Why is the depth of field greater, and thi2/jhnii9 lq5s.2.ob,ae1; yenz q2dr dv9wje image sharper, when a camera lens is “stopped down” tii5 2 jnia;..ohq,9z2y rbl/ qdv12e dnj9sw eo a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that thjopcayr.o6 -r8x j(g/e depth of field is greater an 68j-ra .xc j(yopo/grd the image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved c6nlco+cd)4 k farther from the film to focus on a closer objectc+ dolc4)6nkc ?

Why are bifocals needed mainly by oliw1 ilh-v )5qazczj lg; 4z1232z uoyqder persons and not generally by younger peopy 21qiq 1 -wo 2z5ulia;)gcvzzhj3zl4le?

  Will a nearsighted person who wears corrective lenses q( ht+fsi aa.m.3qrh2in her glasses be able to seema (3q.+2iqsh ar.fht clearly 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 farsighted by looking at the;.5 xl*8k clk a3 oq9ri(nxxor width of the face through their glasses. If the person’s oal *l(x5 qxrck9r xni8.ok;3 face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squ7 ipu8v:1 ten0si1me lint. Why does this help8lt e:smei 7u1vp0i1 n?

Is the image formed on the retina of thez9 k1nnt;o 0ro human eye upright or inverted? Discuss the implications of this for our perception of object10o9k ntz;on rs.

The human eye is much like a3go,7hkfu f0 q camera — yet, when a camera shutter is left open and the camera k,0u3foq fg h7is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use convergimrm09,m5.w+r0f -vtm8 uv azt z.fyding lenses. A simple magnifier is also a converging lens. Are reading glasses therefore magn5yv0+it0uv tmmmw.dr8mfr a -.z9z,fifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for childne l dq7e-/pq (ki9)t whc3u5dren’s use usually produce images that are colored at the edgesed 3nw uq5p tlc7ied /-)9(khq. Why?

Spherical aberration in a thin lens i n hpow4hy8:ib4k9v.j s minimized if rays are bent equally by the two surfaces. If a planoconvex lens is8k4hb.4 ip :ow nv9jyh used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (og0svb l*m+.u-qv *tsfr are greatly reduce** glssv0 .q+mfv bt-ud) in the human eye?

Explain why chromatic aberration occurs for thin lenses bt/qu,m-0jz eopdp63rf5 /us m44e q ocut not for mirrors.

  By what factor can you improve resolution, othertsqv)) p 1 *jg*xif8kipa 7(jq things being equal, if you use blue l*(pqtsik a8f x* 1pj)jv7gq)iight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for ti w: ;mr,zsv:hwh75l h y1zw.hhe use of large reflecting mirrors in astronomical teleszsz 1vhhw ;r:7,5 hwwilmh :.ycopes.

Which color of visibleb jpajai46 j (ga4t(*r fmz4m3 light would give the best resolution in a microscope? Explain.aj3maaf4*4zj(j 4 migrt6 p(b

  Atoms have diametersv.9.v x*l nzd)w6cnry of 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 ranginl3x3 5 p:zksghg2wvc (ekc;z: r9 i-wgg 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 lensw vvz; / e4pi.nvkx.y- has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reportsr gr/crld*r+-*cvob ig p/ee4g 4z57u that a camera setting 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 at +5v- rw n98b/h45pdbdt-ns1xzucxs r $f/16$ 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 2006ucsp5n; x,sv 7,kjplmrl.m; .0 mm to 206.0 mm from the film. For what range of object distances cs l c,pvmp;7ul6r,nxm .5j ks;an it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtg;b, gnlqk2+hall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm heightggk+; lbq2n,h of the film?    mm

A “pinhole” camera uses2in *w0xq4 ro bty9j1s wkh; r;gvl4;h0e dph4 a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camerak2o;h d4eb;vqwnj01stlgwr 9p0 ihyr*4x;4h . 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 expo,v gtf6 8 oe8qi4ybvq72mx)hni i0gn/sure 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 abovz1ypi1y. 6zqqb9 h2.ujf:f rvv*x .tut 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 Example 25–6 wore contact lenses corp d5i*hdc z6 t+o+gz5rrected for the far pozzi t5+ dd c6r*o5+ghpint $(=\,\infty)$ 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 neede 91w tazl;3lp/gs.klyd 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 point of 1jjn6 7. jxp/3ij;v3;hmmv tvs4 $cm$. 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 holding0k.q *.xzx+ f-xywshv 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 b pyl85f o*jdqk. 7 4ltftk/,ois corrected 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 see objects clearly only if t -z hrc.d9x7ycbkp/7vbh5 a5they 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 neu9 8 fs8zfrctw7m)8+mw(wu81o mmcpkarsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a v4unpvdu+w w-5 u4q;u e:5rpyfocal 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 syst,.zj63 )qkydl cxcp,lem 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 has near and far points of 10.0 an0 5nid ba w;h2r1md6tdd 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 omz,hub arot,r n,* 5h4f a lens used with a relaxed eye if its focal length ibt,ar5u4rhz on ,,h* ms 12 $cm$? =    $\times$

  What is the focal length of a magnifying glassrhs+x+ y-t.qq yk1h6m of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedgf4oi2r j3iolql5);uz4 nu cowva r-y23nd54 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 a 9.00-pxa*(6oex+jpep8w.) d fdn szt )r*9 x$cm$-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 woe39 r*jxkeu3hkxj g3.. 3lvgith 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 placed 5.55 ea ,wsw0v k0if*zm-kkud/d */$cm$ 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 focal length ofo a(ja aje6we k/r/l8+ 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 x xn( i;z /lykg0(pvx /tf((yct,eul )rated 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 telescope whose objective lens ha8pznxrxzh (7 ((uaf b/wnt6af52kw (o+;hjtgs a focal lengthpn n 7g ;w((xaht 52 8wab6r/ko(tz(fx+juzfh 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 xb 1 k*lex-pb: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 telesc;yxqc )/ xb qqo)i09nm1b;rgj ope has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two ls6( urg;pup ih*-7tjhg:+) l gbx*q,;jisierenses 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 f -m9znwx 5ku*gor 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 a 4sj;/mw5br :znup* w9vjxcyr3n g()zstronomical telescope using a reflecting mirror x*gp9zwsn ;cur 4y/n35w)jbrj m(v:z whose radius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magtasb/6ncx 7odz a.x6-nified 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 radius of curvat nw)8kmco.rgur )t3deq5- ) kw ,gqfn/ure of 3.0 m for its objective mirror and a radius of curvar,8t3fg cw)u-wdgk./)kr5 n o mqenq)ture 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 9m b:rd2 vsdy4focal 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 12.0dest p+6ic9(p e ludz8(l1r2 y$times$ 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.fhg9: b/o,gm v8-$cm$-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 im7j9ub26cui the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has kf f:gmlk gs,b5g(sh8ru/7o6 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 leon iaa75puy(t 0 d:* yd4s3arhnses, placed in contact, that have f (7ayt35as0ho diy4:u* rnpad ocal 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 abej u i-v; hg6bu-mrp :0r/ra40kaf :tbprration in a particular situation. A planoconvex lens of in: h; p6vmuigt-/ urbj0k-rpa0rf4a: b dex of refraction 1.50 and radius of curvature $R=12.0\mathrm{~$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) setfr xhvj 84)5cu by diffraction for the 100-in. (2cxh54vj)u fr854-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that ca gdc8*z)mqyl3 s:j3d jn 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 cam 6xb,k:hj.h;y 0/eh rfzdvy/hera has a focal length of 50.0 $mm$. 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 resowes4k;/2,eixa e3 pow6u6y uilved 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 disti,; 7xs: xnd6wr tvm7px:jcnc5 nguish 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 by abou3 b;xmp3wri b3t $400\times10^6\mathrm{~m.}$ 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 cvx(kp,-tr1to i-hb0 on a crystal whose atoms, lying in planes, are sp1--,po0(r v cbt xkthiaced 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 unlq9 : i0 z0mrxu j7)9uokrai-bknown crystal. The second diffraction maximum is recorded 0u z-o9r)0xia9mqi7jk: r ubl 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 observed p9/a- pyak4we*f zjk5 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 the X-rak0w6d2au4z a yy beam consists of parallel rays. What would be the magnification of the4dz a0akwuy62 image? a the magnification 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 sunlight got more ik2 amjkqw/o8(k1rh:h1- n abh ntense, a photographer noted that, if she kept her shutter speed constant,:qn2-o hw1/ 8h(kjk kmhabr a1 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 objectbnk*.4i ai1)- 4cx o/xzm lndss very far away (assume infinity), the magnification of a camera lens isik- /oxcnb)i4xl4a s*dz.1 mn proportional to its focal length.

  For a camera equipped with ae8g:/ o,bx vbq1bk3v s 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 only when objects are vrdqg ,mo5s0cbs8*;ubetween 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 pawp8n zxmt )zr+50g+i oint of 15 $cm$. 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 magnifyin98ypv(xh b,bk)4e vbng power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tr06k ;rg6frboyies to make a telescope using the lenses from his reading glasses. They havfr ;rogb66 y0ke 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 usesa: gi27 5ux)krfmz wxwflt ).1 $+2.5-diopter$ 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 atgd:(lti6 .m m.h h2xr2e v ) *9j7xcpz;jqzloltitudes (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 increax7jed ch n/-: 1ag.vassed because of the increased distance of the len7jc:dx.v -hnga1/ seas 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 eyepihbw d/lb5 6hlrf-v d0*ece 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 diamewatc4 izw+: v*tuz.y8 ter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction ofauvt+tw*8cziwz .: y4 light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one wit*q6 reqqih7 l p;d:2. cd+tl5b /yvsqxh $f=4.0\mathrm{~cm}$ 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 ab3fy(s 5 9hcs- 7arqju magnification 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 toa d:f- of.g*lw photograph license plate numbers. Assuming it is :gwd.-fo af* lnecessary 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. Belo uh6y1(6f3gjf l5 nrlcw) has one flat 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