State the double-slit condition for bright fringes.

State the double-slit condition for dark fringes.

A double slit has \(d=0.20\,\mathrm{mm}\), \(L=2.0\,\mathrm{m}\), and \(\lambda=500\,\mathrm{nm}\). Find the fringe spacing.

A point has \(d\sin\theta=3.5\lambda\). Is it bright or dark for in-phase slits?

For \(d=0.40\,\mathrm{mm}\) and \(\lambda=600\,\mathrm{nm}\), find the first bright-fringe angle.

A double-slit pattern has fringe spacing \(2.0\,\mathrm{mm}\), screen distance \(1.5\,\mathrm{m}\), and wavelength \(500\,\mathrm{nm}\). Find \(d\).

The fifth bright fringe is \(18\,\mathrm{mm}\) from the central maximum. If \(L=2.0\,\mathrm{m}\) and \(d=0.30\,\mathrm{mm}\), find \(\lambda\).

The first dark fringe in a double-slit pattern is at \(y=1.2\,\mathrm{mm}\). If \(L=1.0\,\mathrm{m}\) and \(d=0.25\,\mathrm{mm}\), find \(\lambda\).

A double-slit experiment is moved from air into water with \(n=1.33\), while source frequency, \(d\), and \(L\) remain fixed. How does fringe spacing change?

Two coherent slits have source phase difference \(\phi_0\). Derive the modified bright-fringe condition.

A source phase difference of \(\pi\) is introduced between two slits. What happens to the central point that was formerly bright?

A double-slit setup uses white light. Explain why the central fringe is white but outer fringes are colored.

A pattern's fringe spacing doubles while wavelength and screen distance stay fixed. What happened to slit separation?

For \(d=4.0\lambda\), what is the largest possible bright order? Explain the constraint.

A double-slit measurement uses \(y_m\approx m\lambda L/d\), but the measured fringe is at \(y/L=0.30\). Estimate whether the small-angle approximation is reliable and what correction direction is expected.

Derive the exact screen position formula for bright fringes without using the small-angle approximation.

A double-slit system has \(d=10\lambda\). How many bright fringes are physically allowed over all angles?

A thin glass plate is placed in front of one slit, adding optical path \((n-1)t\). Derive the shift in fringe order at the original central point.

A detector sees the entire two-slit pattern translate by \(3\) fringe spacings after a plate is inserted before one slit. If \(n=1.50\) and \(\lambda=600\,\mathrm{nm}\), find the plate thickness.

Prove that the small-angle fringe spacing is constant, and identify the assumption that makes it constant.