Why is the depth of fie b0i5.o: foabxld greater, and the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore daoxbb.5: i0ofiffraction.

Describe how diffraction affects the se q u(7jgk15 p1zm)qgr.dgi c/tatement that the depth of field is greater and the image sharper when a camera lensd1cgk/e )m (1rz qqpi.57ju gg is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a closer3, f+i; (2tyqlmtt.fvtq s gw9 objeclmt. tq+ fftwy2qi39,t s;gv (t?

Why are bifocals needed mainly by older persons and n.cc fqs.rkk ;)ot generally by younger people?c sqckr .)k.;f

  Will a nearsighted person who wears )j06+h9yrd ,kh) xc xrgoh;ut/wse0vcorrective lenses in her glasses be able to see clghx0r0rhvey)6h /c sd9)wxk , uj+o;tearly 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 nearsighted or farsig*uohy bl9 1r/gsqo wt4z8 fc99hted 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 farsihc9 t8r*ob l /s 4g99f1qwoyuzghted or nearsighted?

In attempting to discern distant details, people will sometimes squint. Whywx4 f za 6 vn e0g.zg,*hm ee1)qb,*3vrjps;tu does this helmqb1n g,spu)afjgrvvw ;*z,4e3x0 6he *et. zp?

Is the image formed on the retina of the human eye upright or inverted? Disxgdxpf/d9 te 2(9 cyc8w5 dzrt/s pd.4cuss the implications of this for 5 .pdxsdtrce4/(/dp92 fz dxg8cw9tyour perception of objects.

The human eye is much like a camera — yet, when a camera shutter is 9fyp* slabj:j tqxs:pb/ +r3.left open and the camera is moved, the image will be blurred; but rtqb/j p9s3yp+:lja x:*.sfb 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 converg7bva , qf*ww0flhv:,;m3 o3shyu b1 m1j r1qkping lens. Are reading y1a*f,ojwqbvf hmr,;sp ql m31uvwb0h 3 1 7:kglasses 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 0r su nbh/pzrsf89;u:w5g t *)cxbe )oimages that are colored u /) ecn* ;subxtg 8br09z5)rwfs p:hoat the edges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equb xe. v0wy,o+mg )i9qpally by the two surfaces. If a planoconvex lens is used to form a real image of p v+iy 0)g9mxb,qe wo.an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present sfy(cg g(1,-1h ( 1t hfh-qjvact iqo7in a simple lens are not present (or are greatly reduced) in ts thg(gt7f (v jf1-hcy(oq ic1ha1q -,he human eye?

Explain why chromatic aberratio:*5n xqf aw rh(ab;,x) itlv5) gvn1ttn occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other things dp dn0i m+d +1wh,3wdrbeing equal, if you use blue ligw0+w, rdp31mnh id dd+ht ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflectin0wwr0w;b yzqe (ufujg+en1.2ab o+5cg mirrors in astronomical telescopeu (+be 0;uoa15yqwf g.n20rzw bj+wc es.

Which color of visible l4yyrf1h0lemb.7i 6nv:z5 *np ua eyr4ight would give the best resolution in a microscope? Explainel f*04b6uhy zyy nnie5. p:r71mar4v.

  Atoms have diameters of abi(kg(w;xy;;g gce t (kout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops /n8po bt8yn (e0vk1ri 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 len1// b 7goxoszko (srvy6gl l4/s has 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 cameqsq;zzy 57l* o4.w mmnra setting of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photograph is(aj16 8vsgb gsfnm5bmu,;kj+q( gmw / 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 tha +g d.g.+n):ubpbm*sx4ln sgct it is 200.0 mm to 206.0 mm from the film. For what range of object distances can i+gn:n.l)p*m + bud.s bg c4sgxt be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree frq5 v bx j7.:ou3ks)./*lp1fdysstrwk om a distance of 58 m. What focal-lengtl:bkpqo7)y*sdt1.xuj . f/ rss3w kv5h lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole61vt6(x(frdtn/ dr,h7ov1dxoaw za8 instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed n(vt6oxr or1/a6w ,h 1dzx7dd8(vt afusing 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 ex r:f .qwdv6ygt: zgd;drd*r1l:h6ig3byk) ,bposure is $\frac{1}{250}\,s$ at $f/11$ Under the same conditions, what exposure time would be needed for a pinhole camera (Problem 8) if the pinhole diameter is 1.0 mm and the film is 7.0 $cm$ from the hole? $t_2$ = 1/   s

  A human eyeball is about 2rm 7q pe 5.tq oyil/6upt8;eb5.0 $cm$ 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 contamosnf509kxrkf+ h/ yh a-8v,ect lenses corrected for the far e0kxorf sf h+-v8nm/5a9,yhkpoint $(=\,\infty)$ 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 phcun 4;*ob+eh18a hua oint 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 point3 .h:dpwagg g(f-;r2-vrqmqmwh1nu : 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 holdino-.qboo: w 5a 4vjy6ijg 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 correctedabl( 3skq9tcs 94(oci ku 3qyy3c7)zh 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 o)d+qte8ekihi b o( a +h.o)5rubjects 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 nearsighted eye in Example 25–6 than e)-8bj d0*jxeza axq h;*e3dxthe 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focalo8(6vk,v7o pz*4lmse b4jixdiw2 7iy 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 object1tqp4tga*4 5iwu0vz4wf xu h2
(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 and.c4v evspq 2;f fd,s9g/zbb.n 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 awd(dnxs g,ux2k+5 jn/ lens used with a relaxed eye if its focal length is 12d5n+ u(d/2swxjxk ,g n $cm$? =    $\times$

  What is the focal length of a magnifying gl5bb yo x;o rq8x7/o/,1xy qtb ;wo7iyuass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated.)yxdv/nk13i il2;x kyi 6w gw 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 usictewn b;x6:iv; vrk++ng 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 0 ns:v zb;qe)a 5pgzt15azfi :+oz9qd is 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 placed x(, ;sx 1g19xp sjdhbk5.55 $cm$ 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 ls9*su gpok0j+ uu va/pz.szl1 (6fk0k ength 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 rai k2 19w.uopmh a9u:jgted at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnification of an astronomical telescope whose objective lens. zelh cg42bkq hod*6, has a focal leb,ceg*h.6ld q zok2h4ngth 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 duagwd8xxr )fo0lypcf-e*om+c y 29-8esired 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 telesc jcdqhj ovc0 z8ad03,.ope has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its twf7hi3z- nhjpadka7p1 q p:,c4o 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 ejy 2b9pf: f5qrelaxed 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 powernke48 t*3ncowlp1q,g-qj r 1 d of an astronomical telescope using a reflecting mirror whose radius of curvature is 4,ejoc qklq t rpgd13nn -8*w16.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be krb 5qw)r(f bp3+nfl4magnified 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 it1x jdv5lm,w-fx h19vbs objective mdb1 jv, 1xwxmlh9 v5f-irror 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 eyepa5ge6n -hs5p12 g8jgzno fjx 0iece 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 12.+b6gvp6a9sl 0u,j vub ot(* qj0$times$ 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 gfza7j/ib 8b2.8-$cm$-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 thg v ya4 /,j(agspb8 l.exnbt24e 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 hae,fo*ra ; e8j6sd axlxjdp, 92s 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 madcgv mxy(o 86d0e of two very thin lenses, placed in contact, that have foc0g cmx6v oy8d(al 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 spheri v-e q-z8i) *hhtmkxn)cal aberration in a particular situation. A planoconvex lens of index of refr-8 h nqi) m-xvet)*hzkaction 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 resolution5b cu)(4becj :l trbi1 limit (degrees) set by diffraction for the 100-in.)bt14( :l u icbjb5rce (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to co,vjbdqkoai +)8i9 1lnen : l-rnstruct 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 focal lengu8wy1c /na503fnvbo / j mw4boyw r1v.3,vzamth 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 ref 7 qp8 xu.do4jp wmrm;5z9d* trpg(q+solved 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 distina 6vde i2i,rm: 4kmjd(z-a6az guish 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 abo*g exbj,mf 97bo5rvr5 ut $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on aa2h hf s-i9kbua:5 qutv9s( f5 crystal whose atoms, lying in planes, are spaced 0bafhaf h9:v(qst-s95 iu 5uk2 .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 0b6 +wd ovy/e nb vxzv)4mq7--f.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed +b - be-vz/mvfnd7vw 4)y6xoqat 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 observed atylm,4 bxc82khunww;9 $\mathrm{25.2°}$ 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 comze4 tje fm;*3nventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the m zm*j;m34fe etagnification 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 thlfwj61,dvr d.e sunlight got more intense, a photographer noted that, i.f,ddj wr1l v6f 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 very far away (assume infinity), the magnification o +dw6: r0ejf.3 0n srdo:nieu17zpw ljf a camera lens is proportional to its foc3u 7z61pd0ordw0 e l: ejjs:.wrfinn+al length.

  For a camera equipped w*p ljpko6a aui p-/+ g,ud*5xwith 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 e-h1fqt lpke; 4z9z: nykum(8 fye 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 of xv2 utew:q5 i-ps jck;i9 +a0w15 $cm$. What is the maximum magnification the child can obtain using an 8.0-$cm$-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
$M_1$ =    $\times$
$M_2$ =    $\times$

  What is the magnifying power of-5k k-xfoci4z 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 telescope using ,a9i yuxh*kipcx wl.(+ c3lq*the lenses from his r*ail+c,i(wh9 * cxxuklp y.q3 eading 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 uses d6(l7 qmplp )x$+2.5-diopter$ 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 extrfovpmeu *e8xb.kv .j)cgf;kc9 +x9+jemely high altitudes (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short distances, exposure times must be inur a*s 0me/2pwcreased because of thrsp20wm*eu/ a e increased distance of the lens from the film for a focused image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens ant8u.ywv 5 jm)j3wzulg;smt /8d the 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, iefi*0cimoief2: b )4mpb1c ;es viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 55*ebic ; oimfbcfep 21)i0 4em:0 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one wia*77(1ph e2nuiekbwt zb ot: (th $f=4.0\mathrm{~cm}$ 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 magnific)efzzj).3 jhgation 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)nf +oe44r 9rw sa9uap spy satellite to photograph license plate numbers. Assuming it is necessary to resolve poinw+pr) r9aou4a4 f9nests 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 w;pt3 qe +wuk;(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