The condition for constructive interference for the given condition is:

$\overline{){\mathbf{2}}{\mathit{\eta}}{\mathbf{d}}{\mathbf{=}}{\mathbf{(}}{\mathbf{m}}{\mathbf{+}}\frac{\mathbf{1}}{\mathbf{2}}{\mathbf{)}}{\mathbf{\lambda}}}$

m = 0

This implies that:

2ηd = (1/2)λ

d = λ/4η

The minimum bubble thickness that will produce interference color is:

$\overline{){{\mathbf{d}}}_{\mathbf{m}\mathbf{i}\mathbf{n}}{\mathbf{=}}\frac{{\mathbf{\lambda}}_{\mathbf{m}\mathbf{i}\mathbf{n}}}{\mathbf{4}\mathit{\eta}}}$

As a soap bubble with n = 1.333 evaporates and thins, reflected colors gradually disappear. What are

(a) the bubble thickness just as the last vestige of color vanishes and

(b) the last color seen?

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