What phase shift occurs when light reflects from a boundary to a higher refractive index?

At normal incidence, what is the optical path difference for reflection from the two surfaces of a film of refractive index \(n\) and thickness \(t\)?

For reflected light with exactly one reflection phase reversal, state the dark condition.

A film has \(n=1.40\) and \(t=120\,\mathrm{nm}\). Find \(2nt\).

A soap film in air has one phase reversal. Is a film with \(t\to0\) bright or dark in reflected light?

A film with one phase reversal has \(n=1.50\). Find the minimum nonzero thickness for reflected darkness at \(\lambda_0=600\,\mathrm{nm}\).

A coating has \(n=1.25\). Find the quarter-wave thickness for \(\lambda_0=500\,\mathrm{nm}\).

For reflected light with zero or two phase reversals, state how the bright and dark conditions compare with the one-phase-reversal case.

An oil film \((n=1.45)\) floats on water \((n=1.33)\) in air. Count the reflection phase reversals for reflected light.

For the oil film in water with one phase reversal, find the minimum nonzero thickness for reflected brightness at \(\lambda_0=580\,\mathrm{nm}\).

A film has \(n=1.33\), \(t=250\,\mathrm{nm}\), and one phase reversal. Which reflected vacuum wavelengths are dark for integer \(m\)?

A film has \(n=1.33\), \(t=250\,\mathrm{nm}\), and one phase reversal. Which reflected vacuum wavelengths are bright?

A film in air has \(n=1.20\) on glass \(n=1.50\). Determine whether reflected dark uses \(2nt=m\lambda_0\) or \(2nt=(m+1/2)\lambda_0\).

Design an anti-reflection coating for glass \(n_g=1.50\) using coating index \(n_c=\sqrt{n_g}\). Find \(n_c\) and the quarter-wave thickness for \(550\,\mathrm{nm}\).

Explain why a film can be bright in reflection and dark in transmission for the same wavelength.

A wedge-shaped air film lies between two glass plates. Explain why fringes of equal thickness appear, and predict how fringe spacing changes if the wedge angle increases.

For a film with one phase reversal, derive the reflected bright and dark conditions from phase difference.

A film thickness is slowly increased from zero. For reflected light with one phase reversal, describe the sequence dark/bright/dark in terms of \(2nt\).

A film is designed to cancel \(550\,\mathrm{nm}\) reflected light at normal incidence. Explain why it does not cancel all visible wavelengths.

A film is between media with indices \(n_a<n_f<n_b\). Prove which reflected condition is dark and explain the limiting case as \(t\to0\).