Why is the depth of firx tz/);j94 hei bo.j+e jkun;eld greater, and the image sharper, when a camera lens is “stopped down” to a larger f-n9+e;ji tj;znekb hu/r xj .4)oumber? Ignore diffraction.

Describe how diffraction affects the statement that the depth of field is greatejn4brc(ui 8y0 r and the image sharper when a camera lens is “stopped d04j nb8i r(ycuown” to a larger f-number.

Why must a camera lens be moved farther from the*io. ulxh /c os(:mt8q film to focus on a closer object? o *o8lqxm(.su hci:/t

Why are bifocals needed mainly0y-yplk5uc h7 by older persons and not generally by younger peop-uck0yl h 5y7ple?

  Will a nearsighted person who wears correz;f+l cln* mr0ctive lenses in her glasses be able to see clearly underwater lmzcf n0lr+ *;when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or farsighted by looking atp dgiz17f *u-q the widthu1d p-7 gfizq* of the face through their 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 squint. Wnjrmx (vxs1+l-p 3o 4qhy does this help?sj34+x1 n-ormq(plvx

Is the image formed on the retina of th0ag)s:d n+i az8o pk/i p93tzle human eye upright or inverted? Discuss the izakd0i3p a o gts i/:lnz98p)+mplications of this for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter i446 oluhjyr2 ks left open and the camera is moved, the image will be blurred; but when you move your head with your er y64l2u 4hjkoyes open, you still see clearly. Explain.

  Reading glasses use converging lensequ .h4dmq+e cm6ksoe7 r381ocs. A simple magnifier is also a converging lens. 6 7k8co e 3o4rmm1suhe.dqqc+ Are 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 fo*wu j(0kf 69xre v.-q95z la0jowkr zhqi:zp, r children’s use usually produce images that are colored at ier-: hrq0kzf,wu6o alx zz*9wjp0(5.k 9 q vjthe edges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equall7u4q axe 6:do(orvae.ehf jrf-qf* :.y by the v*a67: ee jdfexqh4ou.f a-.orr (f:qtwo 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 present in a simple lens are not prz; /xd5qi 2(wtd/kc upo,anj/esent (or are greatly reduced) in thea i5uc/o2p( z,d x kjwq/n/td; human eye?

Explain why chromatic aberration occurs fo.ey (gkbj-sq 46m jts9)oi sz2r thin lenses but not for mirrors.

  By what factor can you imtb q)on,+d1)kqi)nf4 t9:p ndv m2uuiprove resolution, other things being equal, if you use blue ligk u qi1,ttn+u2miq o9):)vdpbd4n ) fnht ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting 0ej8oj 2el;w qmirrors in astronomical je; e02j 8qlwotelescopes.

Which color of visible light would give the best3on5p*xnu y:j resolution in a microscope? Explaiyu *on:j35 nxpn.

  Atoms have diameters of abyokb/, 2 r xwrhm0p0 (b4tgla*out $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangingqs .2ifjwxe+1 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 ha7/1tzahr(co7hr wy 8rs 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 settin*c ,z zfq1dak)g 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 isy/gyj, -e +uyy 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 it is 200.0tbmlk7mm-gtjqd5ck b( 6);enh v*8v( mm to 206.0 mm from the film. For what range bk ) *- 7g6tm;jvvqndbehtc 8l5(( mkmof object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree frozhii0wyn( m0;r+ q5j zm a distance of 58 m. What focal-length lens shouldn;h w0rqi0j5zmzy(+i be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead o+wkaif+ wvx )7f a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinho)k w+iavwfx7+le 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 ise9 jo i0o(ceuiah9wuo .,8/i b $\frac{1}{250}\,s$ 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 2kl 1x7 qu-zgg:r o*wy/.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–+3:w dppnn io7u;k0 mf.a2 xdn6 wore contact lenses corrected for the far pointn+d 2 i7ounf :.pk3 0pdxnmaw; $(=\,\infty)$ 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 nx4fyfar8 ( h6,z;uqymeeded for a person whose near point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point of 1e p;8 ijnl46j(dbqno44 $cm$. 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 bybapls8hqp(s(/ :5 qpt gl0feqbl, y06 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 corrl7 c.r t+fdou89ry ki6ected 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 only if they are bet0lsbh * zg1zge o8d8z*ween 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 )xgnx t88zoj9 yfw *7l5wd7idthan the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fou-;rs i eiqh*40 -qfl c syksmk5,)(tpcal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewing an objz+ g4 * tmbxugx()qp)) wwc+prect
(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 xeo;fr2vbbhqq86u n:-7i1 3 fa i6mvvof 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 k.c1n mdcw,se*mj40o0xk3bg relaxed eye if its focal length is mw 0b1k ,m k*sgd4oxccj3e0 n.12 $cm$? =    $\times$

  What is the focal length of a magnifyiz.maaxz 83 v.fng glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated *x c tv7v5ljfw+f6s;:h jn(xl 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 ) 8 lg5hmzvup.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 with a 988-)t d zo+5er 7ewdcjqe ipm,.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 plach7px 2lv hhr8s3mp/ixcf0 r22ed 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 syxv+pkpg;nol* 66f8 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 at6c tp.49wtteyfr urp36ki s*- $3.0\times$ 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 objective v3pj2cp f+(xylens has a focal length of 76 p2j3f(pxc +vy$cm$ 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 magnific vf 04r 06gkzav)ce/kl8q+rxu ation 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 w *t1/j;d jwv p+nusdh+ww(i 9eith focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has itip k+h-h b*ec w/)/py s0pm7rms 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 adjusjsdk zqtr1yt*(/wsel8 5 vt5-ted for a 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 p0*mcp-hy7j8u q- tu qan astronomical telescope using a reflecting mirror whose radius of curvatujqcutp*m -0p8 qy-h7ure is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appei:p3 ka9y isygt70/ abars 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 8 8ls/-1) eyfl*prpl oe5f khmradius of curvature of 3.0 m for its objective8 /1 -fe)spl lmk yprfoh5l*8e mirror 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 wb;d8 t-vohp6:hmo *ja 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 12.0.ab ez 4zc1n/y7uiigj +m)o i:$times$ 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 1.4 vg8eylbrvmc dv/ 9//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 imaq*7kg 4 vvhe(cge is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal lengt *g aqboy,ayqc0+o 8i88em(ug h 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 lenseskq :8cbxz;pcmb6ihbv8 (z 2 8al1ee.m, placed in contact, that have 82pembz.(kbh8: cz m ;6 eivb caxlq81focal 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 aberrati;kt6-/ bn31rj ucxamm on in a particular situation. A planoconvex lens of index of refra;b um1rtmx/-k jca36n ction 1.50 and radius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction for the 100-i,bl gc;delz)9v8ac +v:xy lt 1n. (c1 :8cegad +bl zt9;v v,lxl)y254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telesc :v3ch kg e*;:aevur6hope 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 ilhen.t vj)3d8x0,sdn ) r-dnfocal 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 aw-t/btd qlz (.kay are barely resolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye distinguish two car headlight:n ,h6zl3 xofps 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 b+--no b9i7uf6axlk fvy 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 cryss rtfk20bagd7 vu9;pqsq2,5 7k 8tbgetal whose atoms, lying in planes, are spacg2fk 97rs5p0eb tqd7a8 qg;u2 kts,bved 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 are directed at an unknown crystal. The s(v5+5 rsnz gi74dl b+fqpqp2becond diffraction maxr+4 lppfg q2dnz+b5bi5s7 (qv imum 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 obse /cnxn74;*0hw,ygwa ::o vdq,nq bdsv9l 0fn mrved 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 im :oes*0sk n tiz7 gh))*m9kicbage that the X-ray beam consists of parallel rays. What would be the magnificaikbhs m9: 7* itcgzk)0oe*sn )tion 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 morc;f /z1 vg qf8rwthl.,e intense, a photogzv f,rg8lt ;/qf1w.chrapher noted that, if she 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 ve/v17yz pr f6id:/hzqbry far away (assume infinity), the magnification of a cavz1i/:/ p6ryz h7dbqf mera lens is proportional to its focal length.

  For a camera equipped12hv 7 euoj3+x3u 1dubouq 9uy 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 whfhu uw. n p20c5m-jc1ith her right eye only when objects are between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point ofw;cl:x:zz8 to*f) e/ljc.l v v 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 magnifyinitpm+s 3q ts+2g power 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 telesco l apvhmw onqq64f0re9b0gvg4,bv * (1pe using the lenses from his reading glassee 1vlq* fb0 mgvp0q 9r4(abh4gv 6own,s. 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 us3ksxfg3 r*.:v urjf3 wes $+2.5-diopter$ 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 (25) 4t eblblgz:qp4ut/- $km$) 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 bed2w7 sb8idcx w. 4yyc/ increased because of the increc4b/si d7x2.wdyw 8ycased 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 ten(a: jbg24ea ,1r2wbvahkd o 4lescope 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 viewingqvx0s jd)9im t7 tmy6i,fyz,( the Moon. Estimate the minimum distance between two objects on the Moon thf0ii vtmz,)( stqx96,7yyjdmat the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one withhmx.i 2 s+9yww $f=4.0\mathrm{~cm}$ 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 cbtt rn-7:.b srx5(zb 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,p1ul k 9tie.k satellite to photograph license plate numbers. Assuming it is necessary to resolve points separated tl1pke9,k iu .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. Below) has one flat surfacfena)h f;ku,s0( ax9b sgi sd5fk(;5r ,u: baee 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