Question

To make up for lost income during the quarantine, a student that usually works in construction begins to make jewelry.  While finely sanding down some fluorite to use as a center stone on a necklace, a thin layer of oil (n = 1.299) is left on the fluorite.  When seen in the full visible spectrum (400 - 700 nm) of sunlight, the fluorite reflects back all but the wavelength 650 nm.  

a.  What are the two smallest thicknesses of the oil?

b.  Was this light interfering constructively or destructively?  

c.  How many phase changes did the light reaching their eye experience?  

d.  Complete the diagram showing the composition of each layer and explicitly where any phase changes happened.

Answer 1

1) for smallest thickness path difference must be minimum and because

so

so minimum thickness for 650nm we get

and next for destuctive interferance

so we get

2) so for minimum path difference we getting destuctive interferance .

3) So light reaching after two phase change first from air oil interface and second from oil fluorite interface of phase shift by each

4) here n2> n1