A glass surface is covered by a uniform oil film with a thickness of 1.00 10⁻⁴ cm . The refractive index of the oil is 1.25 , while that of the glass is 1.50 . Determine the wavelengths of light within the visible region ( 400 nm to 750 nm ) that are completely transmitted through the oil film at normal incidence.

Step-by-step solution

For complete transmission of light through the oil film, the reflected light must undergo destructive interference. The light reflects from two interfaces: the air-oil interface and the oil-glass interface. Since the refractive index of air ( n = 1.00 ) is less than that of oil ( n = 1.25 ), the reflection at the air-oil interface introduces a phase shift of . Similarly, since the refractive index of oil is less than that of glass ( n = 1.50 ), the reflection at the oil-glass interface also introduces a phase shift