Why is the depth of field greater, and the imagpyso0yz/o qgj3r. q.)e sharper, when a camera lens is “stopped down” toj.p s0qrz3oqy/) o. yg a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of field i1mt7z tfjk 8r5s greater and the image sharper when a camera lens is “stopped down” to a larger m1tfjkt 875zr f-number.

Why must a camera lens be moved farther from s awt2pi-r36r the film to focus on a closer object?3 asr26wti-r p

Why are bifocals needed mainly by older persons and not genq p+r-m4bqyo7 vgq dnv+j;+9 zerally by younger peopv rgq+4q p;-b7 v oyqdz9+mn+jle?

  Will a nearsighted person who wears correk;h,ja3q;jibhzyoyp6yv ej f-d5)/gja ). a6ctive lenses in her glasses be able to s3 ady6 -,hpj y)jg5abvhko6i/q.ja) ;; f yjezee clearly underwater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is neareny elv9 mv3q4:78 c+b znij2fi82aao sighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through m lf beoj7yan8vqni32vaec48z9 +i2 :the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squint. Why akmf4zrpb6 q3 m0;p4 bdoes this helpkmab4pz b qpr3;046 mf?

Is the image formed on the retina of the human eye upright or inverted? Discussscudi9azbysc,x(o i. i 5qddb ;e;/16 6 o(5d 1iibcq.z,a d/i;9sbu ec;dyxs the implications of this for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter is left xcn: ( 5a7jarpopen and the aj :7nrap(x c5camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a convergin0kf1l/t cfs:4q;vb m/ a4iv hog lens. Are reading gl4qcfbimt4/;k0a f /shv:l vo 1asses 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 ima1zhjk md3,cbmgh;seq;b*l 2* o,:fkhx t v/7oges that are colored at the edges3t ds l;k;k1 mb:ghe hqvcx,* j2/*zmho7b f,o. Why?

Spherical aberration in a thin lens is minimized if rays are 7hbp 7sas c4juea5,2e, ftu7 s27olykbent equally by the two 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 whye,u7p uh2osacs ft7ka74yl5,7 b 2sje.

Which aberrations present in a x v5s ,4*lvvocsimple lens are not present (or are greatly reduced) in the human eyelxvo54,s* v vc?

Explain why chromatic aberration occurs for thin lenses but not for mirror9( // 0qsp emr,pey 0yq.tppkedv*)mls.

  By what factor can you improve resolution, other things 6bl:d zk9c-jv +p-lu sbeing equal, if you use blue light (k 6-zv-9d bluljsp :+c$\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for thstcm+wty95 k x(o: em:e use of large reflecting mirrors in astronomical telesco9wtmk :5+mox:cteys ( pes.

Which color of visible lign;v :6dgs:pit ht would give the best resolution in a microscope? Explas6p :t:gnidv;in.

  Atoms have diameters78h22lj /q lxlql 1wv5wrpd248r yt+fcg kt4l of 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 fqgl( tsuxw+.jha351o-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 has89n/c cj9 hrak 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 se6hj gah(wi1ff: ,lt4ear:ld 8 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 photogr1yc4su* 8/0ywgpl jzvaph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be adjusted so that j ; /a(qm rpzx762tzjz/t;xfuit is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjuzzj qxmza6;x/;7 fut 2r/ tpj(sted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tre6s(j am vm04+qvrv fz6e from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-4f6+0qsvz6 mmj v v(armm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instqxoi2b h/+0fa ead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. Ih /b2f +oqxia0n 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 -/b-jfvb vj4u $\frac{1}{250}\,s$ 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 abo ojwe74dlw+n(73fmix ut 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 wop 6re:i 3vd)1 16 sglxlmy;e(m hers/wre contact lenses corrected for the far6rp(el mx:ms1i1d; /v) r 6y ee3glswh 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 wha 4nahht(o5h2xdo v, t2t 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 point offyfl(l5mi6z a s *-8jx 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holding a book at ard t: l1 *uj qh se(n;rxiid-92;,7jsll3mebgfm’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 by a5may rk5xg8 5p $-3.50-diopter$ 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 objtl8u6 )mpgxk:3brq4 vow /vq3ects clearly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nea. 9y 65 zw;3iltbocjvvrsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal length of ,9n6uoqtipvj +4mb d3 $-22.0 \, cm$ 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 t-iuj3sn84m)iqbe 0ktm0 e 3 ,jwkd rd)he eye–lens 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 poi(q0e5+ a5t4 :s:jc0hazvoua;qnwo nm nts 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 relaxed eye if its focal lengtq(5th*ycr gr ww.:tp.km;9woh is:tgt rr wkwh9py;wm*c(o.q5. 12 $cm$? =    $\times$

  What is the focal lengtlbg1a 9jnxjq1 f6y e7v79, * w(t nyp:0cksmhyh of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated ax-ak*a:ltsd e0 nbe*i r 7b2hak 9os57t $2.5\times$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 9.06 g)-txztxmc a-/i t,q0-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle is viewed with a 9d -yjnzn35 gm4.50-$cm$-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 placej itvch)p322,q 1v rxxd 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.h oln..6i oaf-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 ra yjx5 yxc66s(ated 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 astronom q2.btvbn4i7mq 8- lyyical telescope whose objective lens has a 2qb-yb.mvltq 4n 87iy focal length of 76 $cm$ and whose eyepiece has a focal length of 2.8 $cm$? What is the overall length of the telescope when adjusted for a relaxed eye?
M =    $\times$
L =    $\times$

  The overall magnificaacdq6xd/ v:0gtion of 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 witgbm 5xsr24 bj o9z5ada)i+ud6h focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescocnl zz g* :ga k,k6y4/u02gkuj ;/eqfape 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 relax+ ew3 3kg)ommded eye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope using a reflecting mirew1 fex 3)ve5sror whose radius of curvat)fv1 e 5ws3exeure is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears cpw zzd*id75)to be 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 radius of curvature of 3.0 m a2 zgh9 wxct1pm+1xh8f9zou9 for its objective mirror and a1hzxp+fu8o91 zca2 9g t mx9wh 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 eye 8:fedbojgbs6wg9 pnj8 (,s9u piece with a 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 12gq ),jch mzb+).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-/ rr3iv7kvp3)8:btvb 7zt aiz$cm$-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 locate-rdy3y7e*2 ywk5wqed d 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound muj u ,fw 9k9qp-ex,kxb501i(gz b.k tiicroscope 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, placed in4rmjrto m5l3j+u+,9j *: l xhdhwuo5 c contact, that have9jjr3*4utol:h5, r+lw5hd u mo + mjxc 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 sitw60vs am(: jwpuation. A planoconvex lens of index of refractionjv (0a6sm wp:w 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 (dexy0e)s cbz0 w1rl9)t qgrees) set by diffraction for the 100-in. (254cqt0x)w sz1 9elbry0)-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve features 7(2 z(*y vubosakhhoq; hd-l91.0 $km$ 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 aijk -z /an)n5( toydk7 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 barnrp6.0xtpb6jdjw pvgr3-m 4 +dn5ka 7ely 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 headlight y k yjzhk3n6 ;bvaf*klr-9b24s 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 separatc)hdlx 157g0fzs (wtzed 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 0.133 nm fall on a crystal whose atoms/n lk, yd.j9n:audo0y sy 4uo), lying in planes, are spaced 0.280 /yl4saudky9jnnou).0 y do, :$nm$ 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 directed at an unknown *09jn0s4p1cc5 jcal phdw e w2crystal. The second diffraction maximum is recoj0p cl4w *2apjs 1hec90n 5wcdrded 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 2.pp jk vti7m6observed 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 o)yrr nau/6,xuf parallel 6x)/u ,urr yanrays. 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 miqjx 9nj*kfa dbi ,qy5tr,ikn)1 04 ep;dday, and the sunlight got more intense, a photographer noted that, if she x)0b i k;a,1,fen5jiq p9kn4jy*tqrd kept her shutter 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), throb)+1uyr1*-u qz s3smn: vvfe magnification of a camera lenuvorv+) :sf1myz 3usb r-1*qns is proportional to its focal length.

  For a camera equippeop dih6 5)2hkyd with 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 are between- phv+on*5l yr 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 pm8t+x*4 f /hllmbj gi9ivnc9 4oint of 15 $cm$. What is the maximum magnification the child can obtain using an 8.0-$cm$-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
$M_1$ =    $\times$
$M_2$ =    $\times$

  What is the magnifying3zi yy3c ti/o8wtfq7 +dh;w j7 power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains ttjcqpgx) 5.;w 5g v+vyries to make a telescope using the lenses from his wvcj;.g5 )+5yqvt xpg 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 usesyupu26 oc, eu5 u(2tdk $+2.5-diopter$ 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 ;0b8 juetu-ff (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 )okxwtk-bc otl6 4; w+short distances, exposure times must be increased because of the increased distance of the len + xwkb)tloc ko6;-w4ts 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 the70sk v 2pa7(uzxdr8yn22 v0rjcm 8ymd eyepiece of a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2.4 m, is viewing theyqds (k82yty 8 Moon. Estimate 8(yty ks ydq82the 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, +0-zq ecj )l55 +9ldhklztmhrone 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 theg+q9g;fbhe3*+g./ocujin- sfu4z h t hj6i h; 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 tooya7 9gd1+-jj) mfxog photograph license plate numbers. Assuming it is necessary to resolve pointsd 9mjg+-x) 7 oyogaf1j 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 (Fig. Bebf/y /yrh 5a vx/jt(6hlow) 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