91Ó°ÊÓ

At night many people see rings (called entoptic halos) surrounding bright outdoor lamps in otherwise dark surroundings. The rings are the first of the side maxima in diffraction patterns produced by structures that are thought to be within the cornea (or possible the lens) of the observer’s eye. (The central maxima of such patterns overlap the lamp.) (a) Would a particular ring become smaller or larger if the lamp were switched from blue to red light? (b) If a lamp emits white light, is blue or red on the outside edge of the ring?

Figure shows a red line and a green line of the same order in the pattern produced by a diffraction grating. If we increased the number of rulings in the grating – say, by removing tape that had covered the outer half of the rulings – would (a) the half-widhts of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place

A diffraction grating has 200 rulings/mm, and it produces an intensity maximum at $\mathit{θ}\mathbf{=}\mathbf{30}\mathbf{°}$.

(a) What are the possible wavelengths of the incident visible light?

(b) To what colors do they correspond?

Light of wavelength $\mathbf{500}\mathbf{}\mathit{n}\mathit{m}$ diffracts through a slit of width$\mathbf{2}\mathit{μ}\mathit{m}$ and onto a screen that is $\mathbf{2}\mathit{m}$away. On the screen, what is the distance between the center of the diffraction pattern and the third diffraction minimum?

If, in a two-slit interference pattern, there are$\mathbf{8}$bright fringes within the first side peak of the diffraction envelope and diffraction minima coincide with two-slit interference maxima, then what is the ratio of slit separation to slit width?

Manufacturers of wire (and other objects of small dimension) sometimes use a laser to continually monitor the thickness of the product. The wire intercepts the laser beam, producing a diffraction pattern like that of a single slit of the same width as the wire diameter (Fig.$\mathbf{36}\mathbf{-}\mathbf{37}$). Suppose a helium – neon laser, of wavelength $\mathbf{632}\mathbf{.}\mathbf{8}\mathbf{}\mathbf{nm}$, illuminates a wire, and the diffraction pattern appears on a screen at distance $\mathit{L}\mathbf{}\mathbf{=}\mathbf{}\mathbf{2}\mathbf{.}\mathbf{60}\mathbf{}\mathbf{m}$. If the desired wire diameter is $\mathbf{1}\mathbf{.}\mathbf{37}\mathbf{}\mathbf{mm}$, what is the observed distance between the two tenth-order minima (one on each side of the central maximum)?

For the situation in Questions 9 and Fig. 1, if instead we increased the grating spacing, would (a) the half-widths of the lines and (b) the separation of the lines increase, decrease, or remain the same? (c) Would the lines shift to the right, shift to the left, or remain in place?

A $\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{}\mathbf{mm}$wide slit is illuminated by light of wavelength $\mathbf{589}\mathbf{}\mathbf{nm}$. Consider a point P on a viewing screen on which the diffraction pattern of the slit is viewed; the point is at $\mathbf{30}\mathbf{°}$from the central axis of the slit. What is the phase difference between the Huygens wavelets arriving at point P from the top and midpoint of the slit? (Hint: See Eq. $\mathbf{36}\mathbf{-}\mathbf{4}$.)

(a) Figure 36-34a shows the lines produced by diffraction gratingsA and B using light of the same wavelength; the lines are of the same order and appear at the same angles $\mathrm{θ}$. Which grating has the greater number of rulings? (b) Figure 36-34b shows lines of two orders produced by a single diffraction grating using light of two wavelengths, both in the red region of the spectrum. Which lines, the left pair or right pair, are in order with greater m? Is the center of the diffraction pattern located to the left or to the right in(c) Fig. 36-34a andd) Fig. 36-34b?

$\mathit{F}\mathit{i}\mathit{g}\mathit{u}\mathit{r}\mathit{e}\mathbf{}\mathbf{36}\mathbf{-}\mathbf{38}$gives $\mathit{Î\pm }$versus the sine of the angle $\mathit{θ}$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" ${\mathbf{Î\pm }}_{\mathbf{s}}\mathbf{=}\mathbf{12}\mathbf{}\mathbf{rad}$. 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?