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