Why is the depth of field greater, and the image sharper, wvcfteq (5/j5ad8za : zhen a camera lens is “stopped down” to a larger f-number? tqaf8e( j/dz5v a:5czIgnore diffraction.

Describe how diffraction affects the st fo p3 *cu(gc,0hgmq1patement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a larger f-q1pguh g *(3cmp,0 ofcnumber.

Why must a camera lens be moved farther from the film to focus on a cll. d,+sg,bn aqxug 5t4oser object?lad s ,4nqg+,xt 5.bgu

Why are bifocals needed mainly by older persons and not generally by youngeremt5iq6*/ vw,yszf b ( peop zbqe,fy*tmi5(/sw 6 vle?

  Will a nearsighted person who wears corrective lenses in her glassesaa2yosem -g6 yuuj //: be able to see clearlga2m uy- //a e6us:yjoy underwater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or farsi9:zt a61/iuo:6 mr*wks upt3bbqt;r nghted by looking at the width of the face through their glasses. If the person’s face appears narrower through bruz/3awnt; k:qbot: mrp6* 6tui91sthe glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant 3 kw1;4 8jw6oqlv. bne r7ni w)uvmzx.details, people will sometimes squint. Why does this helm4bv wn wnoxr;)zqv3k1.87w u6ej .lip?

Is the image formed on the retina of the human eye upright or inverted? Discusrau 91 ad94j pird6k2fs the irdjaf1469pr kdui2 9a mplications of this for our perception of objects.

The human eye is much like a camera — yet, when a camervv735db -n9c:ve/b gg b z.fjaa shutter is left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still sv3 7dfvc5gb:g.e/- j nvabb 9zee clearly. Explain.

  Reading glasses use convergingaa .t wz32l +.ei*k;zul bm9cs lenses. A simple magnifier is also a converging lens. Are reading glak9l2 wliuz a;z.b* t3 m.+caessses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s use usually produce p ;2u 43h1gcwm. gpqukimages that are colored at the edges. wpcu2 h;quk m3 p41g.gWhy?

Spherical aberration in a thin lens is minimized 3q128r2 i +pqpab4edj2 c9llljah)nc if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of 1l22caiblhd4q) 8aep 9crj+3 qj2lpn an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simp2fh29tam v27m kpph1ele lens are not present (or are greatly reduced) in the human eye pa 22mtpv12hkfh9em 7?

Explain why chromatic aberration occurs for thin lenses but not fowpkr-vb j/ 8v+r mirrors.

  By what factor can you improve resolution, other things bei8x l7 3 zlfl6dy szp+xmu(p((cng equal, if you use pxd (uyz7(z m68f(3slcx+p llblue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrorsmgb6h rmj 8 +vphv dv(7b+8u0a in astronomical telescopes.0v ba 8hm6 d+v78jpr+ (gmhbuv

Which color of visible light would give th- 4ovi5wi y axu1t6k;9 jki swv5r3ao.e best resolution in a microscope? Explain.5;oi a 1 .s9iv5w 4kivyrtowx63ajk u-

  Atoms have diameters of about 40 al9t:poe4s xdyiw .$10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops ranging fr;odp;tim -obir rv56gz 9(c0lom $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a6virpq h+ rnyh;+ji4m/ij:c 4oes -/ c 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera settvwem6,jo 2ra-aehwq)(u)s7ying of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photogl5f ;on*u0k hkraph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be adjusted so that it is 200.0 mmt 4ee22 (fvjy7;bhbaq to 206.0 mm from the film. For what range of object di(je 4b2h2b ve;qyfat7stances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 2 ua je0quks99k th.u9j4 z*l+ t3ixxb28-mtall tree from a distance of 58 m. What focal-length lens should be used i0xu kk et 4a*hs.l9zbu32xj+q9 tju 9if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, ui pd)v gg0fn*fhy(3 7ko-x5oysing ray diagrams, how reasonably sharp images can be formev-gfo5px)yod7 hfy 0 i (3ng*kd using such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct exposure ix g6wqvfoe0i ;;;j*fj s $\frac{1}{250}\,s$ at $f/11$ Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 8) if the pinhole diameter is 1.0 mm and the film is 7.0 $cm$ from the hole? $t_2$ = 1/   s

  A human eyeball is about3-2w o 6t(3o wwqbqjjj 2.0 $cm$ long, and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens? $ f-stop$ = f/  

  If the nearsighted person in Examplevxm20 .m/rzl+o,1m mtsfxw) f 25–6 wore contact lenses corrected for the farv/ z mm1sx 0xr)m.flt+2wo,mf point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person whose nsxa ,b5xd )e8)y n9ioxear point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point pf 0ewzp/ow/qe)).gx of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to rea u fji)yx9b1gv,trf6. d by holding a book at arm’s length, a distance of 45 $cm$ away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 $cm$ from the eye and he wants to read at the normal near point of 25 $cm$? +    D

  A person’s left eye is corc0yu.2hewx 1szm 8ab5)dsy6srected by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can seeslbru(k /l0)i objects clearly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsiptu9 at1h9hv4ghted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has *qnk:0 i yy8m9uj:ln.c.c kbca focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system whes a arh77v mi+e5rv.n8n viewing an object
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has near ucgen 0(p g32pand far points of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of tg3)3bdd bf/xa lens used with a relaxed eye if its focal length igdfbdt 3)x b3/s 12 $cm$? =    $\times$

  What is the focal lengt)raklu0o n ile(4- hx9h of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at ypfop.azs+ 8+ duc,g2$2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is using a mz-abt92l :rw9.00-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle /s(nyhj(+d 9j7yrzv,h)aq wsis viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placywv*ic/zeya8 1w au4bk2z-i.mz 5pk (.d nl5jed 5.55 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass with a focnftk mn0t7r- 1+(eg3u /fdy bzal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass is ranet * t l2-x1;dxds/qr vjn8e 7(qku5rted at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnification of an astronomical t7w qt o;/qcd;delescope whose objective lens has a fo ;dqqw toc7;/dcal length of 76 $cm$ and whose eyepiece has a focal length of 2.8 $cm$? What is the overall length of the telescope when adjusted for a relaxed eye?
M =    $\times$
L =    $\times$

  The overall magnification of an astronomical telescope is desired tt,-ysf -juq:a;jnk8 so be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

  An 8.0$\times$ binocular has 2.8$-$cm$-focal-length$ eyepieces. What is the focal length of the objective lenses?    cm

  An astronomical telescope has an objective with focal length 85rmc*og9)ocw70hqoi + $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has ir23hy -oleb c,ts two lenses spaced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for 1z*ni zftyu/hvqt a : ;;7ksxg6fzw /)a relaxed eye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope using at.cw ).1zj;bb(o+u5ysxd2ux d9n xyn reflecting mirror whose ra jb+du.; yy xuot.51 9wz(b) n2xxcsdndius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears m:em k o1(ux.xto be magnified 120$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

  A 170$\times$ astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
$f_e$ =    mm
$f_o$ =    m

  A reflecting telescope (Fig. Below) 6rmqb)74a(py4cvw f r has a radius of curvature of 3.0 m for its objective mirror and a radius of curvatu7p6qv(a m y)bwr 4c4frre of $-1.50m$ for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the photographic film to record the image of a star? $d_{2i}$ =    m

  A microscope uses an eyepiece with a focal length of 1.40p:fykqm g;).ni/ 9m5+o(zk zpqf9dqt8 7b nyz $cm$. Using a normal eye with a final image at infinity, the tube length is 17.5 $cm$ and the focal length of the objective lens is 0.65 $cm$. What is the magnification of the microscope? =    $\times$

  A 620 $\times$ microscope uses a 0.40-$cm$-focal-length objective lens. If the tube length is 17.5 $cm$, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity. $f_e$ =    cm

  A 17-$cm$-long microscope has an eyepiece with a focal length of 2.5 $cm$ and an objective with a focal length of 0.28 $cm$. What is the approximate magnification?    $times$

  A microscope has a 1ldz3u8 o.z 3bl ,r+ymm2.0$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1.8-ea71ekb g, .ae su)at+$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the final imq-ei8voc*c2x+di (ngage is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope. / tms rx3yi6n4jmp4)r 5h0yqlxf b.s has a focal length of 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin 876r*ripznn ted )x-blenses, placed in contact, that have focal lenpr-8it x6n7) zebdrn*gths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular sizxs.qd77qwdc oi 1y.5tuation. A planoconvex lens of index of refraction 1.50 and radius of curvs5qi7.z qc1d d .w7xoyature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction for the 100-if7ol/ap e/; brn. (25el/7ap/rf ob; 4-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resiwba2) pn /(k(+c ptgyolve features 7.0 $km$ across on the Moon, 384,000 $km$ away. You have a 2.0-$m$-focal-length objective lens whose diameter is 11.0 $cm$.
What focal-length eyepiece is needed if your eye can resolve objects 0.10 $mm$ apart at a distance of 25 $cm$? $f_e$ =    cm
What is the resolution limit (radians) set by the size of the objective lens (that is, by diffraction)?
Use $\lambda=550\mathrm{~nm.}$ $\theta$   $ \times10^{ -6}\;rad$

  The normal lens on a 35-mm camera has a focal length of 50.(urt/d/v6cjklk v 3* o1/ vp:romn8sd 0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years away are barely rt )b x*b0ff4phesolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a huwz w itsp v-;-8n f;*ayj-i-.kuo es+tman eye distinguish two car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separated bye: eto-t .tec4vg.c:2dffvr1 about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crystal whose atoms, lying in pt ga)x;,8kzp p *mv*x c95z;4kl iyxstlanes, ar,c p4 * xlyt9p k;tm z;v8z)xix5skga*e spaced 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The 2i -q+7l d/ n-hrrvd uni98lhnsecond diffraction maximum ishu/8 h9nrd 7ninl+vrl2 iqd-- recorded when the X-rays are directed at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is obseraa 4*u5max navw8b4a w1t uf,(ved at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that tp;jq 9ttl2q8 5ee zb,yhe X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificlqb5ty 29 pjeq ;zt,8eation is   
(b) Suppose, instead, the X-rays come from a point source (as in Fig. Below) that is 15 $cm$ in front of a human body 25 $cm$ thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that results. $m_1$ =    the magnification is  

  Sam purchases $+3.50-diopter$ eyeglasses which correct his faulty vision to put his near point at 25 $cm$. (Assume he wears the lenses 2.0 $cm$ from his eyes.)
(a) Calculate the focal length of Sam’s glasses.    cm
(b) Calculate Sam’s near point without glasses. his near point is    cm
(c) Pam, who has normal eyes with near point at 25 $cm$, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.    cm from her eyes

  As early morning passed toward midday, and the sunlh)yjhkvpw1 g-l:/ j +edc)ol3ight got more intense, a photographer noted that, if -)w) 1lged jp:k+y/3lhvo hjc she kept her shutter speed constant, she had to change the $f$-number from $f/5.6$ to $f/22$. By what factor had the sunlight intensity increased during that time? $I_2$ =    $I_1$

Show that for objects very fsi 4 0fk(kvz6htn: o(sar away (assume infinity), the magnification of a camera lens is hkviz:s4(tof(0 kn6sproportional to its focal length.

  For a camera equipped with agdlmv* sw2).5 so7xrp 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye onlyn bb8zfmt/eq ko.2m-1 when objects are between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point of 1 j2wmuiq +5a7w 11lkga* c(fmq5 $cm$. What is the maximum magnification the child can obtain using an 8.0-$cm$-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
$M_1$ =    $\times$
$M_2$ =    $\times$

  What is the magnifyin.jun*/ m+sfw p1zc wp9g power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountaiik4( u:i7 kq*r /ddnyp7j( ij--pxxgz ns tries to make a telescope using the lenses from his reading glasses. T (x-up4i( iz/i*kkdj xqrng :j7d-y7phey have powers of $+2.0-D$ and $+4.0-D$, respectively.
(a) What maximum magnification telescope is possible? $M$ =    $\times$
(b) Which lens should be used as the eyepiece?    D

  A 50-year-old man usesu ovohksr7zo9l:s;j9 c e*qdzi),1h2 $+2.5-diopter$ lenses to read a newspaper 25 $cm$ away. Ten years later, he must hold the paper 35 $cm$ away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 $cm$ away? (Distances are measured from the lens.) $P_2$ = +    D

  Spy planes fly at extremely high altitudes (2:e5*v;rwd b bvj)w,8zle2dur 5 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short distanc4,iq; cvmcl: ies, exposure times must be increased because of tqimc vlc:;i ,4he increased distance of the lens from the film for a focused image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece,go(ma jrwevp 2gp:o0 g*szi.4o 6t 5n9ib ks: of a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2.np0 (4 +3h.rw8ubn ki (fv+portqqr1 v4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffract1 q+pvt+ir(f 8knwor(pnhqr. bvu0 34 ion of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one with /l bx2e3js1wd $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnifi u)l)j /kap+yu)qaae5cation of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license plate numbers. Assuvxvt 2 m/w3t 3plm*js.ming it vp*vw3s/l2 mttjx.m3is necessary to resolve points separated by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below) has one flhu y (eqa9jq be:2i;-hat surface and the other has $R=18.4\mathrm{~cm}.$ This lens is used to view an object, located 66.0 $cm$ away from the lens, which is a mixture of red and yellow. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? $d_{i\,red}$ =    cm
$d_{i\,orange}$ =    cm