Why is the depth of field greater, and the image sharper, when a camera lens 3jkix0,e0 a/mlc sw;i is “stopped down”ali;x30cm i w,e/jk0s to a larger f-number? Ignore diffraction.

Describe how diffraction affects the stat ,dk o/cu:4(sw vywl2 gis,sl1ement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a larger f-numbek2,s:ul sd, coisv1w( y4 wlg/r.

Why must a camera lens be moved farther from the film to focus on a cl,1g;k94gw vy qx 0vkcroser objec wgxkv,y0v1rkg; 49cqt?

Why are bifocals needed mainly by older persons and not generally by youngera2/iojh o:8 cc peoplhci:/82acjo o e?

  Will a nearsighted person who wears corrective lenses inlv lx sm4p9.zzws s2xa.4tk8c- y-v(u her glasses be able to see clearly underwater when wearingp z9x -s-4vckslxs(82um.y l v4.wtza those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsightef g h)vpjd*ghdm;7hgjc4 j);ut 02r5pd or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower t;))5vuhhm;dtfj gjrc*24g0pjphg d 7 hrough the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squint.tb tqxd 829:p-6qtnpalq jy6 - Why doesqa-jdptt2yp qx9l8 :nb6 tq6 - this help?

Is the image formed on the ree7bfdqz ,+cstjg ,-z*tina of the human eye upright or inverted? Discuss the implications of thitbzzdg+j *-7 , c,fsqes for our perception of objects.

The human eye is much like a ca5t-hibd,3qq a mera — yet, when a camera shutter is left open and the camera is aq,h5 3 qdb-timoved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnif;m /j+)l /lmnq.lqap *r -yjmvier is also a converging lens. Ary qr+ al llj;jn)m*.qv//p-mme reading glasses 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 de yomw5 z+/8lnd(:e2a7iq ae produce images that are colored at thmznilaw5(ad2e8dq/: o7ye + ee edges. Why?

Spherical aberration in a thin lens is minlc( o i-z8qjjg*hk1n5j (-q tkimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real iq koig18z(tlq n( *h-5-jkcj jmage of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations prsqn9j hi.tl )8 u- fxjx.sie73s w9ux3esent in a simple lens are not present (or are greatly reduce h ls3isxjuw.789j.t3nsxf ue) -ix9qd) in the human eye?

Explain why chromatic aberration occurs for thin lenses but not for mirrorejp-4jd i 35zyssy r+8v4 ty2es.

  By what factor can you improve resolution, other thinfas: itqk6 vl1 fh cbwf7*;22dgs being equal, if you use 7sicvh2t b;klqf 2: *f16wafdblue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for t9kkhzfr b*8fci1z,8vn dn 95 ahe use of large reflecting mirrors in astronomical telescoped f8k 9z5n89bvc kfh1niraz*, s.

Which color of visiblea:yw*(2zl*f -mw2kprckr jx dbc)9jsy0.gn* light would give the best resolution in a microscope? Exp9. ld -xyyc kw( mrrw0:*bzp2n) *f*s2jajkcglain.

  Atoms have diameters ofn2ml r4mmr i)0 about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangi;gt/ iee9 f9 lv**zymnncd+b9ng from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a 14uk.1gu6ojt.;0 jg gyi -$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera settinw:wryi b/(u-m g 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 photograph is taken atbm,+k-/0 c)lenblbsc $f/16$ 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-lengthff ,b ks;:g7uknya6+:rv riwg u7.8gh lens can be adjusted so that it is 200.0 mm to 206.0 mm from thg7 ugk+;nfh,::b8kgr 6 wiv fu. arsy7e film. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to/+bl m ,mfery 3k6f3kw photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm height of yf36 lwk3mfmrb+ e, /kthe film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using ray dies5u ; 6qlz4vcagrams, how reasonablyzvq6 u;s4ce5l sharp images can be formed 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 exz 7 yd jgtt(3z5gmb;;aposure is $\frac{1}{250}\,s$ 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 about 2.0 w6 p)ghiynk, rf8 fhp)(1ck,e $cm$ 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 Exampldb ssh wq95cpy-r5z:/(tte f(e 25–6 wore contact lenses corrected for the far pszt9 bdwc(p/5qr 5ty(:f es-hoint $(=\,\infty)$ 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 nni: xd/u)v ffz7a4c 4eqw+p-keeded for a person whose near 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 poinghh7l ,lqrs9cjae: )c. i s/o yp/1pm4t 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 read by holding a bb:3clcnb5)- drj/r zrrv;y-gook 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 corrected by -y(1fobdjc/k.g956uq13x3p:syw rccmjr t f 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 see objects clearly only if they arfcha g:0ytdaq-x8283d.g yz:k 76 qrkdtva;he 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 nearsighted eye in Example 25–6 i3or3r1f1 z fwp(r/2gi asnk/ than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglx 3 q 2dm/*uahly+ylr9asses has a 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 sys q4h 3,r;zpgqrr ta7.d*xxy *ptem when 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 hs a8tsw byn(zvsdv7,msk,,4/as near and 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 a lens used with a relaxed eye if its fofw ,um zg0 t8+1i)wna 1z/ayc3kpa4f ycal length aa1y1n+w zaf cguw/m ,ty)pzk834 f 0iis 12 $cm$? =    $\times$

  What is the focal lengthxf8p/tnfajm+l0g i ;) of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated 7 e:5slf;p0z9ri owoc at $2.5\times$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 4vxp xs;goii vhf, 1a/o 3e1u5a 9.00-$cm$-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 is viewed with a 9.50-8ufcj02d ld a5$cm$-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 placed 5.55 t p;,xm;o:zqj$cm$ 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* m-bg s .elqcud(;we-w fqj.-ve;4 wg focal 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 rated at 4t t*0 wwfvo1 ch8jcj($3.0\times$ 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 telescope whose objecti5s 4nh8zpyv:l ve lens has a focal length o4:zl5yhsvnp 8 f 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 magnificationo9xt8 qqi mk*qd o2d1; of an astronomical telescope is desired to 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 85h + pp63+tm/0e ryxoba $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its twociqxi4d vj,16 l(kqx 1 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 a rw3:2,zsgzau z )e /bqgelaxed 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 4m wuu-hp ,x9r.pgu5b. c6v;)z wwmlhusing a reflecting mirror whose radius ofhr h9g vml-., wmp4 5bx.w zu6w;puu)c curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearsp)t9nbpus xa6z ;d*q0+n: 6e newz4iu to 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) has a radrq4*h5 (roru7mf0t fsius of curvature of 3.0 m for its objectiv5mr qst rh*o704(rfu fe mirror and a radius of curvature 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 hv 4 2-xy4yctfeyepiece with a focal length of 1.40 $cm$. 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 1zbdh/c) h-c+q qfu 2+h2.0$times$ 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-iqfm xwl*k4 en85(or3csq.oq6 9 8aii $cm$-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 image is ii60 xnhxs b7.located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal nfn: d ,n5uvz2length 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 lenses, placed hs-l g.gwq. m+in contact, that have-qhs m.+.lgwg focal lengths 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 sitarjhy l0 wh)r)u0: ,:rpbq) gluation. A planoconvex lens of index of refraction 1.50 and radius of curv lqj0ry)h w) r0,:u)hlr:b gpaature $R=12.0\mathrm{~$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 (p74c5fkan w5tjx 2 e5kdegrees) set by diffraction for the 100-in47at p5f kcnke j55wx2. (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to conx/air*5o g.v f+ .9tg2tq krpqstruct a telescope that can resolve 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.t5 oyz7,l kh4m0 $mm$. 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 arel z9x5pw-l7qn barely resolved 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 human eye distinguish two car headlights 2.0)spv yyo+dd0(o 3 jpxawv7q.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 separa +vc(t,y7c-px kb8.jjm;spanz h:na- ted by 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 cryscpdpvy,bd:fn m 1;.f 4tal whose atoms, lying in planes, are spaced :pdf4,pcmnd1f.vb y ;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 crysttx0y3by5m8l u al. The second diffraction maximum is recorded when 8bl m5ytuy03 xthe 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 diffractiops )+1pjbdrw was*hc b 2pm(,;e0j0 djn is observed 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 conventionawyq -s*uo+gn 4l X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificatnq*ug 4s y+w-oion 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 sumzr l5ia1 5kgo hzv/7q82l av8nlight got more intense, a photographer noted that, if she kept her shutter hol/ 5maq ra5g2vzv7 i18zl8k 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 3ykkocvb( 1*he*cdp u/fe 568hwd /snfar away (assume infinity), the magnification of a camera lens is proportional to its fk*56ddekc 8u*h/fsn 13v(y ohp ceb /wocal length.

  For a camera equipped v x -tm.pp g)jgu8egc;)h(*slwith a 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 4ueu )o lelx (g9sjj:(her right eye only 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 15 octck3klljw 1 e)8j,wz-,+/ pcz ilq*vg8l2r$cm$. 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 magnifying power of aszrco lq-8rtn dm(hb-b*z2.- $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mount2pe:cgee .b t4ains tries to make a telescope using the lenses from his reading glasses. Theyceetb24 g ep.: 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 uses :udd -memgn/v4rs8. jk(qc7n $+2.5-diopter$ 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 (fgkhl+7 s,qkdx w20d*25 $km$) 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 distances, exposure times must be in( bx8 ba/;(dras/ bcjvcreased beca ba8svbj ;d(bcra/ x(/use of the 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 of a te,x4 o4aexd9.dyu zsl g*uz(h(lescope 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 26+w(pco x/p fnyatp*mca10 2i.4 m, is viewing the Moon. Estpmca(1ixf2opp c a0y*n/ +w6timate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, on1u;*k o5j0qo( tb8t8k frgb h(ks (ep+takfn8 e with $f=4.0\mathrm{~cm}$ 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 magnification of 8.0. If the two lenses are 28 su5u( jky:ohgn6 (f9h:j ; kzq$cm$ 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. Assun 2liknuv:ep 626 fd3tming it is necessary to resolve poinp:62n uik fn2lv 36dtets 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 flat surface and the o1 2d4hfn0pwcother 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