Why is the depth of fieluili:t/ iou (yu-c-p3l; sh7vd greater, and the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore di/lu-:pii t;o3- u(7vlsycuhi ffraction.

Describe how diffraction affects the statement that the dept: ljicmtwb*; 5s2(l f0 9ojiiph of field is greater and the image sharper when a camera lens imj9l(o0*ibs2w5p t:; i lfjcis “stopped down” to a larger f-number.

Why must a camera lens be moved fartag7rm-:/ lyhn9e pc8gher from the film to focus on a closer objechan-gmel7y /:rc9 8gpt?

Why are bifocals needed mainly by older p3qk g2m5,bzz8tc4ro versons and not generally by younger people,k4 5gvbz28 mrczq3ot ?

  Will a nearsighted person who wears corrective lenses in her u jr9oc8dra6mr-su 1: glasses be able to see clearly underwater 9 u1ujsd6-am:ro8 crrwhen 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 wi/xf(0;ntqr q hkvyvw5a 8z: (d.uol+m dth of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below),no8.5qv(h xrq;tf+ku :/ d0lmzay wv ( is the person farsighted or nearsighted?

In attempting to discern distayb4 jks p2ebh*c7 jqw0o4p wh irg)1/6nt details, people will sometimes squint. Why does this help?gwhq 4sjb 2o7c*0 r6wkyp /)i jeb14hp

Is the image formed on the retina of the human eye upright or inverted?f bbx.c)n+j,cwq*ex. Discuss the implications of this for o). +cwbf*,qxexb j.cnur perception of objects.

The human eye is much like a camera — yet, when a camera shutter is left open ak8-h,*ur)s5rjvf nw;h j/p2sni t tm-nd the camera is moved, the imrm28sp-,rhf-i k nvtj wnt*/ ju)5h;sage 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 magnifier is also a conve ckrar /zcrx l7m8*do0/; /6kr eozv,prging len r;/m7o*8la/cc kezk0 dx6 pz r,orr/vs. Are 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 usualc(h cw+ qc6rn98rilbxz(do92ly produce images that are colored at thez2cb9(rhr wnqc( 8ld 6c+xo9i edges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equyd1:ho.z *zg)h12az7acm v2uf c*ow n ally by the two surfac2.gz7a:n1af ) owh mzovy1 hcduz**2ces. If a planoconvex lens is 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 (or are grea mjctvq)0sg7f;, 9ex dtly reduced) in t 9,j)0mdxvts;eq g7 fche human eye?

Explain why chromatic aberration occurs for thin le knjt z0;kmkkdsv+z0z ,g+2c-nses but not for mirrors.

  By what factor can you improv8): vynnte uf a/7m0n4i4 qlkle resolution, other things being equal, if you use blue ligh0/ltnakfmn4uqi 7ey) lv n4:8 t ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the usdke 2zo6 0)m9oj)b* vgzqaam1s;hk5se of large reflecting mirrors in astronomicd kgemvj)o61am* qzz s50ak2bo;hs)9al telescopes.

Which color of visible li- sjcl1szt* .hght would give the best resolution in a microscope? Explain tzl -.scsh*j1.

  Atoms have diametersy+//k 17 porwjptw4 aw 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-s (fd4yx4lf9fvtops ranging 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 hfs c1wog31v :z6rz9j2w; z xwwas a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a c/yxx h)1aewu6 )go)wa amera 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 (-jkglbo6, tdgp z)voo wo63vxv21: jat $f/16$ 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 l1* uszzuc)4g oens can be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range ofguc4)*zu 1z so object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes q4 b)vk5q f6lopx:bf +v3bup3 to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill theq3p3b 4u 6v v)op5bfxq+fk:bl 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole inst 2zm026pz5snwmhs7,1 ) fdr*ofw zsp mead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. fdwn6wpm1m p*szs02h z 5,o 2sfmrz 7)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 exp dgt6 l): uqaav:.i;4uoy wj6tosure 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 avig r9du *c-:+23md dp;zsi bwkob*9kbout 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 corregx1()uk:*szada k(gs cted for the far p*)k xzgds:(( aku gs1aoint $(=\,\infty)$ 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 whatu z /usi+i2 /i 2umk((mrz142hrfxmex power are needed 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 +.xyxuj(f z nc2xn ;r vc+j)5y14 $cm$. 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 torkr)ii )i7(9m8jpo )p; idcdd read 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 corrected byhg /a39 bk.hm9yhb7cw 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 /vidk3s p /a5tpj5./xih.fvi3bo q*athey 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 nearsighted eye in Example 25–6 thang rm lh: /uw./vw5 uc.07ig.me(odqhi the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglpo vei.we4(x ;asses 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 systoo11 otl bwe./:vm0ce em 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 anz.d-u*l f+ i*o,qpt -mfwti + cu-f3yvd 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 uxbyrzh m4 31n-; ,nvz.t- qywwijh47l sed with a relaxed eye if its focal length v;bx. 4my w-zn q4yhl-n7z t wrjih,13is 12 $cm$? =    $\times$

  What is the focal length of a magnifying glass 1dzb ru41mu)tb7y ow5of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at cstq4tr )5wov2 f a/ng1vfa3c0pdn43$2.5\times$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 usinge:yu5m z)ps2e a 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-zxa dsnzzr01u5y1yrgy :7 :h vt:f+r7$cm$-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 plakhl 3 1 drwg+0jw+pc6aced 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 focalchyyc34 lh+r;-6sc as 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 aq,cu( a;zh5 p8oaxdx+k oy5q:t $3.0\times$ 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 astronomz 3z8 b75rzauwical telescope whose objective lens has a focal length 5zz u3zwra 8b7of 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 astronomia 0t nkx7ibg9:cal 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 telesc t-yoe6 ;jeyi6,81yeamjh;h dope 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 lenses ib3 m)tsnl,/n (n 9zpmspaced 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 relaxed eymj0syywc n7d5l)8 m( de 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 usinx;b3tf xrsa ; ; jagf5ypa07k7g a reflecting mirror whose radius of curvafyjx; 7kaxp7a;rsbg 3; 05tfa ture is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified 0*3m hi z+fy-kwyq1hy120$\times$ 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 curvature of 3.0 m forwa qxqp)im kax+h/,4+ qilu5ss8 l;b( its objectivlh ux qip4)lx /; 8+ s(5,w+isqqmbkaae 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 p77jgein; a,nb +9xlrn9,phk eyepiece 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 1 yls 3p c/ 0xi5mo0rj-nelepwzd6u7.92.0$times$ 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.:89 t mnf y mdz,cqyro 5v73slut0+5sf8-$cm$-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;wctu-xxqn76/y )rhrt/ b kb0 is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compoa rnvcr 2j,o49n)n*qw und microscope 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 v79 4nfx b2jes+1bkh ucery thin lenses, placed in contact, that have nk7c2jfs+h b1ebu9x4focal 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 partsp (qg3.,4x8b3q: jqeijrh g micular situation. A planoconvex lens of index of refraction 1.50 .i3 xgbep4mhqsq3q,(jj :gr8and 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) set by diffrazih2o+pd66a+ln-vkqe ed+*z ction for the 100-in. (254-edp6* +qzli n 6+zehkv+ d-ao2$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can re4s*br ichq0 wk1frwec(8:y +n+w z6hesolve 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 foe8nb+:ujwr dc5sibh- qwu*.:cal 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 resolved by a.uh*tt0ub. 8w8w zp o;yi;ng p 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 distingqhsja8a3 ur sfs8ta*v-xav06z *1-pguish 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 sk bt v:(fe+9wpeparated 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 (7k 7cctp o8eyfall on a crystal whose atoms, lying in planes, are spaced 0(t7 ypke8coc7.280 $nm$ 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 sq+ *-bw7dywp.cf0y0h ww +e rrecond diffraction maximum is recorded when the X-r q+r0fwcy*0 bw.hpe ry+wd7-ways 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 diffractix7:x6tu01gktxxq 1 igon 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 conventional X-ray image that the X-ray beam consists mez61vfjm c;:+ca 9xsof parallel rays. What would be the magnification of the i1:z9 mcxae;f jcsm+ 6vmage? 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 the1kxq exw;g1d-f;,f g p sunlight got more intense, a photographer noted that, if she; pex xf;,-1fdq1gwkg 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 veryk8wbh2x+ (76zsl up yh far away (assume infinity), the magnification of a camera len k6uysh+x2h 7 bzlwp(8s is proportional to its focal length.

  For a camera equippedp)9 t1 . 1.0to gcu9wvchxqakg with 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 w)fill bm.6r(eith 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 ,g;ek *j3if are3 uqq*pp:d:n15 $cm$. 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 p p5-p6m qbis.anlci)9 ower of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tri0ox; sjp lm- gu:fijifg2.o28es to make a telescope using the lenses from his r gupmoiif-2.x0 :j8jo;f 2slg eading glasses. They 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 usesfd/6qa7 (sg br $+2.5-diopter$ 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 extremel/n7 s8mspoa-yd2:ks qtze* nadu4;n3 , km:zpy high altitudes (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 pictures2vuu.c;fvxlflv 3 2o 5 at very short distances, exposure times must be increased because of the increased distance of the lens fro3cfuf25 xl;.u 2v ovlvm 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 telescope are spa 9za1kxtlm5 j97iq3 )i47 xsk bdl/lmvced 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 2.4 miqq;f.3 z vgj3xng j ,0bwf35i, is viewing the Moon. Estzj.qf,x n 03g3j5q;fb gwi3viimate 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 lenseh 0tq *+.gvnghs wdb-q.:p f;ix 0.nlks, one 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 ma-:)gvedh.ja hlf 7dj (i6t9jpgnification 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 toi m k ,zk7ae9z.-oqs0jl3 ,fbo photograph license plate numbers. Assuming it is necessary to resolve points separateli eo-k0z,7jzkf .b,9som aq3 d 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.fx.frra6,1 zrk*f5bx Below) 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