A thin film of ethyl alcohol (n=1.36) is spread on a glass slide (n=1.5). When illuminated with white light it shows a color pattern in reflection. If the strongest light in normal incidence is green (500 nm), how thick the film is?

184 nm

Explanation:

Given that ;

the refractive index (n) of ethyl alcohol = 1.36

wavelength () = 500 nm = 500 × 10⁻⁹ m

The difference in optical path length between the adjacent light rays can be expressed by the formula:

where;

= relative phase difference

d = distance between points of reflections

= refractive index of the film

If we replace for in the above equation; we have;

where; m represents the order of the pattern of the light rays;

and θ = 0; m = 1

Making  d the subject of the formula; we have:

d = 184 nm

∴ The thickness of the film =  184 nm

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