Why is the depth of field greater, and the image /a.07 f+kp+ chll7 0s4ey7ymn(no-fvol bp wpsharper, when a camera lens is “stopped down” to a larger f-number? Ignore diff0fly v7b-loa/ 7pwm0y+o(np4n.hpse fc l7k+raction.

Describe how diffraction affects the statement that the depth opxx/pcgy- g bgc3.*;mf field is greater and the image sharper when a camera lens ;pmg*/ 3bcy xgpg -.cxis “stopped down” to a larger f-number.

Why must a camera lefp6qxg)a )9v pns be moved farther from the film to focus on a closer object)xf9 gp 6q)vap?

Why are bifocals needed mainly by older persons and nw/cr :*7acn2fflvmwua;.yy vl3g/-kot generally by younger peoplem/ygalflw:vf *y2wc;.r k/ c7 un-av 3?

  Will a nearsighted person who wears co/ )fu9d yl1u6nh 4wcwtoaa/8n rrective lenses in her glasses be able to see clearly underwcw w)/a8h o6ut1n/ln af9 uy4dater 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 fa2)dve6)rrqna0yr jh, rsighted by looking at the width of the face through their glasses. If the person’s facdy20r v h r,aneq6)r)je appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details rfl s-c)qtnkqnhq2w,9c4r 5;, people will sometimes squint. Why does this hef45cs)qwtnr ;qn,qr2 l9kc -hlp?

Is the image formed on the retina of the human eye upright or inverted? Dt4 1- m i/c7vbrzznmk5iscuss the implications of tt5 -4zn7imzkbvm/c 1rhis for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter is lej5l* g 35puxppft open and the camera is moved,3p5u 5lgjpp* x 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 als* pt(23gz itkkdd3un,gw4j d- o a converging lens. Are reading glassg,* ukkzgdpd3jn(23twi- 4dt es 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 images t(zlndk g m1s30hat are colored at the 1s (mzl0nkdg3 edges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equally by thg6d kx3so79owe two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? o79dw x3ks6 ogUse ray diagrams to show why.

Which aberrations present in a simple len;l/gm x bivwu8yjc+*.s are not present (or are greatly reducedl/muv x wic8j.;y *b+g) in the human eye?

Explain why chromatic aberrat ume)+re (x2htq ya2mm/ -6fbfion occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other things being equal, if you usl :)wxmomfyo ; ou62;re blue light (6 oo)u;f;wo yrmm2 l:x$\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflrmuz a -3/+0l-wemhhaecting mirrors in astronomical telm3/a0re- uwh zl ham+-escopes.

Which color of visible light would give the best resolution in 7i+b5 (yyx lsq*uql3z a microscope? Explain. b( lqzix ly7uyq3s5*+

  Atoms have diameters o4zwz( y;rqpne64tz(w-k 2d9a1 qh o+ xamvac2f about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length ly3d gkgujc8)0, k5nqn ens has 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 has ab04wz g9jynh.;* m.kud )wp ag 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 set 1/0xf-yfxgntwtj, r0ting 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 2m5keu+ +q)bd z p;rob$f/16$ 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 itjpc8 8q1u.eq skvu;1-u6a 8 xe mo8amo is 200.0 mm to 206.0 mm from the film. k61jxse caa8p-mvuueqq8;umo1 88 o . For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distanceza zen3 )57jem of 58 m. What focal-length lens should be used if the image is tznz 5 3jeem7a)o fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using rar b-lub(qt8; jy diagrams, how reasonably sharp images can be formed using such a pinhole camera. In p -j8r qtb(;ulbarticular, 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 i- u3la3*, tl 6shmd (zchxb7phs $\frac{1}{250}\,s$ 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 aboutr:1(o zokqv 3ey* qkogra.*/i 2.0 $cm$ long, and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens? $ f-stop$ = f/  

  If the nearsighted person in Example 25–6 wore contact lenses corrected foifr.jl7invpqb3 :j 6d tz2 z6*r the far poiidqf6nr:2p3l 6*jb. 7vtzzj int $(=\,\infty)$ 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 1/;a l9sf/d6,t. ntfga tqcfs015 $cm$, 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 14 j2q-rh zfu3iv wn+gwzz7t9fg05 11 ip$cm$. 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 holdinq- s.h 5, qmo7fb(pno1g1rpdrg 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 coa/se5cq m.p ss)d 70fgrrected 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 clearlp/m (gpxtr90 .1k e3b*iz9 j*em num i7yo1eiey 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 eyed0 btqgy 6hr q, y0+s1*dd5yh4cffkn 9 in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eylj-nh s2+*tvkb 5ekn k6gu6k0 eglasses has a focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewi m ,j04mz(ivkang 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 an ( ylf -ror0ms;amr 3eyww,j5-d far 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 with a relax/., atld yljvb6ylqgv0,c / v1ed eye if its focal length i/1djqyb ,l.ayc/ tgl,0vvlv6 s 12 $cm$? =    $\times$

  What is the focal length of a m1y 4.yze (toi a:l3bmwagnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at 3-- kry r/qjsin+g. 1pntnbd*$2.5\times$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 uo 2w jrws1zbqndshr2:,jm+23 sing 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 is9phmm a2.fwh) rgwfc52(wb1 d viewed 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 pl/1beijnddgn-,sm- v4a.4 o t vaced 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 8.5dlwz4+*bhz. p $cm$ 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 z9wp(2 yn:grlrated 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 whoq*kuf-nv) q8mse objective lens has a focal length of*uqvn-8m kfq) 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 magnificati2fw8gt08:bmj je:(hnt kh 8d aon 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 with focal lengtwzz2cx .l.qaa6ez; k1h 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two ltl (hkl f c:oa1h;)x.l 2afy9ienses 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 a2 p(bldbgur/;/*ooid 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 an astronomical telescope usin ,/q4;yp6soawcs5 a*ety9k feg a reflecting mirror whos4cy a ef;6*tsqkpyas ,9/ 5weoe 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 magnifiedvly 93vmy4ijqp) . *ha 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 for itn9o+cck vl9kzr// 5sas objectivzlkon5k /s 9c+9a/ vcre 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 a focal length of 1.9 nl aisno.mdk/)o2u9 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 12.0xmk,xs8op b 9*$times$ 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.vwrbno t8k3gq;n a go912-o*p8-$cm$-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 assuminfc t; )5wcmiibdl.w:2 wtx6u 3g that the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal (dais)/2u /x d2alqeq 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 verylzc t mx)q)1o6 b o0n d3c(-buqiv+,u:kx.mi h thin lenses, placed in contact, that have foc tmmq+kh(:qo c.lxbv )3i0dzi- ) bu61 un,oxcal 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 p6h33wp* bps vrlanoconvex lens of index of refraction 1.50 and radi hb3 rw*6pv3spus 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 resoluti zi6tvzy 0uj.8on limit (degrees) set by diffraction for the 100-in. (254-6zt.8vjyuz 0i $cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construchz1yp nt(6n ;et 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 focuz 8le6*4hw 2ig29tbl 1fkw ical 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 barely9 i2i1oxe bu9t 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 eye2lde8jvods5 x9qv m1: distinguish two 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 tuzv;-tkfsp .xj8 q ry+.,.aslr)i x2 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)h2d y co;wfb1 a crystal whose atoms, lying in planes, are sp ;hy o21cbfwd)aced 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 pe2k18 0 ap+qafaem +man unknown crystal. The second diffraction maximum is recorded1me+0mpqa8f+a2e ap k 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 ob9k (bg;ijy hg9served 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 -zv. ktmsig, co; (k/othat the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnmk .,(otsiocv- gkz/ ;ification 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 mb.8rf9 h+4i wk d 9ej,guxan0+2el ijeore intense, a photographer noted that, if she ke0u 9kl28. geje9enrjxwd h+4i aib, +fpt 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 7opkg(lmy ,mnz-xr*up p ,)i4 s v9yz9infinity), the magnification of a camera lens is proportional to its rmz9up*yp, (ls9no)kg4,p - ivy xm z7focal length.

  For a camera equipped+*zll z*pe fziqa *8m.s/j yz, 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 betj )wqv4dzdd- 1p7+nh hween 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point of 15 0hwck-pz;6 .ez km cekz8v*jj)(v v+of7 wt,t$cm$. 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 magnifyingi1c kmx/rfd e8 ,p4i;y7 a4.wvcpd*rr 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 mg)x-p wtmj-i9t7x tbef j. r7(ake a telescope using the lenses from his reading glasses. They have powe-x-mbgtp. jit7 9jwet(x7 )fr rs 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 usegfee y,nry b/):8a c0zs $+2.5-diopter$ 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 g2zl39c( lecq $km$) 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, expo(gpd b9 iw44ywy (q-ue g7w:dzsure times must be increased because of the increased distance of the lens from the film for a focused imaw p9i ugyq:( 4g74w weydzdb(-ge.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece of a telescope arj*:wtu/k5 ek.lwh swxn-*np u: yfyr:7)(b e me 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 viewjdiwo vthq0p)1mi ;bn3gm awz08.p 9,ing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can diszmj0mii), .3daon0t p p bqv;w819wghtinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one with cip kw11:r yn)$f=4.0\mathrm{~cm}$ 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 b54jr//jmjmxq(uybn nyq3 7hz: 1 laoykp35: of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license plate numb bxbz: 5 rz mpkx(6on*9een)gaig2*q;ers. Assuming it is necessary to resolve points separ;n9ox5 m :eg e * a6b(i*zn)2gxrpzbqkated 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 )kosuxd2y* b(hkuf 9k0kj27rld: 5b q(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