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adrian116
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Homework Statement
A source S of monochromatic light and a detector D are both located in air a distance h above a horizontal plane sheet of glass, and are separated by a horizontal distance x. Waves reaching D directly from S interfere with waves that reflect off the glass. The distance x is small compared to h so that the reflection is at close to normal incidence.
a). Show that the condition for constructive interference is [itex] \sqrt{x^2+4h^2}-x=(m+\frac{1}{2})\lambda [/itex], and the condition for destructive interference is[itex] \sqrt{x^2+4h^2}-x=m\lambda [/itex]. (Hint: Take into account the phase change on reflection.)
Homework Equations
1.[itex] d\sin\theta=m\lambda[/itex] for constructive interference
2.[itex]d\sin\theta=(m+\frac{1}{2})\lambda[/itex] for destructive interference
3.[itex]\phi=\frac{2\pi}{\lambda}(r_2-r_1)[/itex] phase difference related to path difference
The Attempt at a Solution
I have tried to find d as
[itex] d=\sqrt{h^2+(\frac{x}{2})^2} [/itex]
and the phase difference as
[itex] \phi=\frac{2\pi}{\lambda}(\sqrt{h^2+(\frac{x}{2})^2}-x)[/itex]
but i do not know how this related to the equations (b) 1 and (b) 2
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