Question

A film of oil lies on wet pavement. The refractive index of the oil exceeds that of the water. The film has the minimum nonzero thickness such that it appears dark due to destructive interference when viewed in visible light with wavelength 678 nm in vacuum. Assuming that the visible spectrum extends from 380 to 750 nm, what is the longest visible wavelength (in vacuum) for which the film will appear bright due to constructive interference

Answer 1

Step-by-step explanation:

For destructive interference , the condition is

2μt = nλ

2μt = n x 678

For constructive interference , the condition is

2μt = (2n+1)λ₁ /2

n x 678 = (2n+1)λ₁ /2

λ₁ = 1356 n / ( 2n + 1 )

λ₁ = 1356 / ( 2 + 1/n )

For longest wavelength , denominator should be smallest or n should be largest . The longest value of n is infinity so

λ₁ = 1356 / 2

= 678 nm .