will be phase shift

You are right, there are no phase shifts at the boundaries, so maximum reflectance occurs when the phase shift inside the layer is integer times 2pi. Your formula is correct, but you need to clarify what lambda you use in the formula: it is not the vacuum wavelength.
Yes sorry, it should be the wavelength of light in the soap film

Thanks