Why is the depth of field greater, and the image sharper, *ujbxk7k5k k a7omg 0otz /*-vwhen a camera lens is “stopped 7kovjx0uk k k-o /tmab*5gz7* down” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depthvx+ x*2aaz 8vcq 1.smu of field is greater and the image sharper when a camera len18asx.m zxqc*+v2vu as is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a clz10(e+ey+vxd 5g ad7 zzyz+evoser object?e( ag e0z7+x+ veyzdyzvd51 z+

Why are bifocals needed mainly by old80jceywr j i lfj 0d+f:-)ekw6er persons and not generally by younger people?e 0de6 0ijkwfj):w-jlcy+8fr

  Will a nearsighted person who wears corrective lbv/ b)e*da m1wenses in her glasses be able to see clearly underw*1)b da/ mvwebater 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 looking0f 907 -yeoqr1 ojknyf at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted orkyjff -01e qo97yo0nr nearsighted?

In attempting to discern distant details, people wq p0we6br9cb+ ill sometimes squint. Why does this 6cp+ qrweb 09bhelp?

Is the image formed on the retina of the human eye upright or inverted? u o.t6d pu9aq2a0ee yd1bp6b 4Discuss the implications of this for our yqbo66 1p2b0 a e4deuap d9.tuperception of objects.

The human eye is much like a camerar:r5:r a kf ici;c:z25 zoffh: — 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 your eyes open iffckr: :5;o2:fih5rz: car z, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a convergc)*vad(tr4mzpcw y2(4ro8 fying lens. Are reading glassey)4f mc(( y4rptv raz28o wc*ds 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 images th+*j wx-1kb 9h*5bwow xkys0khat are colored at the e*ko1 h w-kby 0jh5b+sw*x9kwx dges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equa9mkwhl-bgo6cyta a )1e0t1wz84bw+ rlly by the two surfaces. If alazb)g4rcm9ww1-0ty t 6koh+ e 1b8wa planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are nolm9l q 5v//6brwi:ofp 8p9smqt present (or are greatly reduced) in the humanvqwpf:poml/im6 b 9l sr59 /8q eye?

Explain why chromatic aberration occurse r r3y-ldk61nuxye: -.(hovg for thin lenses but not for mirrors.

  By what factor can you improve resolution-qzco(x9q cm fpq11 lfb..a *p, other things being equal, if you use bluc mcqoqq9. f(xbpz-1lapf 1*.e light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantagebh83 cb29htp7k7ew hk22g tdgs for the use of large reflecting mirrors in astronomcb 9t 72kgdeb72ghh2tw 8p3h kical telescopes.

Which color of visible light would give the best resolution in a microscope? Euy/qn(s *q .( jxut pkdgp :5nxm54b4hxplain.4: xbg nksu.q(yq/ xd5nh m(tjp4 u5*p

  Atoms have diameters o-zz q ,v+9wc3ucxuxa, f about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length l-* dxamkn2w lbeo4(.7w(x.vbocm+tl ens 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 lens h nph-k. t.qdn6as 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 camera setting of 5 egsann1 bnhu9hi;/ +e+ u8qx$\frac{1}{250}\,s$ 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 photographzo op4vql26zvo* n1dvf0x k-) 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 bc)d c) n nynk4iif.09vvr9l *ge adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it rfg 40nlcv. idic9yn)nv )k9*be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wia0 uyz0au:rvwp 4be230wmmn7shes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens 0bum0uweyw 3r7:0za 4pm an2vshould be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinh+pf8 3boiretk/ ;80;hlgeabz ole instead of a lens. Show, using ray diagrams, how reasonably sharp b3e;h/r8gb et a k0zlif;o8p+ 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 correcmf3c-*7 *reymz om ,ro,9 -kwp5gtdxot 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 ar .0p5mk+2yt rlan )zvbout 2.0 $cm$ long, and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens? $ f-stop$ = f/  

  If the nearsighted person in Example 25–6 wore contact lenses cog9rmu5z/yzk) d 6 zne)/xki0nrrected for the far py/dg rk)znmn z 95ku0 ie6x)/zoint $(=\,\infty)$ 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 po4535fzprz,dhx -ra+z;nw e db wer 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 14bti+ wb+6zf+ m $cm$. 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 4/c ,jg -eim q.hw27lwjsc5 5xq5 $cm$ 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 0jg;f fjo,j: aa $-3.50-diopter$ 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 25d ;t7zc 3pl6ea 45hwvy zghgi1g7u8j.s;.huz $cm$ 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 tha pv; mo-3iiyepd0t- wl69m4 ksn the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted pe9rn0j7z wbpl9 ri++yx rson’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 system when viewing.bk8b egu j5tez62nqipp f3.2 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)h ybjpke5, 5wi.9fo t 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 rea8hs/oj q2a o:p,qu 2ulaxed eye if its focal length q 22sqauo/hau:p8 ,ojis 12 $cm$? =    $\times$

  What is the focal length of a magnifying glass rg2 x aooyc,,*pi w.0uof $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedmi42o 0ydr8,,lxfcd 48 8eksa1 qzkjk at $2.5\times$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 9.00- ka(c8via)k0 t$cm$-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 withbcx8 0(m w ,;d/lfxgjkspu n7* 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 place eh9r:rs6g,7sk 8p bkzd 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 of 8.82h hcx)w-jlcs ;tc;h5 $cm$ 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 ra7ku3cj-y5d t/t- cx crted 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 astronomical telescope whose objectiuz p dou)hnk 3lf8sl)hf34 /i5ve lens has a f/ u) h) kn5o4d 3lp3uils8zhffocal 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 astronomi aqq0oss6uay70g)v s4 e2g(dmcal 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 r 3t*e4;ywmby objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two )s 3j rx/ebb jbe;faj+5 pf-(n 8wa6vqlenses 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 relaxed e) zvnkcco0fb;3r8 8 koye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope using aweqkdc ./od.2x ,bvpa+ k /ut: reflecting mirror whose radius of curvature is wv ,t/ddk + .ecaxboupkq:2/.6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be mack 4m qc14sy4cgnified 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 cur* gg(u/,qsvd45mhu.zhr pw+xre fb7bkv5 ** fvature of 3.0 m for its objective mirror and a radius of vqu*4gbkfrrszpe7b .5,+/uf mhx*w 5( dvh*g 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 ;onnfc, o.fq hku*g,/:lbut ;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 1aii5(q mnz3;gea7uj3 2.0$times$ 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-:q,fflgu jp*( $cm$-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 located 24s/nzbtp1j 717z lblft fxy 7)5 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscop3 4j ;j y1ty):jglyuybe has a focal length of 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin lenses, placedl5c r-f4jnk1r in contact, that have focal lengths jnr1 -lc5k 4rfof $f_1=-28\mathrm{~cm}$ 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. A planoc bs.j vpph0dsxo6j 9+/onvex lens of 9o+s 0p.x6p/dbsjvjhindex of refraction 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 dinom9u , cu sv+*io8s kv8evo/:ffraction for the 100-in. (254-/k8ooso:vi v* ,eu9um n sc8+v$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescli l tce9wkn(*rgu + 7e+veu-wji; 64iope 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 focal lenga x.70nsl efej9ighic 9x- 8;gth 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 awgas7(ua 8q r:yay 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 dist mwufpt6x0 *b41e ws,qinguish 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 abou-i* e - t4su3clc1c3a+uva 6g/nv ywplt $400\times10^6\mathrm{~m.}$ 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, xg(-w9 11 nhug0apdi qlying in planes, are pd(i qxah-nw109u g1 gspaced 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 0.0fy0.kvuzp -sk7 :f3+g1 tvt uv973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle of 3p:v-.v t7tuu k0gvsz+fy1k f$\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffractio (3awu-,vzt9ne cet9 gn is observed at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that the X-raymarwv*-ax41u71-u2c ws f wovv( ) oog beam consists of parallel rays.w1vvm(c w--r7uugo1* v ) 4aoosfaw2x What would 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 passed toward midday,f5gy * pt armnp7b*i-qc;u +4n and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to chc4 +qu 5mgynrnf7p-*t* pb;aiange 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 magnification o 3a(hwip/hyi .:a).xbz1 awdof a camera lens is pro.ybdawwzoh1/pi x(. a 3ih):aportional to its focal length.

  For a camera equipped wito7 v1jliou3/xifd+9 0e 8mbdzh 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 rightb*92us: tylv0pw t; bx eye only when objects are between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point oiq 5xzjbe2rc hsi6(06f 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 om* ; ydau9kct0f a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to ma/m.f61ddm5k+ uoutkc.k 4 ly mke a telescope using the lenses from his reading glasses. T ymmd/k64k mu5u+.oft1d .lkchey 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 usesjs5.l lesj6b+ $+2.5-diopter$ 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 altitu 6a;aabku g19/r 2lv7frdy- fldes (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 vzh0 qv.1vd 8.k ztoum45p,bstimes must be increased because of the increased distance of the lens from the film for a focuv dbu1z o, 5vp s.q0v4mhz.k8tsed image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece of a telescope are spa cqp /qe-,3o+av,d yfpced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with any xs-o( :1lled objective diameter of 2.4 m, is viewing the Moon. Estimate 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 nearl( xedy1 -o:ls the Earth.    m

  Two converging lenses, onv8ne:j vtw f+(e 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 of 8.0. If thd7grjhq p5 )ii1m /4kpe 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. Assu;y867eflcdy+h xhv )9efa ks( ming it is necessary to resolve points separated bf;9k)s8ea+y evc(hf dlh6 7xyy 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 l6ahne: nwu/;f(m3cvu ens (Fig. Below) has one flat surface and the other has $R=18.4\mathrm{~cm}.$ This lens is used to view an object, located 66.0 $cm$ away from the lens, which is a mixture of red and yellow. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? $d_{i\,red}$ =    cm
$d_{i\,orange}$ =    cm