Why is the depth of field greater, and the image sharper, wae5dpj jjs24r9d*7t s hen a camera lens is “stopped down” to t5 9j*j27e s4pdrajsd a larger f-number? Ignore diffraction.

Describe how diffraction affects the n89cbjlq+t, c dnw.i2statement that the depth of field is greater and .w,jbn9 i2q nc8 cld+tthe image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be movedtr;v1wm+scefb 2c 4 5a farther from the film to focus on a closer objeccw2; b5mae1t+v 4rscft?

Why are bifocals needed mainly by older persons and not generally by youngeriu)nw p6+lh+; i wzl )h,wh9qb people?w ) lqhzw9b+;lwn,i+hhi pu)6

  Will a nearsighted person who wears correct zqd :*5mtyw,2jv,ypvive lenses in her glasses be able to see clearly underwate zw5yq2d, :,*tyvjpm vr when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a px twg,o w /c3/kq*a+jaerson is nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person,/go aa/t xc3qww+ jk* farsighted or nearsighted?

In attempting to discern distant details, people will sometia) k4ep 7bse/6zlw 6bdmes squint. Why does th)eb74dwspa/k6ez l 6b is help?

Is the image formed on the retina of the human eye upright or inverted? Discmjrn),5f iwh)uss the implications of this for our perception of obj,fw)m jh)rn5 iects.

The human eye is much like a camera — yet, when a camera shutter is left open au2paxqpk:,n 54 7 lcognd the camera is moved, the image will be blurred; but when you move your head with your eyes open, 2k7q :x upocnlg,4a 5pyou still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier izug- xwz0bpy61o1pjc + ;rq6u s also a converging lens. Ar6p p1 b+ o0 jgx-ruzw;z1cy6uqe reading 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 u gk e8.rgs/mx6.+ymu:f ikn5rse usually produce images that are colored at the edges.m: ref8xu+sik/mg 6ryn5. gk. Why?

Spherical aberration in a thin lens is minimiugkqtyq1 - 1;qg by0;vzed if rays are bent equally by the q ;bqu;qgg1tyk1v- 0ytwo surfaces. If a 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 premr o8n0 87 6zetmlnh p+ k5e*rr15lhzgsent in a simple lens are not present (or are greatly reduced) in the human 5r8e*1mkonehr67+ ltz m0r5 8plzngh eye?

Explain why chromatic aberration occurs for tab g5o6 nnz-l0hin lenses but not for mirrors.

  By what factor can yfja- 2*r) adr1c 1u*-lrzp rozw8h/pfou improve resolution, other things being equal, if you use blue 2- zfl/f81zrjr1p wr ad pohca*-r* )ulight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for t1jdx ;x20qn jw9/uq )oe l4o+3i vpotche use of large reflecting mirrors in astronomical 3)q/n4txi9+w 1q; uv oopejjlo2dc0x telescopes.

Which color of visible light would give the bes2x.q ea.-xc/h2 7 )rc jrqtdklt resolution in a microscope? Explaixjx caq.-t/q) . 2rh d7e2cklrn.

  Atoms have diameters of about -mzyyv,t, y)xskew ,(/ yv)wg $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has fzzb/7o ;eg .fsooa m(rqc 4k y./8u0eq-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 njj6lfn2u( 03 nbr3hms 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 seuu ooz o(9(tj a4+++spjjqb(d tting 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 photograph is taken at/ d9v5w kzib 0:idbx(/ot4uxa $f/16$ 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 mmuqewf z1z8/7 b to 206.0 mm from the film. For what range of objez78qb1z wue/ fct distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wish)e rcu)8xbyt8/v1uj aes 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 height of tr))tx ubeav8/8yu jc1 he film?    mm

A “pinhole” camera uses a tiny pinholexnw 7+wi95 z7f:/ie 5 oacznya instead of a lens. Show, using ray diagrams, how reasonably sharp ima zix7w59w+aez5y 7in o/ c:anfges 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 exposun1c( jxwx 9vn,re is $\frac{1}{250}\,s$ at $f/11$ Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 8) if the pinhole diameter is 1.0 mm and the film is 7.0 $cm$ from the hole? $t_2$ = 1/   s

  A human eyeball is ab g8a1s e2j:f-n /sxyij:7 jl1nia d3q+c0ebahout 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 wor-)r7b-kz e++bhwc gjse contact lenses corrected for the far point b )j+kgs 7-ehw brc-z+$(=\,\infty)$ 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 whauu 8u4h3mn vjgx.k 9d(w1nh/ at power 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 p-gt6bhtow 6/ mf9cw4ioint 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 bookpsaps46d2 2- -iy 7; ozqhicvg 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 isi/ j1 /u,:ztav3 stw -*etvyaj corrected 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 clearly onle) u5 2tc82uvj8uy)2b wxg5ha4bhjm ry 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 than the+7cu nh-s:lz7dcxdj4 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a f (qlez,oyho3 jt(,)kk ocal 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 syjdz i h 8bsp8k;5;4ed9e76a(x v ohgngstem 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 an 0v3 gg/6uk5ncm6atayd 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 relaxed eye if its focal len3 *,alduvdaewjcg f2zs:r tn*l+)2q( gth is3nd:qua*rjda+w e l2gvs f(t2 ,) *lzc 12 $cm$? =    $\times$

  What is the focal length of a ma x.9*(xbc. lch f/kfougnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedkp5 pbv;-t.l2/n;mysxj gd w) 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 9o.txnf1:r cv ,:o)mus .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 -+a6pa:n fyau 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 t vc0)j4 )ungj5.55 $cm$ 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 foc7zm,u1e5roe8k l;o udal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass is rated a,y klk9+4q viit $3.0\times$ 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 telwt9cw 70,t*d8r7ohny ( rrkbk escope whose objective lens has a 9,7 b hd8kwt(rtk0*yonwr7r cfocal 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 5vz. ;;kmh.+wglw, ypt :ici edesired 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 ob7iupu khdm +b4y1;f6mghnj:*jective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses sm-kt*6885usi iy9oi1g w oukwpaced 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 asat)oyl(tj- 1djd o12 5oa+dm 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 poy022nfjd 9 i9c bdmkt+wer of an astronomical telescope using a reflecting mirror whose radidkm+9229n f0cyjb idtus of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified 120ds 7b/i hcdl,dsol1bo9.zgv*y *3 8oq$\times$ 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 )- fq j37ydww;krt0km(Fig. Below) has a radius of curvature of 3.0 m for its objective mirrokyw7ftq3)-d; mr0w jk r 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 le( kwq :usqa(noo9uf0,m ny 2n-ngth 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 12a.mr6j+j j6 un.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 1.8cc riy6n9x;afs) hj-+p )ks,x-$cm$-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 locatemon9n , s w6x2aui hd/9m2x0agd 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length of 2(se2keqef m . )6fksl*.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 qo(()zysz09g lmx z9 y*3fbebadkl7+made of two very thin lenses, placed in contact, that have g9xz(zl+ y)79eb0lasdb3zyfok m q*( focal 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 situv xi0k s-:;io er5a zeyw v.,bhfn6d1(ation. A planoconvex lens of index of refraction 1.r( - fad:vei .;sbvk5io ,ny6 xe01wzh50 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) sc 0n;5,pr+ylzxrj9 ywet by diffraction for the 100-in. (254-l5 ;y c,xwzpjr9r+ ny0$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construaje/q9hbg: h3euy u*n4 4q q1hct 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 foca8ihj;hb6cb zy1r3z5aect l 81l 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 bv k,j8yxsm0h o, fvn61y 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 tqo ,gzp :kg s-)q+;djcj uq2(mwo 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 08cvd /e:gt wp1wu*baseparated by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133i5.pu( flfu:+zbww q . nm fall on a crystal whose atoms, lying in planes, are spaced 0.280b(: p+uf5i.lqw f.u zw $nm$ 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 0.582.u0m,aj xrat3r2svj)mh qm : udwt0973 nm are directed at an unknown crystal. The second difm,wtj0 a5ausvm u )j2d: trq8 rm3x2h.fraction 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 observesdaw(0kz9 z7 wd 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:egxcpp:fh6kj7 )6 sn the X-ray beam consists of parallel rays. What would be the magnificat sh7ppf::k6cg6jn xe )ion 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, and the sunlight got miq-k k dyzuyiv-n.0pyp/; ,3t ore intense, a photographer noted that, if she kept her shutter speed constant, she had to change thdp3qi 0tvkyp- ;yiynzu-.k / ,e $f$-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 eklrqiw 9c; *;magnification of a camera lenswier9;*c;l q k is proportional to its focal length.

  For a camera equipped with a w.ckn (hqk0 mh+)uo;r50-$mm$-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 are betwe u iddmp:d4tg va. cz7p1(:z)uen 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 1)h3q8vewjhyektpax+6h k) ( ao . i84o5 $cm$. 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:ff)i- 6mkfx d 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 a telf1 q1 zxj ,pkb6lwir4r b)x7q(escope using the lenses from 71l)6w ,ir(4kb rjxzfb xqqp1his 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 us)hnwo,,2w *ysl4 nf xmu xzd3: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 extremely high altitudes g-q y 8q50idin/hyaq4+j: xab (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 be incgsnajx0pfk 5 5;yn 8:c+duy 6g,4aekoreased because of the increased distance of the lens from the film fy8xd n5g fng;as4kpy a ku5 +e60,jco:or a focused image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece of a telesco*2 d)0lalgkqdo cc :p3pe 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 ob(yzsu pd:1:/y 88(*sjjvzaa0rlw cthe Moon. Estimate the minimum distance between two objects on the Moon that the Hubble /vas:yyubp( 88a0d*szzcrl(ojjw 1: can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, as(fxt -9n rg(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 telescope has a magnification of 8.0. If the tya -lo 7p(i4wzwo 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. Assum7 nzopwt 3 pwtg14o-j*d-3kiv ing it is tvk-npjo-p1z*3 i o7ww gdt34necessary 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*gcj9 awdiw2z1 f h7n+ vve4b, (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