Question

A thin soap film of thickness $3 \times 10^{-7} m$ and $\mu=1.5$ is spread on a glass surface. When white light is normally incident on this sheet, find the wavelength of colour (in $\,\mathring{A}$ ) which will be reflected strongly by the film.

Answer 1

For strong reflection of a colour, its wavelength reflected from top and bottom surface of film must interfere constructively to which the path difference in the two waves must be an integral multiple of the wavelength.

As shown in figure, the path difference in the two waves reflected from the film is given as $\Delta=2 \mu t=N \lambda$
$\Rightarrow \lambda=\frac{2 \mu t}{N}=\frac{2 \times 1.5 \times 3 \times 10^{-7}}{N} $
$\Rightarrow \lambda=\frac{9000 \,\mathring{A}}{N} $ for $ N=1,2,3 \ldots $
$\Rightarrow \lambda=9000 \,\mathring{A}, 4500\,\mathring{A}, 3000\,\mathring{A} \ldots$
White light approximately ranges from $4000\,\mathring{A}$ to $8000 \,\mathring{A}$ so here light of wavelength $4500\,\mathring{A}$ will be strongly reflected by this film.