Why is the depth of field greater, and the image sharper, when a camera l a(4qrze+e t.uens is “stopped doqut .ze+(r 4aewn” to a larger f-number? Ignore diffraction.

Describe how diffractdwplv4pt 0-lzxy z(1 z)jw0 73qm6n uqion affects the statement that the depth of field is greater and the image shw-qzlp ) l04 03jv(1tzundmypwzx 6 q7arper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a 01f, jbxt*s ew( tjbfx 3bb(d-closer objeceb txd 3-(*,jtbbf0bxs fw1(j t?

Why are bifocals needed mainly by older persons and not h+nr4chl d;m iq* au//generally by younger peoph4 *+udla/ /crqm;nihle?

  Will a nearsighted person who wears corrective lensem.: .dfjl owii f9ucv;(m;3cvs in her glasses be able to see imv;3uvcdwmc i9( f:;j.of.lclearly 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 neah d*.xou;f ncht-ve (0rsighted or farsighted by looking at the width of the face through their gla*e 0fdnoctx.(h; -vuh sses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometiq1o:wt 78r2in.um1ux +rb*wn9 2 nj lzvxze3cmes squint. Why does this helj831219b rxn7*rwz nev. 2:mw+xcqouuit z lnp?

Is the image formed on the retina of t;tbm,p5gzq,o nec ec.g7in 0/he human eye upright or inverted? Discuss the implications of this for our pm,;e /ne.bo0ngtpg,ci5 zc7 qerception of objects.

The human eye is much like a caic-:qm027 v h wv4++u tcdqxuk6w st8nmera — yet, when a camera shutter is left open and the camera is moved, the image will be blurred; 4x6uk++qcvtsmidt : w-cvn20u hq78 wbut 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 conver73e:mex f, w93yu0hyr g7yunsging lens. Are reay0h7mf, 3u39ysyux :7ge ewrnding 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 u o wb0q2j7 q*cu4z)l/cmely.children’s use usually produce images that are colored at the edgql*l jw eubcqz0. co7 yu)/4m2es. Why?

Spherical aberration in a thin lens is minimiz5 j1kx/ yb ,+rs i+lq;5vsyooied if rays are 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 face the object? Use ray diagrams to show 5i1+y+isoy5b o;v lks x r,jq/why.

Which aberrations present in a simple lens are not prese t 63n(rei132zcyzrfj nt (or are greatly reduced) in the h(f6 e2rzity3njc r3z1 uman eye?

Explain why chromatic aberration occurs for:muzc +fp9yu( thin lenses but not for mirrors.

  By what factor can you improve resolut lhl( 9dvsp(6.siedc7ion, other things being equal, if you use blue6lsp 7dis h9.ec(( dvl light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors in ast s(7 cqgileu8az6d0 7fronomical telesc6ulfe8 7d0qg( sz7aciopes.

Which color of visible light would give the beyei9nvap*. ue1 dl9*c st resolution in a microscope? Explain*yciela v9en*udp.91.

  Atoms have diameters of ab9ac5xi u0 xmm7jc gc(f-6wi/ bout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops ranging frosg5y 4-(8aulsn pb 3ez d-5hism $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera 4q s s/bxcg+2slens has 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 calk 4m/2i 6cvdxm b3c3ymera 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 isb+shgsn3:9 n)- dkzyg (iq8+q 0tlc k/;nupgh taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

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

  A 200-mm-focal-length lens can be adjusted so that d41mdxa g jn +dohf(q182v ,dait is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjusteda d28 f,+(mnj4x q 11oagvhddd?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wiv- yq*ui+qu4f 9a se*x,g. r9)sgvrqzshes to photograph a 28-mtall tree from a distance of 58 mzu9qrsv*9i q 4 *. eq,v+-xgg) ursyaf. What focal-length lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a0r uw 7w .re 17zfn3 3 qryum+)iwgdd5arx7(ml lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consi7a)ngr+r1 uwqm(zi3w 0yw3du7md7xf r r5le.der 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 expw7 s1 s))n:u5bx :eu uak3mpuxosure 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 abo7wdsl0fty pdg 0k (z)8ut 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 personv/0zsvq0 f mra:c.+ j) lowht7 in Example 25–6 wore contact lenses corrected for the 7rqj s+ v. oaml0w0zh)ft:v/cfar point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person wcyl,usgd;n4y.. jnd 5p osta4h. v;r+hose 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 p(en:p5jzn3 jj5akx:y oint 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 tm/ ht w5p5j)z,y;p8tjwg kaf1o 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 od 9vza1k(k500t t eepby 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 c*hk4p8o7cjtxetp 3 p:learly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Example 25–6 than the 2.bu8;mzleh n6q gnv7 4(0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s euzz*a+w rk jx 8u;+1adgyje6,yeglasses 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 systexev/:6l2p ju9 h8 giowm 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 adnjjg-)mm* w 0nd 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 ii4,m aecb*n;g n)iy1b s-f )w q,zw;waf its focal length isf;mzi-g))s 1*;wnqcb 4 ywai,wbne ,a 12 $cm$? =    $\times$

  What is the focal length of a ms h)sgw-78wwqagnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated ao6 b nkd5 (t4p8ik(qdyt $2.5\times$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 usin0+xv *i :w+-/m/cvvoe qa,i soyeo/ arg 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 is3otd,nhfb75yg.t k v* viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placed .sk ld7,ixwi(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 focal length c 2s)g zi1) s5aspfyv ) i63p.h; ru(eigmyh9zof 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 auhx4h om no 6ojsq;ktp/k+ig(:8-9s $3.0\times$ 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 astronomic:k;un3fxqrgm e6gvy:1:; b ifal telescope whose objective lens has a fog xf3gq1:nf:; ebvuyk: ;i6 rmcal length of 76 $cm$ and whose eyepiece has a focal length of 2.8 $cm$? What is the overall length of the telescope when adjusted for a relaxed eye?
M =    $\times$
L =    $\times$

  The overall magnification of an astronomical1 5mtj ,xhc-ei 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 lengtn 0.nrgecxg1t* q n.,oh 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced i.y 67u1srl8qgllxe* 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 eye is * p heeg/ha;4k32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying powerc -fskrtj8q(l01pag3afb l21 of an astronomical telescope using a reflecting mirror whose radiusfta b08g1cla l(1frkqs-3j 2p of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnifiedtun+5f1 sw/j g 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 curnn)rq49he8qd6n bu/s vature of 3.0 m for its objective mirror qd8n9qrnbn/ 6)u esh4 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 eyepiece withs+1ji.w oix8v8 s1bs n 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 12.0l c lb,e+xsr,,$times$ 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-u*+)dao2v;d, q my0lboc+yym $cm$-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 fi3h9 vjh-g ooancg9+7anal 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 foca0ck3zzimv lm/4,h8h c l 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 lenses, placed in contact(kc9fizl0 ga ub;gv(5, that have focal lengc ugg5 zkf0i(;lb(9avths 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 si)-54tl . diaqwzuxx. ur7q8vx c/i5 4 sav8yzztuation. A planoconvex lens of index of refraction 1.x8 iuacz qx-di 845 /) r4xtzzyuvvswaq7.l5.50 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 ,,3lvwgc.+9qgpz; :p -zfynllk 9jbpq2/hq c resolution limit (degrees) set by diffraction for the 100-in. (29 g,v 9p qfjpchg cy,zl/zn:2q;l l+.kq3-w bp54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construc*t 0f,hyw pp355vkgzqv3cj;ht 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 alnu :(j43j z4svrt4ihas 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+ qzo. .+8vemtr6jnrn 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 diio3) d*fkmg:g7gr ;xt stinguish 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 abo zlprr u+1a5q,ut $400\times10^6\mathrm{~m.}$ 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)s( 0xvsmtd; r 0.133 nm fall on a crystal whose atoms, lying in planes, are spac0 dmx)(tr;sv sed 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength 0.0973 nm are directed at an unknown crystal. The sec/-lc9 lsl5uefti y( s9ond diffraction mayefl/ ts9c5 (lul-9i sximum 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 diffraction is observenif((j l)jso/ xgx-n9d 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 imamlqrt*e ukoq+i 5g r81(. y;xjge that the X-ray beam consists of parallel rays. What wox.( ;18lq +k qotgj urey*im5ruld be the 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 passe lj j3ff0iqx)/d toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant,flq fj)/ij 0x3 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 far away (vd re4 af(,(gmln7t8bassume infinity), the magnification of a camera lens is proportional to its focal lengt4eagfm (t(nl,7r8 vbdh.

  For a camera equipped wiw-5z 9ida) gwgftl.c- r /d.ytth 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 ob85gy8hci fn/rjects 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 o3kaacj3 j/ 9*aglhisam)2e(ygva -1 cf 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 magnifyiyqyo;mmtyf k77tpc4l(9z9m *ng power 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.brxp0 8nfg03xk x* yw make a telescope using the lenses from his reading glapkxbx w080f n*rg yx.3sses. 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 usesvj f)ydkl2cfo k4bwf)6 0+m9m $+2.5-diopter$ 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 7m ijbzw2+-hu psg 3w1high 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 very short9/dgqy qvhh6* distances, exposure times must be increased because of the incre /gqhqhdv6y* 9ased 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 telescope ar.0 fx1geaa9.zz h i49roa5pl te spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2.o7p nrtpj5 u9+4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can dirnjt97pu 5o +pstinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one with )eyxi iqj7h,/ 4-l;sdimp.vk$f=4.0\mathrm{~cm}$ 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 magnifpp4sv+ bod /6ptc56zlication of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to phot(-v7rp d io,obt7sz*f ograph license plate numbers. Assuming it is necessary to vb*-pi (7r,stdfoo z7resolve 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 s3w1g8r 3lbjd gw6kz7 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