In the below figure, a broad beam of light of wavelength $420 \mathrm{nm}$ is incident at $90°$ on a thin, wedge-shaped film with an index of refraction $1.70$. The transmission gives $10$ bright and $9$ dark fringes along the film's length. What is the left-to-right change in the film thickness?

In the below figure, two light rays go through different paths by reflecting from the various flat surfaces shown. The light waves have a wavelength of $411.0 \mathrm{nm}$ and are initially in phase. What is the smallest and the second smallest value of distance $L$ that will put the waves exactly out of phase as they emerge from the region?

In the following figure, assume that the two light waves, of wavelength $515 \mathrm{nm}$ in the air, are initially out of phase by $\mathrm{\pi } \mathrm{rad}$. The indexes of refraction of the media are $n_1=1.45$ and $n_2=1.75$. What is the smallest and second smallest value of $L$ that will put the waves exactly in phase, once they pass through the two media?

In a double-slit experiment, the fourth-order maximum for a wavelength of $450 \mathrm{nm}$ occurs at an angle of $\mathrm{\theta }=90°$.

(a) What range of wavelengths in the visible range $(400 \mathrm{nm}$ to $700 \mathrm{nm})$ is not present in the third-order maxima?

(b) To eliminate all the visible light in the fourth-order maximum, should the slit separation be increased or decreased and (c) What least change is needed?

Three electromagnetic waves travel through a certain point $P$ along an $x$-axis. They are polarized, parallel to a $y$-axis, with the following variations in their amplitudes. Find their resultant at $P$.

$\begin{array}{l}{E}_1=(8.00 \mathrm{\mu V} {\mathrm{m}}^{-1}) \sin \left[\left(2.0\times {10}^{14} \mathrm{rad} {\mathrm{s}}^{-1}\right) \mathrm{t}\right]\\ E_2=(5.00 \mathrm{\mu V} {\mathrm{m}}^{-1}) \sin \left[\left(2.0\times {10}^{14} \mathrm{rad} {\mathrm{s}}^{-1}\right) \mathrm{t}+55.0°\right]\\ E_3=(5.00 \mathrm{\mu V} {\mathrm{m}}^{-1}) \sin \left[\left(2.0\times {10}^{14} \mathrm{rad} {\mathrm{s}}^{-1}\right) \mathrm{t}-55.0°\right]\end{array}$

In the following figure, two light pulses are sent through layers of plastic with thicknesses of either $L$ or $2 L$, as shown, and indexes of refraction $n_1=1.55, n_2=1.70, n_3=1.60,$ $n_4=1.45, n_5=1.59, n_6=1.65$ and $n_7=1.54$.

$\left(\mathrm{a}\right)$ Which pulse travels through the plastic in less time?
$\left(\mathrm{b}\right)$ What multiple of $L{\mathrm{c}}^{-1}$ gives the difference in the traversal times of the pulses?