The element sodium can emit light at two wavelengths, ${\mathrm{\lambda }}_1=588.9950 \mathrm{nm}$ and ${\mathrm{\lambda }}_2=589.5924 \mathrm{nm}$. The light from sodium is being used in a Michelson interferometer, as shown in the below figure. Through what distance must mirror $M_2$ be moved if the shift in the fringe pattern for one wavelength is to be $2.00$ fringes more than the shift in the fringe pattern for the other wavelength?

Add the following quantities using the phasor method,

$y_1=8.0 \sin \mathrm{\omega }t$, $y_2=12 \sin \left(\mathrm{\omega }t+30°\right)$ and $y_3=7.0 \sin \left(\mathrm{\omega }t-45°\right)$

In the following figure, a light wave along ray $r_1$, reflects once from a mirror and a light wave along ray $r_2$, reflects twice from that same mirror and once from a tiny mirror at distance $L$ from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength $350 \mathrm{nm}$ and are initially in phase.

$\left(\mathrm{a}\right)$ What is the smallest value of $L$ that puts the final light waves exactly out of phase?

$\left(\mathrm{b}\right)$ With the tiny mirror initially at that value of $L$, how far must it be moved away from the bigger mirror to again put the final waves out of phase?

A light wave along ray $r_1$ reflects once from a mirror, and a light wave along ray $r_2$ reflects twice from that same mirror and once from a tiny mirror at distance $L$ from the bigger mirror. (Neglect the slight tilt of the rays.) The waves have wavelength $\mathrm{\lambda }$ and are initially exactly out of phase. What are the smallest, second smallest and fourth smallest values of $\frac{L}{\mathrm{\lambda }}$, that result in the final waves being exactly in phase?

In the following figure, an airtight chamber of length $d=5.0 \mathrm{cm}$ is placed in one of the arms of a Michelson interferometer. (The glass window on each end of the chamber has negligible thickness.) Light of wavelength $\mathrm{\lambda }=500 \mathrm{nm}$ is used. Evacuating the air from the chamber causes a shift of $60$ bright fringes. From this data and to six significant figures, find the index of refraction of air at the atmospheric pressure.

In the double-slit experiment, as shown in the following figure, the viewing screen is at distance $D=4.00 \mathrm{m}$. Point $p$ lies at distance $y=20.5 \mathrm{cm}$ from the centre of the pattern, the slit separation $d$ is $4.50 \mathrm{\mu m}$, and the wavelength $\mathrm{\lambda }$ is $650 \mathrm{nm}$.

(a) Determine where point $P$ is in the interference pattern by giving the maximum or minimum on which it lies, or the maximum and minimum between which it lies.

(b) What is the ratio of the intensity $I_{\mathrm{P}}$ at point $P$ to the intensity $I_{\mathrm{cen}}$ at the centre of the pattern?

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?