Phase shift from path difference

  • Thread starter kankerfist
  • Start date
1. The problem statement, all variables and given/known data

A wave front moving horizontally encounters a block of glass that has an index of refraction of 1.50 in its upper half and an index of refraction of 1.25 in its lower half. The wavelength of the wave front in air is 700 nm. At what lengths would the glass block cause constructive interference (bright spots) and destructive interference (dark spots)?


2. Relevant equations

n1=1.50
n2=1.25
λair=700E-9 m


3. The attempt at a solution

I came up with the following when I encountered this study problem and I was hoping someone could double check to see if I did this correctly:

Constructive interference should occur when the glass block length causes a phase shift of (integer)(2pi). When 2 rays leave the block they will be phase shifted by (2pi)(length of block)/(λ in n1 and n2). So the total phase shift for 2 rays going through the block:

(2pi)(L)/(λ in n1) - (2pi)(L)/(λ in n2)

and:
λ in n1= λ in air / n1 = (700E-9)/(1.5)
λ in n2 = (700E-9)/(1.25)

so constructive interference should occur when:

(2pi)(L) / [(700E-9)/(1.5)] -
(2pi)(L) / [(700E-9)/(1.25)] =
(integer)(2pi)

this reduces to:

Length of glass = 7(integer)/2.5E+6

So constructive interference should occur when the length of the glass block is any positive integer times (7/2.5*10^6) in meters. If anybody could take a glance and see if I messed up somewhere i'd appreciate it!
 

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