If soap bubble shows strong colors due to interference of the light that reflects from the inner and outer boundaries of the thin soap and water film. Light striking the outer surface has a phase change on reflection of pi. that is, its phase is flipped when it goes from air to the water surface and back out. Light reflecting from the inner surface, where it is in water then comes to the boundary with air, does not change its phase. Suppose you see white light reflecting from a bubble as it increases its size. The film making the bubble gets thinner and thinner and the colors reflecting from it change. If the bubble glows red, and then gets even thinner, what will you see just before it bursts? a. Blue
b. Red
c. Darkness.

the bubble appears DARK

Explanation:

This problem shows the interference by reflection of light on the surface, let's take it into account;

* There is a phase change of 180º on the surface when it stops from a lower medium to a higher index

* Within the film the wavelength changes due to the fraction index

if we plug this into the expression for constructive interference we have

       2tn = (m + ½) λ₀

for destructive interference it is

       2tn = m λ₀

apply these expressions to our case

indicate that the incident wavelength is red λ₀ = 700 nm

Let's find the minimum thickness that the film must have to have a constructive interference

the refractive index of soap is n = 1.4

from the constructive interference equation

            t = (0+ ½) 700 10⁻⁹ / 2 1.4

            t = 1.25 10⁻⁷ m

just before the soap bubble explodes the thickness (t) of the film less than the calculated value there is no possibility of constructive interference, therefore the bubble appears DARK

no. dot product   =0 when vecs at right angles

answer and explanation;