91影视

$\mathit{F}\mathit{i}\mathit{g}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathbf{36}\mathbf{-}\mathbf{38}$gives $\mathit{伪}$versus the sine of the angle $\mathit{胃}$in a single-slit diffraction experiment using light of wavelength $\mathbf{610}\mathbf{}\mathbf{nm}$. The vertical axis scale is set by as role="math" localid="1663169810058" ${\mathbf{伪}}_{\mathbf{s}}\mathbf{=}\mathbf{12}\mathbf{}\mathbf{rad}$. What are (a) the slit width, (b) the total number of diffraction minima in the pattern (count them on both sides of the center of the diffraction pattern), (c) the least angle for a minimum, and (d) the greatest angle for a minimum?

Figure 36鈥�35 shows the bright fringes that lie within the central diffraction envelope in two double-slit diffraction experiments using the same wavelength of light. Is (a) the slit width $a$, (b) the slit separation $d$, and (c) the ratio $d/a$in experiment B greater than, less than, or the same as those quantities in experiment A?

Monochromatic light with wavelength $\mathbf{538}\mathbf{}\mathbf{nm}$is incident on a slit with width role="math" localid="1663172390189" $\mathbf{0}\mathbf{.}\mathbf{025}\mathbf{}\mathbf{mm}$. The distance from the slit to a screen is $\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{}\mathbf{m}$. Consider a point on the screen $\mathbf{1}\mathbf{.}\mathbf{1}\mathbf{}\mathbf{cm}$from the central maximum. Calculate (a) $\mathit{胃}$ for that point, (b) $\mathit{伪}$, and (c) the ratio of the intensity at that point to the intensity at the central maximum.

In three arrangements, you view two closely spaced small objects that are the same large distance from you. The angles that the objects occupy in your field of view and their distances from you are the following: (1) $2蠒$and ; (2) $2蠒$and $2R$; (3) $蠒/2$and $R/2$. (a) Rank the arrangements according to the separation between the objects, with the greatest separation first. If you can just barely resolve the two objects in arrangement 2, can you resolve them in (b) arrangement 1 and (c) arrangement 3?

In the single-slit diffraction experiment of $\mathit{F}\mathit{i}\mathit{g}\mathbf{.}\mathbf{36}\mathbf{-}\mathbf{4}$,let the wavelength of the light be $\mathbf{500}\mathbf{}\mathbf{nm}$, the slit width be localid="1664272054434" $\mathbf{6}\mathbf{渭尘}$, and the viewing screen be at distance localid="1664272062951" $\mathbf{D}\mathbf{}\mathbf{=}\mathbf{}\mathbf{3}\mathbf{.}\mathbf{00}\mathbf{}\mathbf{m}$. Let y axis extend upward along the viewing screen, with its origin at the center of the diffraction pattern. Also let ${\mathit{I}}_{\mathbf{p}}$represent the intensity of the diffracted light at point P at $\mathbf{y}\mathbf{}\mathbf{=}\mathbf{}\mathbf{15}\mathbf{.}\mathbf{0}\mathbf{}\mathbf{cm}$. (a) What is the ratio of ${\mathit{I}}_{\mathbf{p}}$to the intensity ${\mathit{I}}_{\mathbf{m}}$ at the center of the pattern? (b) Determine where point P is in the diffraction pattern by giving the maximum and minimum between which it lies, or the two minima between which it lies.

For a certain diffraction grating, the ratio $\mathbf{位}\mathbf{/}\mathbf{a}$of wavelength to ruling spacing is$\mathbf{1}\mathbf{/}\mathbf{3}\mathbf{.}\mathbf{5}$. Without written calculation or the use of a calculator, determine which of the orders beyond the zeroth order appear in the diffraction pattern.

The full width at half-maximum (FWHM) of a central diffraction maximum is defined as the angle between the two points in the pattern where the intensity is one-half that at the center of the pattern. (See $\mathit{F}\mathit{i}\mathit{g}\mathbf{.}\mathbf{}\mathbf{36}\mathbf{-}\mathbf{8}\mathit{b}\mathbf{.}$) (a) Show that the intensity drops to one-half the maximum value when ${\mathbf{sin}}^{\mathbf{2}}\mathbf{伪}\mathbf{=}\frac{{\mathbf{伪}}^{\mathbf{2}}}{\mathbf{2}}$. (b) Verify that $\mathbf{伪}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{39}\mathbf{}\mathbf{rad}$. (about $\mathbf{80}\mathbf{掳}$) is a solution to the transcendental equation of (a). (c) Show that the FWHM is $\mathbf{螖胃}\mathbf{=}\mathbf{2}{\mathbf{sin}}^{\mathbf{-}\mathbf{1}}\left(\mathbf{0}\mathbf{.}\mathbf{443}\mathbf{位}\mathbf{/}\mathbf{a}\right)$where a is the slit width. Calculate the FWHM of the central maximum for slit width (d) $\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{位}$ ,(e) $\mathbf{5}\mathbf{.}\mathbf{00}\mathbf{位}$,and (f) $\mathbf{10}\mathbf{.}\mathbf{00}\mathbf{位}$.

Babinet鈥檚 principle. A monochromatic bean of parallel light is incident on a 鈥渃ollimating鈥� hole of diameter $\mathit{x}\mathbf{鈮�}\mathit{位}$ . Point P lies in the geometrical shadow region on a distant screen (Fig. 36-39a). Two diffracting objects, shown in Fig.36-39b, are placed in turn over the collimating hole. Object A is an opaque circle with a hole in it, and B is the 鈥減hotographic negative鈥� of A . Using superposition concepts, show that the intensity at P is identical for the two diffracting objects A and B .

(a) Show that the values of a at which intensity maxima for single-slit diffraction occur can be found exactly by differentiating Eq. 36-5 with respect to a and equating the result to zero, obtaining the condition $\mathit{t}\mathit{a}\mathit{n}\mathit{伪}\mathbf{=}\mathbf{伪}$. To find values of a satisfying this relation, plot the curve $\mathbf{y}\mathbf{=}\mathbf{迟补苍伪}$ and the straight line $\mathbf{y}\mathbf{=}\mathbf{伪}$ and then find their intersections, or use $\mathbf{伪}$calculator to find an appropriate value of a by trial and error. Next, from $\mathbf{伪}\mathbf{=}\mathbf{(}\mathbf{m}\mathbf{+}\frac{\mathbf{1}}{\mathbf{2}}\mathbf{)}\mathbf{蟺}$, determine the values of $\mathit{m}$ associated with the maxima in the singleslit pattern. (These m values are not integers because secondary maxima do not lie exactly halfway between minima.) What are the (b) smallest and (c) associated , (d) the second smallest $\mathbf{伪}$(e) and associated , (f) and the third smallest (g) and associated ?

The wall of a large room is covered with acoustic tile in which small holes are drilled $\mathbf{5}\mathbf{.}\mathbf{0}\mathbf{mm}$from centre to centre. How far can a person be from such a tile and still distinguish the individual holes, assuming ideal conditions, the pupil diameter of the observer鈥檚 eye to be $\mathbf{4}\mathbf{.}\mathbf{00}\mathbf{mm}$, and the wavelength of the room light to be $\mathbf{550}\mathbf{nm}$?