Why is the depth of field greater, and the i4o(kv h6f7wngco (f4m mage sharper, when a camera lens is “stopped down” to o4m6k4c govw(ff7n(h a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of field i fd9pg1avn( 6ns greater and the image sharper when a camera lens is “stopped down” to a (gafdnv 61p9n larger f-number.

Why must a camera lens be moved farther from the film to focus on a clo 0aksp+w. dsf6ser objeck6sds wp.+f 0at?

Why are bifocals needed mainly by ol e7qhnur13(mcder persons and not generally by younger peoplenm(1qr ce uh37?

  Will a nearsighted person who wears corrective lenses in her glaiz,oz2dm :ba2s qo8b6xexj 09pnl;h;sses be able to see clearly underwater when wearing those glasses?6 ;o 0a:d ;lzjnihpm,bze2xb s 89xoq2  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or farsightess*do/ d )vicb +3ys*sd by looking at the width of the face through their glasses. If the person’s face appears narrower through thesysic+3) *s*/d bs odv glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people 4pqwkkhl .73j will sometimes squint. Why doeswkkl3h7j.p 4q this help?

Is the image formed on the retina w c-as;+patn1 of the human eye upright or inverted? Discuss the implications of this for o;-aw c1pa+sn tur perception of objects.

The human eye is much like a camera — yet, when a camera shutter is left oauv,j s(q v( un1+eggdugjq0 s/2p 16cpen and the camera is moved, the image will be blurred; but when you move your head wiv as+qg10uvj (cg( 2/dp1,egn6s juuq th your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is alj3d ukbq)i38a so a converging lens. Are reading glasses theda)3bijqu 8k 3refore 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 usua2vhcqvxp tds mp:6i+ng) yw9; 04b6rflly produce images that are colore+p6) px nv0rfy6:;9dqscim 24ghvbtwd at the edges. Why?

Spherical aberration in a th.fo(*oe u y0cvin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of anoye(fo0u*c v. object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are :x upuvf/m 0z8*erk6unot present (or are greatly reduc zvm x80*kuer/u6pf:ued) in the human eye?

Explain why chromatic aberration occurs for thin le0pkuvp y ;ut +rp;25cunses but not for mirrors.

  By what factor can you improve resolution, other things being equ +fkvmtlp).h2u wh0k 0al, if you use blue lighh w+ p0.k)0lufm 2vhktt ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the useks+ ,.-c8zvw(b ptaxe of large reflecting mirrors in astronomica8we t,-(cs bkp.+xza vl telescopes.

Which color of visible light would give the best)* 3 3y+ragsa+ w 4xeghrd6-exa9rh oy resolution in a microscope? Expla9+xo4y63r ahe g*r 3+ya ga)hewrxds-in.

  Atoms have diameters ofcl 0ku* i.ct(r about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens hpxacimf.dv)9;*qbp 44 2:ka1s rre iqas 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 ha w*f3(h56s4e *ufr/io+3 hqdjznopc rs 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 g. u;ljf0)mjr fik*phoh/iee94 u.r (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 p 5i* m.j/vq e5barc+ochotograph 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 bex4q4 2rp5hyjula 3rzdzle ;+-t z 9)ae adjusted so that it is 200.0 mm to 206.0 mm from the film. For what rang aldz5+9p z)r ju4-aq2lh t r4;xez3eye of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer ye;qef5 pct yud(qv 1* 01k4gyna2ce0wishes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm heightc0g1a 15;eyk4*y qq2uentd fpv0c e(y of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using ray diaa+z/tex l 9iq: :y8lmtgrams, homel/ t:t+:i qy zx98alw 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 exposur :c0v02:awlrvgpb y ,je 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 about 2.15 9wwcv)vs bn0 $cm$ 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 corrected fg*p5wic4j :ret(8cgs.f0 . cjoe, truor the far point 4g:rei8 j( swtc fgeccu*.5j0,o .tpr$(=\,\infty)$ 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 whose near point is 11xhoo1w ,lngy7bdl z 5 /hn 9w,li,3:im5 $cm$, 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 of6 wk/ng w,r+yx 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 tcwd;*xy)f4tg r b2r)/khnj80i as4vn o read by holding a book at arm’s length, a distance of 45 $cm$ away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 $cm$ from the eye and he wants to read at the normal near point of 25 $cm$? +    D

  A person’s left eye is correctedcdm2 1b( ufsawhu4oh1e - v1n5 by 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 clem nvg6+,jhbb5vpkg h1)fg v6 ;arly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Example 25–6 th lhc; rdz k:rs+wfue3ied;, 47l3c0bgan the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fusq1z27a 07 nrhvu.f 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 whhb.x6jotu v92en 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 f a.,o1pzk i2yaly8ec:ar 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 wb4fs-dz( nyx:a/nc j7 ith a relaxed eye if its focal length is (js:74a n-yxdc/bzfn12 $cm$? =    $\times$

  What is the focal length of a,qw4;s;ze a ev magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated atf a:1jt*udzj3 $2.5\times$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 usingc(z2 n+sanftsls c2 nc,b --o4 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 view 35tpkim/;2w,d-ao i. g2t3azfcxc vfed 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 sqo2fx3by mt+h34li4m7 e n4g 65siz a5.55 $cm$ 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 lex a- zlre84bs7k/mwi46u/hpyngth 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,5mbsk9 kihz( y+dhsh*)jv r : rated 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 1v3 svy/a s3+c +gzihkobjective lens has a focal length oscyv31hgivzk/s3 + +af 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 ;7v6f*kmv7h3gn k zgvof 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 telescope has an objective with focal length 85 j2jx4hj-0fd;xc 3cbj jn6 ;s m$cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical tele ,b3ec 9 hg9hyr5z9pwsscope has its 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 a relaxed eye 8l1 n3ck+ rayjis 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 powe hcpku ;9/ j)dt2*nkpp f9o)rjr of an astronomical telescope using a reflecting mirror wht; uf9) jp9npkco/jp*h 2dr)kose 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 magnifiedsq e.lf5ydgl1d l3-y-o 25sui 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 curvattglr)lblama gf n6 :8lj *)2m+ure of 3.0 m for its objective mirror arnmmlf lt al *agbj)+6)l:g82nd 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(mak9k xb0f+ldd zt7u1*ht4o 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 1j b uy32)deh.u+:ir ua6eqnh 32.0$times$ 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 1ioc;f mui 6ab35u,o q7ue* ae2.8-$cm$-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 im 44 o9s3edcuk lt;s4shage is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a comp/kbe-u g-0us, x caa+iound 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 madek8h tq.*u rvvv7jyd6: of two very thin lenses, placed in contact, that have f 7qjdvv uv:r6. h*ykt8ocal 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 plan va9j,fa*fp d4oconvex lens of indj *9avf4ap,f dex 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 resol.e vx;dof3pu n d.ss* v4)o; .mpuc.iqution limit (degrees) set by diffraction for the 100-in. (254x.d s4v oo pi.n;f .pu.)qcm3edu s;v*-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope thaf pb)2pok dek,f8 hd9b;p+7uxof2o7dt 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 he vd::sa :l uik4u)t;dx2 x6uuy1zjsi13 jw-eas a focal length of 50.0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years away are barely resolved by a 5j 108+pesy (qwpwlh7s 5-$cm$ (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 twop8xk6fig3e 4-i, 4 xu0pqwp ab car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separated by abo .r6m u4p5q1 .ukpez;,qwn ,vhv2uvvs ut $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crxfm; 8ra,w zzxa /17nf7f tb,mr k.qi;ystal whose atoms, lying in planes, are spaced 0.28xm1 zn8w/ ;i7r.x7b r, affa,;tkf zmq0 $nm$ 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 dkj:z:06uk qy directed at an unknown crystal. The second diffraction maximukquy:z:dj k60m 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 diffracthu56,sm; iu.kgg sp/x ion 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-ray beam consists of parale+kddq9 0 epqaw* 45dflel r e*ed4fd0w 9 dq+5qapkays. 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 pas)ml7a9fa ;u: qp/beidsed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her ;eal/ f:m)qu7i9p bdashutter 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), ;ea(f 5ipqv9l: 6jpx0ay/c z athe magnification of a camera lens is proportional to ita0 jpfz:q/a6a yl v( c9epx5;is focal length.

  For a camera equipped w hxtevxuo-x; 8 ra*90jj6zo1kith 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 h9vgw ;ytm6ge )mh8u3 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 o60o bjlq / l: v4izpufc/-9aplf 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 a )8uzi*b. zb qky9zgt5 $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in zvoq57 z2u2 wr.om+*tv qrw +athe mountains tries to make a telescope using the lenses froztq7+m *w5ro 2+u.2wzar qovv m his reading glasses. 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 use5 0y-jjxlg , n 1j/iqjrup(;tds $+2.5-diopter$ 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 exq-o4r: (n,uwna+ .nm an hukx3qqr(0rtremely 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 tiuwla)hb / 6c)nmes must be increased becauseu)acw 6bnl h)/ of the 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 the eyepiece of a teb3)iok i:w:w0o+w 9c7ibj cet lescope 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, w7na1) x:+m./h3 pqjvpxemg jsith an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that q +m)1 nphx g/:xajev.3s7mjp the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lensedth0h : g-xrpjvm+;+ ls, one 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 teleol0aoy6+bc. b scope 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 photog;-dx sbdj +g* cu/4c:puuft :mraph license plate numbers. Assuming it is necescu*ufmsd j4;tgd/c :b:-x+upsary 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 lens nyk k;j46njoq 7p) qvss));oh (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