Why is the depth of field greater, and the n+7f ,b uy0guyimage sharper, when a camera lens is “stopped down” tob7uyf ynu0+,g a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of field is greafoad 8d6tvv85 ter and the image sharper when a camera lens is “stopped down8o8a5 dv6ftdv ” to a larger f-number.

Why must a camera lens be moved farther from the film to focus onbx7 fl,s +qiu o8e.z9m a closer objec.qefoxl+ 8iu,z97b ms t?

Why are bifocals needed mainly by older persons aw. p p k)o(b -:lnjoy4r.s0n6fhzvco ,nd not generally by younger peopj)hpw.6b0 ,fnskpry4 l:o ov- (onzc .le?

  Will a nearsighted person who wears corrective lenses in her glana*9q k+ 9/6zeb xbph5cwi1zvsses be able to see clearly underwater when cnvkxi bw1bzp h95 +9/6zq*aewearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a u+ w d i:klb1t7i; j:*y-njuu 8bpm4tfperson is nearsighted or farsighted by looking at the width of the face through theirj*1im w;b:ltf uuu4t j:pi+y7-b 8dn k glasses. 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 sometimes ziowvf2iyo90twn* n;l 2y.o 6squint. Why does this nniw iywzv62;fo t.o20l*oy 9help?

Is the image formed on the retina of the human eye uprightlh0v8 1r znz2e or inverted? Discuss the implications of th2l 0rh8e 1zvznis for our perception of objects.

The human eye is much like a camera — ye4ilt 51wx7h;lfk)pcwrc nrb v -3v8e/t, when a camera shutter is left open and the camera is moved, the image wilhtpel7 -ww1kv ir8 5x4/3 c)ncv;rfb ll be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A sicbfye5(-ts 6umple magnifier is also a converging lens. Are reue-by(ftc6s 5 ading glasses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes 0d fj1sis1n ervxe,zs/8wl;7 for children’s use usually produce images that are colored at the edj;x,wes1sf1r i/dn z v ls708eges. Why?

Spherical aberration in a thin lens is minimized if rays are benrh;mogi /a6 wkn2 6t8yt equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, 6okay2;m/ngrh i8w6t which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are npp1j ar6/r b0ky5te,e ot present (or are greatly reduced) in the human ee1p,6 a/r5k trb0 epjyye?

Explain why chromatic aberration ocw .q joz:jp2e0curs for thin lenses but not for mirrors.

  By what factor can you improve resolution, othero5r6is;o q. dvo)1 yhz things being equal, if you use blue lz65ooo q)s d;1 y.rvhiight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantagtr*- nnfhusa;1 6g yh*es for the use of large reflecting mirrors in astronomica;u6h *g*snn-ahr1tf y l telescopes.

Which color of visible light would give the best resolution in a maz:/iw i3iqe mcok+p+,c t2zk,w9uic; ls0p 2icroscope? Exp39w+k:kot ae 0cz us2ii i,/ccpzm+i2;lpw,qlain.

  Atoms have diameters g* 6lvjqa(5dkof about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops lyq f 4qqgf*h1 erh63zqktj: 666cm;yranging 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 lensmizq)sgsx4uo / eia 2+q2u;vb6 e.p2i 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 bh yi : h824k i)vmlvj1bm/0rl/z ;ilha 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 photod.q1w9n: jxna8ga k )tgraph 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 ad7mttfc6a; 2n4r .+hknf ehyq5justed so that it is 200.0 mm to 206.0 mm from the film. For what range fhnkf ta4+n5tqyhc 6e;r.m2 7of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a s s-0q9r w ,wiw(: pugp9 cs,b5lqrl*ldistance of 58 m. What focal-lengr: 9,09quiwlb5 c,lss(lgqr-spw *pw th 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 a lens. Show, using rayrk+z )t agacqwdsy*-:dv3m;. diagrams, how reasonably sharp images can be formed us s t+dag;)3c zq.a* kmr-wvyd:ing 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 exposure is (r h siw7 9;zzsycsc-;$\frac{1}{250}\,s$ 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 abou4ks u:pj1cs -ct 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 corrected5 9qmp,c k1vhc for the 9mpk qc,vc5h1far 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 jo1rdoyqx649c x lz; 9are 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 poifbi*pg dq2/.qvc0 r:2 ii+n bnnt 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( fppf -zdgqob qxnsrh8r 4ouz,1 a .1s7-q5-k 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 bzh+6 t3 uxu1hby a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly only if they are betw 3 t:/spb)d)f;u.wc7 wgs b t, msplk9n/kvd0jeen 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 Exam , 0wwfl tv3n3od9zk;rple 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted p d:+/x hjdk)+osb.z zxerson’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–l h/bez hgxxj*pcjq)( j*18wjd 9*bne5ens system 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.)tem, c*wm(pd0 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 u9e e)23v ykvfqu/y/t osed with a relaxed eye if its focal length is 12 q/ oe)ekufy23vy v/t9$cm$? =    $\times$

  What is the focal length of a magnifying glass ofec;f68fi 5fjlji 8bv ; $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated k( o1;iow;w.kuuaz g) 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 u( inls0r/ dwz4sing 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 witz9 . 5 f+;ixo i/hss3zm.4ro6 rmekqjnh 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 5.5l/:* e 8cpmw/*d5n(k hs)cve/eppqed5 $cm$ 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. n4.i qjerz4l)1ys;mh5 $cm$ 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 rateh* 2q hztjn7r9d 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.zanu ; k450z lf ft56tq-gdsi astronomical telescope whose objective lens has a focat5siat5-fq6;.zl gzn 4kuf0d l 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 astronomical telescope is desired to bi5dox d/ocw8; jl 4v/ye 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 -fau0zodf5c:nny,kx )0 l6rn e/qj7f an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has i urnj w.0n cv)bw1pdrt881rw1 ts 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 k7dmwx kvuht069f.xp t +/2ufa 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 anr sb+lqq; .ak7w +yl,v astronomical telescope using a reflecting mirror whose radius of curvaturebq yl. vsaq+7rw;+k,l is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be7(. -h g:aqzyw 5c;c rmu1ceivb 8ze5t magnified 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 radj)nuz7hs hhn ham qab+)*b*, :ius of curvature of 3.0 m for its objective mirror and a radiaujnh mzh+) 7snbq)a , bh**h:us 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 +5 g drigx lq8q/fy7 /fmq)-ryfocal 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 12.0th6zy+m.6s lj kk2s2s;n-qg dj0ol: g$times$ 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 1.88ts)-ol.qo (a a;ni5s od7x 4 zufrfq(-$cm$-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 assum nqcijx9j z;+,ing that the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a comd)mk(dk* o7eo pound microscope 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 veryms+g*2tb+ d 3t9.ivnpcy6kwj thin lenses, placed in contact, that have focal6 kimtd py2n*c3.+j+b g vst9w 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. A planocu+wl9bwlr c )4onvex lens of indel+9b lw rc4)wux 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 resoluy0c tddt3k 9t+tion limit (degrees) set by diffraction for the 100-intdt 9y3tc k0d+. (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that c4. n efg0gn h8e*-y.zhzw.sd2vv s/ea an 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 length of 50.0yovuz1,ya9*asmup agr g)n/; pt38 9f $mm$. 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 barelyiiidiz.. upd fd+e,;ka1 e+i/ 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 two car headligihc fh tp9t9,npm,;ph (gfx 69hts 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 atjs(j 8a+c. whbout $400\times10^6\mathrm{~m.}$ 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.r j;g:y2cqb *a133 nm fall on a crystal whose atoms, lying in planes, arrjgb q2 :;yca*e 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 aret; eg .1wo+vw rpwz):b directed at an unknown crystal. The second diffraction maximum ). w +:z;b1gvwr wpoteis 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 observed atj ,q)bp9w,;oqw hvo7 q $\mathrm{25.2°}$ 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 c bz4./akp8ex that the X-ray beam consists of parallel rays. What would be the magnification of the image? a x/4z p ckbe8.athe 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 dy2uj:0n0h qn9ntd. tul ki7n 3 it2c9toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she72 3 ntduqu.99t nylcki20j:ind n0ht 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 object90tg) ajj 0.g/v jkvcjf,*od4/jhiu cs very far away (assume infinity), the magnification of a camera lens is proportional to ck0* 4i/0gt,j jj/a v ocvj.fjh 9gud)its focal length.

  For a camera equipped with7ql7d 7 d jb6sqdyo*;e a 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when objects arpe 2yb ce+-kilv*i h-ie -j0k-e between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point of 15 elp:a5b/ tn )h$cm$. 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 powe ktg9iwa 6y52z.kuk. /f qbx4cr of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make 0ze il2/x)3f trf hzeud-ny 9*a telescope using the lenses from his reading glas3x-nzetry 29d/u)e*f 0h lfizses. 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 usesj5l*4/:u7colsa7 ja k0 c- tr;wn *.elaalpdw $+2.5-diopter$ 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 (23 4 tc4wc 2luizv9db5p5 $km$) 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 musltu bu)/zl8j .g )km0qt be increased because of the increased distance of the lens klu)lzqm)g.8 / ubt 0jfrom 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 are spaceqf)l a;w*xoev- u- v3r+nf yfj*x3pc( d 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 y .r/s9enac9 wm, is viewing the Moon. Estimate/n.s w9ea r9yc the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one wito-// j;lw evlzh $f=4.0\mathrm{~cm}$ 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 telescoqfkr5mtqbj 42uf ahjl3 k/;.5pe has 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 num.jdm3 jm6 6/7 9jm xq52xmgumsndqs-bbers. Assuming it is necuj35mnm / .gsq2m jqdj smm-6697bdxxessary to resolve 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 le b6:xq70w ::bx (dwtg xd+daml4tqmf3ns (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