Constructive and destructive interference in thin films is predicted using the path difference, Δx.

Constructive interference:

$\overline{){\mathbf{\u2206}}{\mathbf{x}}{\mathbf{=}}{\mathbf{0}}{\mathbf{,}}{\mathbf{}}{\mathbf{\lambda}}{\mathbf{,}}{\mathbf{}}{\mathbf{2}}{\mathbf{\lambda}}{\mathbf{,}}{\mathbf{}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{}}{\mathbf{m}}{\mathbf{\lambda}}}$

Destructive interference:

$\overline{){\mathbf{\u2206}}{\mathbf{x}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}\frac{\mathbf{\lambda}}{\mathbf{2}}{\mathbf{,}}{\mathbf{}}\frac{\mathbf{3}\mathbf{\lambda}}{\mathbf{2}}{\mathbf{,}}{\mathbf{}}{\mathbf{.}}{\mathbf{.}}{\mathbf{.}}{\mathbf{}}{\mathbf{(}}{\mathbf{m}}{\mathbf{}}{\mathbf{+}}{\mathbf{}}\frac{\mathbf{\lambda}}{\mathbf{2}}{\mathbf{)}}}$

Assuming the ray is incident nearly perpendicular:

$\overline{){\mathbf{\u2206}}{\mathbf{x}}{\mathbf{}}{\mathbf{=}}{\mathbf{}}{\mathbf{2}}{\mathbf{t}}}$

Where t is the thickness.

If a thin film has a thickness that is

(a) 1/4 of a wavelength, constructive interference will always occur.

(b) 1/4 of a wavelength, destructive interference will always occur.

(c) 1/2 of a wavelength, constructive interference will always occur.

(d) 1/2 of a wavelength, destructive interference will always occur.

(e) None of the above is always true.

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