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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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