Physics

Physics

Problem

At normal incidence, white light is shone on a λ04\frac{\lambda_0}{4} thick oil film (noil=1.40n_{\text{oil}}=1.40) floating on water (nwater=1.33n_{\text{water}}=1.33) with air above. State whether the reflected light of wavelength λ0\lambda_0 appears bright or dark and briefly explain your reasoning in terms of phase changes at the two interfaces.
Intuitive explanation

The key is tracking phase changes as light reflects from both interfaces. Light reflecting off the denser oil surface (air→oil) gains a π\pi phase shift, while reflection at the oil–water boundary (oil→water, where water is denser) also gains π\pi. Since both reflections contribute equal phase shifts, they cancel out—leaving only the path difference from the film thickness to determine interference. A λ04\frac{\lambda_0}{4} thick film with n=1.40n=1.40 introduces a π\pi phase shift from the extra distance traveled, which destructively interferes with the two equal phase shifts, resulting in darkness.

Intuitive explanation

The key is tracking phase changes as light reflects from both interfaces. Light reflecting off the denser oil surface (air→oil) gains a π\pi phase shift, while reflection at the oil–water boundary (oil→water, where water is denser) also gains π\pi. Since both reflections contribute equal phase shifts, they cancel out—leaving only the path difference from the film thickness to determine interference. A λ04\frac{\lambda_0}{4} thick film with n=1.40n=1.40 introduces a π\pi phase shift from the extra distance traveled, which destructively interferes with the two equal phase shifts, resulting in darkness.

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