On the night of April 18, 1775, a signal was sent from the steeple of Old North Church in Boston to Paul Revere, who was $1.80 \mathrm{mi}$ away: "One if by land, two if by sea." At what minimum separation did the sexton have to set the lanterns for Revere to receive the correct message about the approaching British? Assume that the patriot's pupils had a diameter of $4.00 \mathrm{~mm}$ at night and that the lantern light had a predominant wavelength of $580 \mathrm{~nm}$.

A charge of uniform linear density $1.50 \mathrm{~nC} / \mathrm{m}$ is distributed along a long, thin, nonconducting rod. The rod is coaxial with a long conducting cylindrical shell. The net charge on the shell is zero. What is the magnitude of the electric field $15.0 \mathrm{~cm}$ from the axis of the shell?

A very long, thin rod carries an electric charge with the linear density $35.0 \mathrm{nC} / \mathrm{m}$. It lies along the $x$ axis and moves in the $x$ direction at a speed of $1.50 \times 10^7 \mathrm{~m} / \mathrm{s}$.
(b) Find the magnetic field it creates at the same point.

A very long, thin rod carries electric charge with the linear density 35.0 nC/m. It lies along the x axis and moves in the x direction at a speed of $1.50 \times 10^{7} \mathrm{m} / \mathrm{s}$. (a) Find the electric field the rod creates at the point (x = 0, y = 20.0 cm, z = 0). (b) Find the magnetic field it creates at the same point. (c) Find the force exerted on an electron at this point, moving with a velocity of $\left(2.40 \times 10^{8}\right) \hat{\mathrm{i}} \mathrm{m} / \mathrm{s}$.

A very long, thin rod carries $+Q$ coulombs of charge uniformly distributed in each meter of its length, and a point charge $-Q$ is located one meter from the rod. Sketch the field lines of the electric field produced jointly by these charges in the plane containing the rod and the point charge.

A step-down transformer is used for recharging the batteries of portable devices. The turns ratio $N_2/N_1$ for a particular transformer used in a CD player is 1:13. When used with 120-V (rms) household service, the transformer draws an rms current of 250 mA. Find the power delivered to the CD player.

For a gas obeying Dieterici’s equation of state $p(V-b)=R T \mathrm{e}^{-a / R T V}$, for 1 mole, prove that the equation of the inversion curve is $p=\left(\frac{2 a}{b^{2}}-\frac{R T}{b}\right) \exp \left(\frac{1}{2}-\frac{a}{R T b}\right)$, and hence find the maximum inversion temperature $T_{\max }$.

You are working in an optical research laboratory. One of your projects involves the use of a double slit through which you pass orange laser light of wavelength 590 nm. Unfortunately, because of budget cuts, there are a lot of researchers in the same room, with lots of equipment stuffed in the room, and, in particular, lots of laser beams flying around the room. One day, you find that a second laser beam of unknown origin and different color is entering your double slit along with your orange beam and you are seeing an interference pattern that is the sum of those due to the two beams. You notice that the combined pattern is pretty much a mess, but wait! The m = 3 maximum of your orange laser beam pattern is pure; there is absolutely no mixture of the other color at that point. From this fact, you determine the wavelength of the offending laser light so that you can figure out which other researcher to ask to modify the aiming of his laser.

A mirror on the passenger side of your car is convex and has a radius of curvature with magnitude 18.0 cm. (a) Another car is behind your car, 9.00 m from the mirror, and this car is viewed in the mirror by your passenger. If this car is 1.5 m tall, what is the height of the image? (b) The mirror has a warning attached that objects viewed in it are closer than they appear. Why is this so?

Light of wavelength 540 nm passes through a slit of width 0.200 mm. (a) The width of the central maximum on a screen is 8.10 mm. How far is the screen from the slit? (b) Determine the width of the first bright fringe to the side of the central maximum.

Three polarizing plates whose planes are parallel are centered on a common axis. The directions of the transmission axes relative to the common vertical direction are as we discussed earlier . A linearly polarized beam of light with plane of polarization parallel to the vertical reference direction is incident from the left onto the first disk with intensity $I_i=10.0$ units (arbitrary). Calculate the transmitted intensity $I_f$ when $\theta_1=20.0^{\circ}, \theta_2=40.0^{\circ}$, and $\theta_3=60.0^{\circ}$. Hint: Make repeated use of Malus's law.

Your team is working in an optical research laboratory. Part of the apparatus you are working on involves polarized beams of light. Your supervisor wants to rotate the plane of polarization of one polarized beam by $45.0^{\circ}$. She can do that by inserting a single polarizer at $45.0^{\circ}$ to the plane of polarization of the original beam, but, according to Malus’s law, she then loses 50% of the intensity of the light. She gives you the task of designing a stack of polarizers, each with its axis at the same angle with the axis of the previous polarizer, that will rotate the plane of polarization of the beam without losing more than 10.0% of the intensity of the original beam. She wants to know by quitting time tonight (a) how many polarizers she needs in the stack and (b) the angle between adjacent polarizers.

Narrow, parallel, glowing gas-filled tubes in a variety of colors form block letters to spell out the name of a nightclub. Adjacent tubes are all $2.80 \mathrm{~cm}$ apart. The tubes forming one letter are filled with neon and radiate predominantly red light with a wavelength of $640 \mathrm{~nm}$. For another letter, the tubes emit predominantly blue light at $440 \mathrm{~nm}$. The pupil of a dark-adapted viewer's eye is 5.20 $\mathrm{mm}$ in diameter. If she is in a certain range of distances away, the viewer can resolve the separate tubes of one color but not the other. The viewer's distance must be in what range for her to resolve the tubes of only one of these two colors?

Light of wavelength $5.40 \times 10 ^ { 2 }$ nm passes through a slit of width 0.200 mm. Find the width of the central maximum on a screen located 1.50 m from the slit.