Finding Thickness of glass knowing OPD and refractive index.

[wiped_out]

Homework Statement

A beam of light is split into two coherent beams of intensity I which are in phase. The two
beams are sent through different paths and superimposed at the same spot on a screen. A path
difference is to be achieved by inserting a glass window of refractive index of 1.7 in the path of
one of the beams while keeping the physical (actual) path lengths the same. How thick must the
window be for an optical path difference of 4.5 wavelengths using light from a sodium vapour
lamp (λ = 589.3 nm)?

Homework Equations

OPD = t(n(s) - (n(m))

The Attempt at a Solution

n(s) = 1.7
n(m) = 1.0 (assuming it's in air.)
OPD = 4.5

OPD/(n(s) - (n(m)) = t
...changing the equation around.

4.5/(1.7-1.0) = t
t = 6.4 microns

is this right?

 

[rl.bhat]

What is the unit of t?
What is the purpose of giving the wavelength of sodium vapor lamp?

 

[tomcue]

Yes, your solution is correct. The thickness of the glass window must be 6.4 microns to achieve an optical path difference of 4.5 wavelengths.