Why is the depth of field greater, and -p2 pu)jc+ygu fv90k q5+ vcldi(hhe3 the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore diffractionqlv5+-9 phe+fcud3ck0pi2vgy)ju h(.

Describe how diffraction affects the statement that the depth of field is vc.uox;8j3 zn o:6yix greater and the image shar ozxo xn3.:6iucy8j ;vper 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 clos iw+bo,oce ;z/apmr7b w+ik /9er object?rzmb/kei/o ;caw7 bw++p i9o ,

Why are bifocals needed mainly by older persons and not generally by youngewz6 j+q;qa82hbyyx8r r peopl68xqq +j h8rb2za;ywye?

  Will a nearsighted person who wears corrective lenses in her 92cz*sfn9eu-qn. so rglasses be able to see clearly underwater whenn2szq c-nr*u9 9soe .f wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is ne v.f1ga wq/d2jarsighted or farsighted by looking at the width of the face through their glasses. If the person’s 1dj.vq/ fw2ag face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant delzp84echoa- cu.-: c ttails, people will sometimes squint. Why does thhpo ca-4-:e8uzlct. cis help?

Is the image formed on the retinieu ,.h0v//t l+vkq jna of the human eye upright or inverted? Discuss the implications of this for our perle0 v +jn kiuqvh,/t./ception of objects.

The human eye is much like a camera — yet,krj/c4 eb2a6mo ;c+rr when a camera shutter is left open and the camera is moved, the image will be blurred; but when you move yourr ;ca meok4rcj+/2r6b head with your eyes open, you still see clearly. Explain.

  Reading glasses use c/ t1hbe*gahe0ulfv *:70ls+9dwp i iconverging lenses. A simple magnifier is also a converging lens. Are reading glasses thereforegpuis +edh / 0v *ifl: h1t*0cl7ewba9 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 usuallluha0b0 6hnpi o)- 2eyy produce images that are colored at the eda uo0) 60phn2i-lbeyh ges. Why?

Spherical aberration in a thin lens is minimized if rays are gm apd k:s,)un6jt.a. /mni )obent equally by the two surfaces. If a planoconvex lens is u m pajk/ti.ns.ndgom:,6 ))aused 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 prese7j2k mq (rwsx2nt (or are greatly reduced) in the human ey jm272xwqk rs(e?

Explain why chromatic aberration occurs for thin lenses but not for mb1 xsmqbe p+0+irrors.

  By what factor can you improve resolution, other things beinns n ij7+o8o-xg equal, if you use bl7ox o-i8n+ snjue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflec;kab)0 (lqxlu,u ds7n ting mirrors in astronomical xl()b u u0a7ksndl,;q telescopes.

Which color of visible light would give the best resolutio;jl*fxfm7thai/t o+06 v )tx1drab/pn in a microscope? Explaifmtaf /tx1 d xpatr0 /v*ij+lo)b ;h76n.

  Atoms have diameters of 0+q)wjt tb2e iabout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-sth 3w 0z4u1v*,ewa rsdeops 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 hvdhr,51afu- dy4m1w4.tgl; twk hp h+as 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 7;fev:/y le*pje.umc 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 photogr*9gu:*es rg 9nlytadz ,r2r u6aph is 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 de m c ko.0j9 0m8lw81lrszg+jadjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of obj9zlcw08dj .rkjm0e+mo sgl1 8ect distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance of 58xrnirxk0y) ma/. ,t) t m. What focal-length lens should be used xmrr xa,ni)ty.) 0/ ktif the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instea3 1xwpmz :b,zp0s0d2(xqe uo bd of a lens. Show, using ray diagrams, 0ed2 xx 3wo0spuz,z bmq1:(bp how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct ex:xue2xt/ e e3oposure 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 ab iplcf6+7wia4out 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 g3uehgv) taz-- 2r4keExample 25–6 wore contact lenses corrected for the far poiuekre -zhg 2vt-a3)4g nt $(=\,\infty)$ 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 w qrcj nq,3gk54lt50njhose 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 143 nurzm2mb6h-k/r k.j $cm$. 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 bob 93qwn 144 ijbzo sfdw2j63by 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 by nt2*j1 h3: 1 *gvd0*i2p tzkuiqrb axpa $-3.50-diopter$ 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 theyi*t gv 1s9edu e :z zyp(k(p(oog.(7ic 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 t,k giub mo+u/,han the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal le f a7gpv(m,g3es1, tt86jk imongth 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 viewing an objectn ymk*idbm3c,k1- x-e (hwrp4
(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 poic;et ;z xk kz01b- n/j(lb qnxe8el5;cnts 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 wi(igcsi 06r b/b,n8vyyth a relaxed eye if its focal length ( yc8isyrn i,bg /0b6vis 12 $cm$? =    $\times$

  What is the focal length of /ocl+3tbepy 4a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated axwg0 b9 ;dmtf56d,rga t $2.5\times$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 agj/5g pc3;kzmx-x* hu 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 viewednm 76 /a6gm,berbg wc; 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 5.55jl:kfc 0 *:oacz2sp3b $cm$ 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 bx;msv xr5(/qhx z0c *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 raty 1epboa.wa,fgf6 l y743fxfmh 7oz zau i1.01ed 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 astr8bo*dcoo-gjl r7*mx 0onomical telescope whose objective lens has a f *xo-g7*b oco r0l8dmjocal 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 astronomica 06xz(kufzd 3or7izg6 (wn9 ycl telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

  An 8.0$\times$ binocular has 2.8$-$cm$-focal-length$ eyepieces. What is the focal length of the objective lenses?    cm

  An astronomical telescope has an objective with focal length g:a.1o-s5xivl nsx4c g(mu.u 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two 8nsnt0 / sb3dwkyq rz1w)r0 1nlenses spaced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relaxe 9w 1+toqzqer15tnmw 9ct:wtct:jf; (d 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 po 1dru;.qgq)m tvq, ochyi(x20 wer of an astronomical telescope using a reflecting mirror whose radius of cu1mqt 0(r,cdy q ih;.o 2)vxqgurvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be mabm94,x127 l n)g;rqx aqyojmagnified 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 radius4rv g ka*q;c kz5a4iyw-f5 k(*ihxvt i2/s1at of curvature of 3.0 m for its objectizs5h/-4aikqiitygkf ; *14ak2 cxv(at rv 5 w*ve 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 eyepi)uor6 88aqi jc ngga*dr*ui 4,ece 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 12waya,+g9h m6t.0$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1.8)4 - czkp b/ -1n 8sjnibysen*iavsfi -,;nuv4-$cm$-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 i)j8 s1/q wh)vefnj kp3lgpz)5s 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 z vxq gter*3u, vgu98wacylr-+8u9(o 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, placv 6)9ls u8bjz2vtmah8ed in contact, that have focal v68tba mvzj 8 29uhls)lengths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular situation. i ,yd3ja8f 7aem:h k7itlik0)tzj1t,A planoconvex lens of index of refraction 1.50 and radius of curvatu 3jt ,h:k )aitifk7dtzeyj0l1, 8ima7re $R=12.0\mathrm{~$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 li0q h-o f2a*gh;wvom*nmit (degrees) set by diffraction for the 100-in. (254-mh*-0aho qng2w*o; vf$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can reso- -zxtuy)y3 oilve 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 camer0 2mpl3zta, txo clp83fidqf9,z.x e7qy s):fa 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-yearsb yh9h 7wwol sw2hon8z);1a) y away are 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 distinguikltmk6kas436 k +cs/jsh 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 separahk4+mr+ xc+,2 7r sr.n,v ktqlq9qqa yted by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crystal whose atoms, lyife58hkaz hdmt/v d+ ,/ng in planes, aret hfh8km//vd+ 5e,zda spaced 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 unknown9+vy-fw-ukb p(c / vno crystal. The second diffraction maximum is recyv kpuf9 no-bvcw+/- (orded 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 lop k9 nf2e;euk*9s6os;,eh b 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 ms/ 6opk 1w1 km+tc+tiX-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnification i1wp+ o61tmkk+t/mi c ss   
(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 ygno,q . rm n0s iwy0i) piw8dj902h)lmore intense, a photographer noted that, if she kept h)jir82w.0 q)yh 09siiy ml g0pnwo,nder 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 very far away (assume infinity), tpkj/noyojn87p7k mh0/u/+ ht he magnification of a camera lens is propork /yh +7/0o7 mtnnpkj/j ph8uotional to its focal length.

  For a camera equipped with a 5xh *pa,ql 0a v3., jdncitd44l0-$mm$-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 ,lio3ar uon4ez 38as9with 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 poi er8gw7pesui+l-/8 j1 hd3x-lnkpc 6znt 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 magnifying power of 2aq5dp nuqk6 *a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries h. wh xq+2 c +vi:tce)582jedi*khzvdto make a telescope using the lenses from his reading glasses. They have powersd5+)*ke ch2j :. qihctdwe8+v2v x zih 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 usec(dy v4rbks 40s $+2.5-diopter$ lenses to read a newspaper 25 $cm$ away. Ten years later, he must hold the paper 35 $cm$ away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 $cm$ away? (Distances are measured from the lens.) $P_2$ = +    D

  Spy planes fly at extremely high altitudes (;pzzrztg )kzn.c bc,up bd*,334qen 4 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 times5r1p ap6b7tug rjd kf6g*0 iow6:u tw; must be increased because of the increased distance of the lens from thaf7u;t6k gw6rijp b5w*otp6gu 0 rd:1e 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 telesco;jjr g.y *0elqpe 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, wi3ty bbcwfg-5z9u kx0fy;p(r (th an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can z rbby gct(;p-ku(w 35y90fxfdistinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, onedply8dxa 5 +);pf ew2e7sbs n/ 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 fl.+/p*wdfqn *o v:ce a 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 to photograph license plate numbers. Assasd4pfphio,,( +p fz) uming it is necessary to resolve points se,so 4p fhd,()iz+p fapparated 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. Belj. pj0f m6oef,ow) 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