Question

A very thin film in reflected white light appears
A) Violet
B) White
C) Black
D) Red

Answer 1

When light will fall on film, the process of interference will take place due to superposition of various lights constituting white light. Then using the concept of path difference we can check which color of the film will be seen.
Path difference is represented by $\Delta x$.

Complete step by step answer:
A white light is falling on the thin film, we know that white light consists of 7 colors: violet, indigo, blue, green, yellow, orange and red (VIBGYOR).
When it gets reflected, all these consisting lights having different wavelengths superimpose (fall on each other), due to this phenomenon of interference of light occurring.
The path difference $\left( {\Delta x} \right)$ associated is given as:
$\Delta x = 2\mu t\cos r + \dfrac{\lambda }{2}$ ___________ (1)
Where $\mu$ is a refractive index of material, $\lambda$ is wavelength of light, r is angle of reflection and t is the thickness of the surface.
This interference can be of two types:
Constructive: Crest of one wavelength falls on that of other and resultant amplitude is more. Its path difference is $2\lambda$ and produces bright fringes

Destructive: Crest of one wavelength falls on the crest of the other’s and resultant amplitude is less. Its path difference is $\dfrac{\lambda }{2}$ and produces dark fringes.

Now, when the light falls on thin film, its thickness is very small (reaching towards 0) compared to wavelength.
$t \to 0$ and $t < < l$
Equation one becomes:
$\Delta x = \dfrac{\lambda }{2}$
This is equal to that of destructive interference, a dark fringe will be produced and thus the film will appear black in color, so the correct option is C.

So, the correct answer is “Option C”.

Note:
In general, when the light falls, it will be absorbed to much extent (not 100%, say 92%) and due to this absorption the light does not reflect back and the film appears to be black in color.
We use sign of delta for path difference because this sign is generally used to denote the change in respective quantities.