For this problem, you will only be concerned with the geometric aspects of thin$-$film interference, so ignore phase shifts caused by reflection from a medium with higher index of refraction. $($Because of the structure of a butterfly's wings, such phase shifts do not contribute much to what you actually see when you look at the butterfly.$)$

Part A

Assume that light is incident normal to the surface of a film of thickness dd$.$ How much farther does the light reflected from the back surface travel than the light reflected from the front surface?

Express your answer in terms of dd$.$

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

nothing

SubmitRequest$$Answer

Part B

For constructive interference to occur, the difference between the two paths must be an integer multiple of the wavelength of the light $($as is true in any interference problem$),$ i$.$e$.$ the general criterion for constructive interference is

mm$,$constructive$=2$dmm$,$constructive$=2$d$,$

where$$mm$$is a positive integer. This is usually stated in the slightly more explicit form

m$,$constructive$=2$dmm$,$constructive$=2$dm$.$

Given the thickness of the film, dd$,$ what is the longest wavelength that can exhibit constructive interference?

Express your answer in terms of dd$.$

Activate to select the appropriates template from the following choices. Operate up and down arrow for selection and press enter to choose the input value typeActivate to select the appropriates symbol from the following choices. Operate up and down arrow for selection and press enter to choose the input value type

$=$

nothing

SubmitRequest$$Answer