The light shining on a diffraction grating has a wavelength of 495 nm (in vacuum). The grating produces a second-order bright fringe whose position is defined by an angle of

$$9.34^\circ.$$

How many lines per centimeter does the grating have?

Factor the polynomial. $6 x ^ { 2 } + 3 x$

Light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.$0 ^ { \circ }$, (a) what is the number of rulings per centimeter for the grating? (b) Determine the total number of primary maxima that can be observed in this situation.

High-frequency sound waves exhibit less diffraction than low-frequency sound waves do. However, even high-frequency sound waves exhibit much more diffraction under normal circumstances than do light waves that pass through the same opening. The highest frequency that a healthy ear can typically hear is $2.0 \times 10 ^ { 4 } \mathrm { Hz }$ Assume that a sound wave with this frequency travels at 343 m/s and passes through a doorway that has a width of 0.91 m.

Determine the angle that locates the first minimum to either side of the central maximum in the diffraction pattern for the sound. This minimum is equivalent to the first dark fringe in a single-slit diffraction pattern for light.

A diffraction grating is 1.50 cm wide and contains 2400 lines. When used with light of a certain wavelength, a third-order maximum is formed at an angle of

$$18.0^\circ.$$

What is the wavelength (in nm)?

Decide if the given statement is true or false, and give a brief justification for your answer. If true, you can quote a relevant definition or theorem. If false, provide an example, illustration, or brief explanation of why the statement is false. The equilibrium solutions of a differential equation are always parallel to one another.

Two stars are $3.7 \times 10^{11} \mathrm{m}$ apart and are equally distant from the earth. A telescope has an objective lens with a diameter of 1.02 m and just detects these stars as separate objects. Assume that light of wave length 550 nm is being observed. Also assume that diffraction effects, rather than atmospheric turbulence, limit the resolving power of the telescope. Find the maximum distance that these stars could be from the earth.

A nuclear power plant generates 750 MW; the reactor temperature is $315^\circ C$ and a river with water temperature of $20^\circ C$ is available. (a) What is the maximum possible thermal efficiency of the plant, and what is the minimum rate at which heat must be discarded to the river? (b) If the actual thermal efficiency of the plant is 60% of the maximum, at what rate must heat be discarded to the river, and what is the temperature rise of the river if it has a flow rate of $165 \mathrm{m}^{3} \cdot \mathrm{s}^{-1} ?$

Find $f^{(9)}(0)$.

$$f(x)=x^2 \sin x$$

Two in-phase sources of waves are separated by a distance of 4.00 m. These sources produce identical waves that have a wavelength of 5.00 m. On the line between them, there are two places at which the same type of interference occurs.

Is it constructive or destructive interference

Find the gross income, the adjusted gross income, and the taxable income. Base the taxable income on the greater of a standard deduction or an itemized deduction. Suppose your neighbor earned wages of $86,250, received$1240 in interest from a savings account, and contributed $220 to a tax-deferred retirement plan. She is entitled to a personal exemption of$3800 and a standard deduction of $5950. The interest on her home mortgage was$8900, she contributed $2400 to charity, and she paid$1725 in state taxes.

A dark fringe in the diffraction pattern of a single slit is located at an angle of $\theta_{A}=34^{\circ}$. With the same light, the same dark fringe formed with another single slit is at an angle of $\theta_{\mathrm{B}}=56^{\circ}$. Find the ratio $W_{\mathrm{A}} / W_{\mathrm{B}}$ of the widths of the two slits.

Light passes through a single slit. If the width of the slit is reduced, what happens to the width of the central bright fringe? (a) The width of the central bright fringe does not change, because it depends only on the wavelength of the light and not on the width of the slit. (b) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smaller. (c) The central bright fringe becomes wider, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (d) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes larger. (e) The central bright fringe becomes narrower, because the angle that locates the first dark fringe on either side of the central bright fringe becomes smaller.

Light of wavelength 500 nm is incident normally on a diffraction grating. If the third-order maximum of the diffraction pattern is observed at 32.0$^{\circ}$, what is the number of rulings per centimeter for the grating?