A grating has exactly 8000 slits uniformly spaced over 2.54 cm and is illuminated by light from a mercury vapor discharge lamp. What is the expected angle for the third-order maximum of the green line ($\lambda = 546 \mathrm { nm }$)?

Two point charges are located on the y-axis as follows: charge $q _ { 1 } = - 1.50 n C$ at y = -0.600 m, and charge $\mathrm { q } _ { 2 } = + 3.20 \mathrm { nC }$ at the origin (y = 0). What is the total force (magnitude and direction) exerted by these two charges on a third charge $q _ { 3 } = + 5.00 n C$ located at y = -0.400 m?

In each part, is the given function continuous on the interval

$$[ 0 , \pi / 2 )$$

? (a) sin x, (b) cos x, (c) tan x, (d) csc x

Describe what happens to a single-slit diffraction pattern as the width of the slit is slowly decreased.

An object is placed 10.0 cm in front of a lens. An upright, virtual image is formed 30.0 cm away from the lens. What is the focal length of the lens? Is the lens converging or diverging?

Sparks will occur between the plates of an air-filled capacitor at a lower voltage when the air is humid than when it is dry. Discuss why, considering the polar character of water molecules

A camera lens (n=1.50) is coated with a thin film of magnesium fluoride (n=1.38) of thickness 90.0 nm. What wavelength in the visible spectrum is most strongly transmitted though the film?

In an electric motor, a coil with 100 turns of radius 2.0 cm can rotate between the poles of a magnet. The magnetic field magnitude is 0.20 T. When the current through the coil is 50.0 mA, what is the maximum torque that the motor can deliver?

A soap film has an index of refraction n=1.50. The film is viewed in reflected light. (a) At a spot where the film thickness is 910.0 nm, which wavelengths are missing in the reflected light? (b) Which wavelengths are strongest in the reflected light?

The electric field midway between two equal but opposite point charges is $1750 \mathrm{~N/C}$, and the distance between the charge s is $16.0$ cm. What is the magnitude of the charge on each?

Differentiate the series

$$E(x)=\sum_{n=0}^{\infty} \frac{x^{n}}{n !}$$

term-by-term to show that E(x) is equal to its derivative.

Find the unit tangent vector for the following parameterized curves. $\mathbf { r } ( t ) = 6 \mathbf { i } + \cos ( 3 t ) \mathbf { j } + 3 \sin ( 4 t ) \mathbf { k } , \quad 0 \leq t < 2 \pi$

Complete statement by writing the correct word or words. In a(n) _____ reaction, a compound breaks down into two or more products.

Two narrow slits with a center-to-center distance of $0.48 \mathrm{~mm}$ are illuminated with coherent light at normal incidence. The intensity of the light falling on a screen $5.0 \mathrm{~m}$ away is shown in the figure, where $x$ is the distance from the central maximum on the screen. (a) What would be the intensity of the light falling on the screen if only one slit were open? (b) Find the wavelength of the light.