Why is the depth of field greater, a6ejslnilyb9/46 v cv8 nd the image sharper, when a camera lens is “stopped down” to a larger f-number? Igno6 bl/jn y68cvlsv9 ei4re diffraction.

Describe how diffraction affectbi6nmz-g ;t (ms the statement that the depth of field is greater and t;m(-ni m6z tgbhe image sharper 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 closer obsq oo-kob3fd k+6p -vefb:xl;d0 (st/ jec xkbflktvo-sp0os-;b+f6/(3:q eodd t?

Why are bifocals neede cl)vd 0k6 h3c3 keqdn,tk,g9td mainly by older persons and not generally by younger peopd 9gnq36tdc 0e,tlk khkc)v,3le?

  Will a nearsighted person who wears correc qhulo-f;5agam7s1f:p*c u.rtive lenses in her glasses be able to see clearly underwater wheflsra; c7-ho1.g a: m*5uqufpn 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 atd og8g(;q6z tbg: 9kzb the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or otb6 g qbkzzgg(;8d 9:nearsighted?

In attempting to discern distant details, people will so*tco/rfpmt3 4metimes squint. Why does this f3c otrtp 4m*/help?

Is the image formed on the retina of the /2sf uwmhkc1z( gq gjo +9*j)ahuman eye upright or inverted? Discuss thogg *u 2mfa+)hcq9k /s jj1wz(e implications of this for our perception of objects.

The human eye is muc)e:o )ig ) ae (r(qazf5u)pcqfh like a camera — yet, when a camera shutter is left open and the camera is moved, the image will be blurred; but when you move your head with yoq( fr)qa: f) (5c)zeg)eipouaur eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a convey pwychyc,q )efu/:5sscuc,v; n .m:4rging lens. Are readi.;p:c5n)fceycm ,: c, u4h s vs/quywyng 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 usually produce imagm8qd kaykx2e-+4 jky -es that are colored at the edges. m ka 48-jkkdqy2x+ey- Why?

Spherical aberration in a thin lens is minimized if rays are bent equalleipskp*,+r9 b nmev9 *y by the two surfaces. If a planoconvex lens is used tk,r9**iem9+npb se pv o 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 greatl9 9kht6r lc,c6neoh*u y reduced) in the human eye?lk, 6*trh uoec 9ch69n

Explain why chromaticsimb+ *50l (u 9wwgzuws 9tlb1 aberration occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other things being equal, ir 4+ qa8lbf/v ia(ep*bf you use blue ligbfae*4vl +i8apbr /q(ht ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors i6 1.lqv n8be rmyi ph./q96wsh7o stj6n astronomical te. onshmh8t6wqi . y spb1ejrlq6/v967lescopes.

Which color of visible li b )8pgfr(vfgl8:vy (qght would give the best resolution in a microscope? Explagy: g((q bp8) lrvf8vfin.

  Atoms have diameters of about /m-pg, f:rmwptx((k o $10^{-8}\,$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 fro3jmj y6-b(ki jm $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has jjiy j.yx.:. ooje;/k 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 cam zt9rxrgga:jrgt p 3kpvj4 29r1ts744era 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 pho -vvhcwkpx6qno7v; +2tograph 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 adjusted so that it is 200.0 mm to 206.0 mm frzrv;wl5g ou )ywk759y om the film. For what range of object distances can it be adj5o kvw9rw);ly z5g yu7usted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes t4,kzhrg.t l-b*h neb5o(vj8h o photograph a 28-mtall tree from a distance of 58 m. What, vhb-nzh5o bt(lh*. 8 rjk4eg focal-length lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uaq dakg8 *14znses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp imqaz g4*nka1d8ages 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 expc nejf1*n,;3 yvyz 3vcv 2: 3;bzhxwuvosure 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 abouty wnamoi :r kl6+acw)7+/*x ew 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.)b+e 3e fdi:buvjcm.ef,(lj g : oho+ 25–6 wore contact lenses corrected for the far eegm: o+v,i+.:ohu.jbb ( )jed3c ffl 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 a0yw2j e ua x72a0(z jb9agu+xv 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 pointm9l0y wddqrc 0y8fv2 ;x .vu1e 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 to read by holding a book at arm’s length, a distance of ntw 3;5:bl.q b5uxxba ,g3cb e n6lz2l45 $cm$ 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 bbudin7lc3mmt:/ q 7e-ifs ;8d y 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 61fairwo7pmv n07p+upr, 7ri see objects clearly 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 2 vl ai4vhcnzd,o+0x66j, l3em5–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsigh7 lghj-o7rg lmd6c sh n,./a:+h wd 4xq;or9awted person’s eyeglasses 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 sy15/wopj; lsn+)p da s1u0bdzlstem 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 and 20.0)(-v2xz kuzy m:.l7xtt8z ,lzmzplcuwv m 3 7* $cm$, 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 focal len5 *hke9,i9gqc9s gje b a-3xv/wg0 rmxbr+9eqgth is 12 b gxvihj+-kq9/eq9 rgc be3sr*5 ,0 xa9mew9g$cm$? =    $\times$

  What is the focal length of a magnifyigy(f3*ga4pj udh h b//ng glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at.), wvphv/ fvc $2.5\times$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 usingk*me2. mxc *9ar; y6wdhdsbe0 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 s*i4qf(zcf c1.50-$cm$-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.aled w i-as x:,-ig(h.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 of 8.5 m/d;sncz-8u j bo+pt 0$cm$ 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 any aq4:0wtxw1 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 astronomical telescope whoseiduy-mds cxhv/uog5nhn )i */9 ;ud51 objective lens has a ; u dino-sgiyn)*1u d55xhvmd/ch/u9 focal 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 oq7jg + oicqlbn2*26zy f an astronomical 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 teles0;gmm-k ov kkn(0rid1 cope has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has qy4;g ;k1 nm o .y4;f-qv,mgodm x7mteits two lenses 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 m0okw c )-rew4a 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 astrqpb w;/ gy;capdhi)75onomical telescope using a reflecting mirror5w ;g qd/;ach7pip)yb whose radius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnifi+215a9n6 ezn87evtaz juw4arjn9jnhed 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 curvature6 .-x 4hlskuow of 3.0 m for its object.oluwx s 4h6-kive 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 eyepiece with a focal length of 1.40 :rryyq31 tkk -uajt3 .6gc 9yl$cm$. 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.d) ahxx54i g.hlg4/j k0$times$ 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 1.0f6us g5 tb4qi8-$cm$-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 is lon2y a)97z w-t 8iiefm,d hi*nn.bh kb;cated 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal le 6h3b;q4q6s b) 2pu0.d9azluyo lw yupngth 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 lensesx)7t/w7bxoay zqxl q ,+.ggw40 6cyac, placed in contact, that have g,0owa x4 7cb/ .x z g)yq6ctlq+xyaw7focal 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 si )gk4c9gdxvac3dmn:8e(+vq d tuation. A planoconvex lens of index of refraction 1 cdvq gg9+c v k)4xmde3na8d(:.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 (degreeo3sw /:lde*+wc mif *cs) set by diffraction for the 100-in. (254wfs*+ :d/* ocwle3cmi-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish tt/l)o 2hr+s*i 9 brhkwo construct 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 has a foz:,9 m wr*wpxj*/nhlkcal 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 bac1znas 5;4 f9zv (ncd4mnmy +yrely 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 distinguish 22d*v8etzjg /tbn6 tntwo 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 apw 0 lo 64hqeia5wasal5i(e:n/qk;ssf4.5fbbout $400\times10^6\mathrm{~m.}$ 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 fal 7ku+ xtt*7p 7rvkj:gel on a crystal whose atoms, lying in planes, are spaced 0.280 v7uktxrp:*jte7k g7+$nm$ 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 0.09tji l 6q,l,fys:.gp 6y73 nm are directed at an unknown crystal. The second diffra :6s i p,tql,flgjy6y.ction maximum 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 obser,cu nkub9g4 3qved 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 Xf,r5+vna 8ighu8 by b uk.y* wkbj4i.1-ray beam consists of parallel rays. What would be the magnification of the image? a the magnifi a k1nv.yb48hi,u.rjbg8kfi*+5uwy b cation is   
(b) Suppose, instead, the X-rays come from a point source (as in Fig. Below) that is 15 $cm$ in front of a human body 25 $cm$ thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that results. $m_1$ =    the magnification is  

  Sam purchases $+3.50-diopter$ eyeglasses which correct his faulty vision to put his near point at 25 $cm$. (Assume he wears the lenses 2.0 $cm$ from his eyes.)
(a) Calculate the focal length of Sam’s glasses.    cm
(b) Calculate Sam’s near point without glasses. his near point is    cm
(c) Pam, who has normal eyes with near point at 25 $cm$, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.    cm from her eyes

  As early morning passed toward midday, and the sunlight got more intenses7s k9j07 .exvl jye.e, a photographer noted that, if she kept her shutter speed constant, she had je js 0ke9 .sx7yvle.7to 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 magnifiv;*vm*x)q wft cation of a camera lenqfmtx v*v w;*)s is proportional to its focal length.

  For a camera equipped w0+m1ltq9 mp,x,f savb x+gwe +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 wir0tkk uot-rl3:qx1l*th 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 95e.b dgly(r)0 q 1obxic(jeknt 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 magnifyingo.5 fb t4 lhuf6/sv,gu power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains trqu2sqq5r 1 c nlja9h9l 45-p0eb rwj/mies to make a telescope using the lenses from his reading gla ruh9 0m5qrjwqjeal /9plcn4 5-bq12s sses. 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 usng-/v3t* is ) c/o(5esnf( jjs6gdkbf es $+2.5-diopter$ 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 extrk)(3zsh j dw(+) cnlggemely 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 very short distances, exposure times must bybv p(5uo2rjf531k dgo* ocw5 e increased because of the k u1db5c 5ov(25g wjrpf3o*oy increased 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 ts1e(j ;oub0y 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 objective diameter of 2.4 m, is viewing tr j +r31eidbj 0;0edjshe Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Co;ij 0 jd3ebr0jedrs +1nsider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, ot r ,*1tbhrc5sne 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 magnification/falww6gm.clula m3-n3m :6 x 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 aakr:+,)pjnnvudy0c x1)5 u sh spy satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated b ndu1 csp)yu 5jakhr+n v)x:0,y 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. Beloj3 uwno;* g/bvw) 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