Why is the depth of field greater, and ie 8m )dthmc-dd m+:b( 6yxvy.the image sharper, when a camera lens is “stopped down6+-v.mdxid(yh:ydtc8m m)e b” to a larger f-number? Ignore diffraction.

Describe how diffractiond4 ,g ufv0q7: bl/wbjg affects the statement that the depth of field is greater and the image sharper when a camera lens is “stopped dg/l4u bfv 7q,:gjw 0bdown” to a larger f-number.

Why must a camera lens be m 98 ne.hy- l*l0fjhozck -rmga0; p;oxoved farther from the film to focus on a closer object?xn.;8ge; * o hk-hz09f-po 0y lcrlajm

Why are bifocals needed mainlyks4mav z (5nh7 by older persons and not generally by younger peop 45knhv7am(szle?

  Will a nearsighted person who wfm 5i5 pyi,j2ejta ,ss2u2y c)ears corrective lenses in her glasses be able to see clearly un5i2i5y2 m)2a stju c,sfj ,pyederwater 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 t qgndq-,li w7(he width of the face through their glasses. If the person’s face appears na ql(,i-g7q nwdrrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, u0qne*g7s/vw l4ttg* p6*p jb people will sometimes squint. Why does tgb/v t*q7*6el0jpgups 4 n *twhis help?

Is the image formed on n79 zfk9;em*b 9cr(hej vq 9besl;fr5 the retina of the human eye upright or inverted? Discuss the implications o9f*ek9h b7ezrjm r s9q59n(bf; v ce;lf this for our perception of objects.

The human eye is much like a camera — yet, w)rw o:l hmt*np;53x0fdl4 vf mhen a camera 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)ln*4l;53wt:xhfpdv f r0 omm see clearly. Explain.

  Reading glasses use converging ay 2r7+fz6ahu -ggqe7lenses. A simple magnifier is also a converging lezg2 7ae6q+hr-aguy f7 ns. 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’.p bt5y upc8e6s use usually produce images that are colored yu t56 b.pec8pat the edges. Why?

Spherical aberration in a thin lens is minimized if rays 3hj1 dstt(u57:nwlpu6zn0xsare bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should facest1znlwjp h7 6uns x3(du50 t: the object? Use ray diagrams to show why.

Which aberrations present in a simple lenbt1wujxs db 0;rr3)q d3xg(/as are not present (or are greatly reducedbu 3 1q0gxr)/ sta dbwdj3x;r() in the human eye?

Explain why chromatic aberration occurs for thin lenses but not for mirrors.9zxui idbaub. u74()i dj6n5ll wb69c

  By what factor can you improve resolution, other things bvl z(ch 7hc(zf1x on;2eing equal, if you use bluezhlvxc(cz (7;of n1 2h light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large ref b1n,23;o2x 6cw3ldfu zqwfgglecting mirrors in astronomical tel ,xn22wwlf g6;dc3qgu f3 1bozescopes.

Which color of visible light would give t.84o.b/sno zgprsh17to w em(he best resolution in a microscope? Explain.4rh /e tsn.1. (wz7bo ogosm8p

  Atoms have diameters of abob*+f llos7.xf, cfh 9rxx-,yout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length;lv ljp vvxp3: k.qtpt 5,q64m lens has f-stops 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 len nhg9wnnb9f 8/ a5m)+skpq l+ls has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports dbtg:klkpdo(o48e1s4* 3dz fthat 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 3gw66 yzgk6qcby(; 09pbmq -e0 fmt (x-viwxmtaken 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 adjusto6h-ihck *4fh(gg7ul ed so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances uo(kc hl6 g7g*if-hh4 can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distanceo4p q)gmmq p7+ of 58 m. What focal-length lens should be used if the image is to fill the 2 +o4pm 7pgmq)q4-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using ran oc apdjf1di8:uk, 7;y diagrams, how reasonably sharp images can be formed using suchd8 k;anc,od :pji17 fu 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 correc h75w-8q mi+anf one1dt exposure 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 abouo4 jd9hi3a7dqr69b a jt 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 le xh9qtw nscse g34g1.8nses corrected for the far 4 x.thw 93g8 ce1nqgsspoint $(=\,\infty)$ 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 power5peg,.ljn5:v(6h k ( rd1fahkmo zif2 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 14 -xo tyc-m,)z08.*v fk omxs3a y8n kkr$cm$. 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 book at arm’s lengc,.;x.+w+ m n 4e eujlv*ydabnth, 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 e ugc0kvvi8 9n1tz1 a2corrected 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 they are between 25 lmadn3v xu8osz:;nu 6(8s2nicn k0z; i rnc)+ $cm$ 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 Ev y ;h zy25k(*1r7vn/m ydqlwrxample 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyegc lr7gc -/xin-lasses 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 system when viyl8 v cpcc (dgu,d7vr m2*lwkvz-y:q5;m ;*djewing 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 personp ,+9(08ruor tikgtgtyvh/5 toj mw9- has 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 o -+c 3evhu7bn* hak+tfocal length is+7cuva+no3k *bt-eh h 12 $cm$? =    $\times$

  What is the focal length of a magn(e(k9:wwz re bifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at3nyt0b/ /cspp mw,:hfp1fwe r,v3 2(g )gkk xj $2.5\times$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 9.0jvthsq 5wx)-*ycsm8 0.oc fn2 0-$cm$-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*lroo hvj6 q 9j1cuwxzbl51+ ) 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 5c4e 1*yyrs tl3.55 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass wr3t4 hoz:(rqkith a 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 bhfb n;tb12)qcsx+ u wv x9:d/$3.0\times$ 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 i9)q3zmkg;q o an astronomical telescope whose objective lens has a focal length mqiqzg 3)o;9kof 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 telescou s)7h8+a)f z: s0anwdovbu/mpe 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 ixupt, njcjd.bur4)(tjj 12ckg-i 7* length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75.ou iw*/,2ltj fc3k5kg2 $cm$ 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 adjua+hs;l esab 92 /0wflnsted for 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 ast0g gb/hj ou,-;v n +3w9nxhcxmronomical telescope using a reflecting mirror whose radius of curvature i-/w xgub 3njcn9v+hm ;x0h,gos 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be mja3( *jm +(avto bwqz+agnified 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. Belosrn2)cy)gm j9-tupho ) (ej x5gr11pbw) has a radius of curvature of 3.0 m for its objective mirror and a rajbr)trp(syhun mpo g gx j-91c1)e2 5)dius 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 eyepiece with a focal length ofwv0dvrq7:h;j tq we.: 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 12.0e +k gvrd+* r:erg)2(guighv ,$times$ 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- bl8 2lws/txh($cm$-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 pvt-tj1 htjsj**z wc.oi4 4+r u)oaj6the 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 a focal lengt tnf/(u(nlh/j h 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 in contact, -85x+ e 7np-duhggn jythat have focal lengtn75-dgpyh8 un- gex j+hs 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 sphericx8b )*i4ymec xal aberration in a particular situation. A planoconvex lens of index of refractibx*yc 8mi4e)x on 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) set by g5it9id /haq )x8v u1udiffraction for the 100-in. ( v/dx5g 8uiqut 1h)i9a254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve feat7,zz ab,3k xh w3u1vvcw+1r6 njf ty5eures 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 ak;0*dcw qhe0 jw61 fwl 35-mm camera 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 resolvedr2gfser:z1pu 967d :sb yiz4iqg+s7 q 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 headjeixm4 (pos8 6*i7q dulights 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 aboutyza: a ke.f-j6 $400\times10^6\mathrm{~m.}$ 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, lyin:u 7y zp1r/jehwux1buf+0qp 5g in planes, are spaced 0. ubejyzuq xp1:h w/7 +rfu150p280 $nm$ 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 at79hftt kw0t 8km qh9.c2 skb; ,jel-rp an unknown crystal. The second diffraction max jl tk 9;qp2ft9bhskh tce.,w8rk0m7 -imum is 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 diffract0hzlzo tqfv3mcd-6 + )fn :b-kion 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 th9nyo2 g9b5* ui ycnev01d5i (;ro ctcsat the X-ray beam consists of parallel rays. What would be theve ;ycgn5o2 9 cntsu*bio9 (y5dr 1i0c magnification of the 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 middaygg qf6 :m5dkr,, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, gk rdg6:5qf, mshe 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 far away (assume infinity), the magnificati tkt7ny2*4-h yqe)nston of a camera lens is proportional to -qn*s74tnh 2k y)tyt eits focal length.

  For a camera equipped wpmb hi-xkjd)h t4c; 0pf-r98h ith 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 her right eye only when objects are(yczfh y3d,: 6r kjyg5 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 agn (7 .b9eq9qg3(gk qt*jxny$cm$. 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 dx3p c)nb6i2* fe jzhe5cbk, +of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a telescope usingf+a64-oeew-regw 8p p the lenses from his reading glasses. They have powa 8ow -ewe+e 4p6pg-frers 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 j tx.pf:3*spyx5,9ym bx( ocz $+2.5-diopter$ 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 extremrdzud762: n i1nunef, ely 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 pictures at vp /s e21va0wezfdp1 ;cd(p(dt:fun u-ery short distances, exposure times must be increased because of the increased distance of the lens from the film for a focused ddc(e;f u/-edp1w 0:1vz fupsa2pn(timage.
(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 anddmynf97 c (1wr the eyepiece 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 objective5 c0) 1o. g1mr:)wjgqy diplob diameter of 2.4 m, is viewing the Moon. Estlq:r)51mwgy0j .co d1opi)bgimate 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, one wpahi0r8i,(i-5-m.ow-z u :d- rravi p :nw mebith $f=4.0\mathrm{~cm}$ 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 lensee 8so4cgh4,uz s 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. -;b. zc( fi czj 49nsgeip 5e,tgd)t0zAssuming it is necessary to resolvez9efi0g,dj)eb 4 szct; i- tcn(pzg.5 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 flat surface and the other hys8/d c+ a+fete2 gott-w;+qeip 5ak)as $R=18.4\mathrm{~cm}.$ 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