Why is the depth of field greater, and the image sharper, when a camera le*.gt; o cf2i8az)(t 9baqozh,r+ tqmgns is “stopped down” to a larger f-number?ahtm(2z rif+) ;azqq b9to g,8o* tcg. Ignore diffraction.

Describe how diffraction affects the statement that the depth of field is greats t*e2**tkdsce. d*(k l*fv qper and the image sharper when a camera lens is “stopped down” toep*vkt.fkcs*es* d * t*l(dq2 a larger f-number.

Why must a camera ley ad7ym;pn k0o-zljodn .)t* 9ns be moved farther from the film to focus on a closer object-.oan0 7m 9dy;l*yopjtdk zn)?

Why are bifocals needed mainly by older persons and not genera/.jr,o 6syzaff 9 tiwr/tb5o:4qf2iwlly by younger peoplt2 wsa,9//6:of wqb4 ro.fzi frtj5iye?

  Will a nearsighted person who /xaoim,kfdbl 2x31g3 wears corrective lenses in her glasses be able to see clearly unded 2lk m3g/1ab of,x3xirwater 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 a ,x n7ucc /5a.uqktc1lt the width 5cx .ccnuq,lak/1tu 7of 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 x qf1gkte. 69csometimes squint. Why does this helpx.q91gtfe 6kc?

Is the image formed on the retina of the human eye upright or invertevl7u;:x co:o*di8jloft+ ,yfd? Discuss the implications *vox: ,ly cfiu+8d fo:tjl ;o7of this for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter is eh o y.5r78 ) ftf)4qjsv*giatleft open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you stie4v57 to)s *fya.tj8ir)hq fgll see clearly. Explain.

  Reading glasses use convergi;uh)fq-e 2 cycng lenses. A simple magnifier is also a converging lens. Are reading glasses therefore magnifie-c uqey;)2c hfrs? ----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 produw.ldhh z05+ tko +wl gf3r,e.gce images that are colored at the eor . ewhhggl.+d z,kt53w+0 lfdges. Why?

Spherical aberration in a thin lens is w o7w6b+jz oh;minimized if rays are bent equally by the to j7h 6b;zww+owo 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 notjya:ldy2u h3 z2op4 sdbtscz:t78:df+6) gtb present (or are greatly reduced) in thebtzddzdgysy+l4 :s2 t bhc2t7fuo8a)j 6 p:3: human eye?

Explain why chromatic aberration occurs for thin lenses butmk i0 amy-16mp not for mirrors.

  By what factor can you improve resolution, other things being :3kun 3ld cf9b 2a-tzkequal, if you use blulfza9ud kt: n3 3k2cb-e light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use ofpsc1bf4u l7dtx0n hs :4 2y1gi large reflecting mirrors in astronomical telescopess0217nsy tch44:bpxgl 1fd ui.

Which color of visible light woul/+ngk33uicbe wetm tji+5l5 3 d give the best resolution in a microscope? Expl b m+ietic+l3 3w/jun3k55teg ain.

  Atoms have diameters of axgbu3dxncd43y;8m ; u f5gok eq0o(;x bout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangin/maf ry-;fc :/v6l0mgbbtd ,hg 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.3 h2hu+b rmzd 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 ash86dw(u -uw jqpve6, camera 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 phog;fya+b 2ynb2 ejqif )3z:x 8etograph 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 it is 204lrw ke bv.5h5/1rbx b6+tqia 0.0 mm to 206.0 mm from the film. For what range of object distances can it be/blir15w r +6 kvbthbx45q .ae adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtaltk,q 60a z,-b5uzds9l8e dwul* 9sev1tw (jbtl tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm hek,jq0 d-e,lba89u6vdttts5w9 l(be wsz u1z *ight of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using ray n4 b2d1 cbyz5vzpn *:0ym4u oydiagrams, how reasonably sharpbcnuydp5 v o42y4n: 1mbz* y0z images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct expo e:t s2orz8*jxsure 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 2.- :o7vz nob8zz0 $cm$ 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 coy0 d y xv2sn5 u/97dgtc8:pafmrrected for the far pofgy nvd / 0:muy2ptc8sdxa79 5int $(=\,\infty)$ 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 asom-:b8 c- nejre 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 pointup*80(sdh*fqhfq un0 of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holding a book at arm’s lengczw*0 1isxag3hqbq 6 ;v e2b5rth, 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 i(krpdn uh41 8h8saia6s corrected by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objectshc+nwx n* 24a7il3kmw npv 40o 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 E9 5g si ss 4r8x3)nesd:2fetfaxample 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’sp m5 jz0:vjpet5it e*7 eyeglasses 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 viewigk)bm 9 zg 2j1b:s7dyhhba8f;ng an object
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has near and far points of 10.0 and 2jrkf * 5 me6.d*nrh0lztop.d) 0.0 $cm$, 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 idh c;jyvh/b:+ +tfp w1joo3 ; ez.vsk*ts focal length is+bv .1j efzk * /sh:owd;yp+o j;vcht3 12 $cm$? =    $\times$

  What is the focal length of a magnifying hm a9six 7b1-cglass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated aevie0 x*jmj+*t $2.5\times$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 rc(1-znyho 2 o9.00-$cm$-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 viewei bz 0jec/lae;3 (gevb+v0 (ckd 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 plst15vhcuk;v nmzcw33 lcm 7z;b1c (a:aced 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 withv;n id(m7h(l i a focal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass is rat-f bmun8gl5;n 2*dpn ied 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 magnificav3a xegcisz u)8 f;l.7tion of an astronomical telescope whose objective lens has auc)eg7izfs83la ;vx. 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 magnification of an astronomitz ,zf;o;1w: ly by68dolezr.+0x hkjcal 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 o; mn:ykwc62,h ib9c klength 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced5r7 +jtiej,wf 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 relaxed eye istmw/d/c gn3-kb drl(,sn)z a1 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 19qp(eu lo)iy3lv g;mi-.,;jx+ r(s kk kiscm astronomical telescope using a reflecting mirror whose radius of cukk9j + l(,g.q)-ux1ik;ycs(emri;ovi slm 3p rvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears tof6 *fk6jn(8 oba: xykq 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 telescopeoezt xno;))edf+ 7nu- (Fig. Below) has a radius of curvature of 3.0 m for its objective mirror )nxe-z ;oeontuf d7+) 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:mh .mve3zjiun 6xi6,u xja71sm03 pz 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 12w l;2 /i,q s 5k 4erxnkksyztj5d;xo tpk)25d/.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. aycespl+l1 7ej.tt638-$cm$-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 o4e h868yixgwis located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound mi,sva xv8x)iq+croscope 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 v hixlrcgd685/ ery thin lenses, placed in contact, that have focal lengths of56rhdxl8 gc/i $f_1=-28\mathrm{~cm}$ 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 planneo i6 rla (mdtag*l5ct---3 poconvex lens of index o5 n l3-*it6gt-er dcl(-paaomf refraction 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*dqh-c .6ry jc-in. cqj ryh6*.- dc(254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope thati5zn blhd :**fh2nz jt6c*.vcla, nw. 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 camera8izhvz/t tm;368xr1lu 2dv;ktu0vqv has a 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 barelyr(5bj n+0tljo :c3rm z 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 headlmy 5xm :ddu13agbs o9yuf6,z30uoz y,ights 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 areu6w8vh(q kf9b separated 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, lying in planesw61d n0skg0 eo:j- jvy, are spacv :k06-sdyn j0gwoj1eed 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 0.7v*cp4u rk+yw,yzp4 , -s zcjo0973 nm are directed at an unknown crystal. The second diffraction maximum is4z4j7u y +c pzc rswk,o,v*-yp 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 diffractioj * rio9y-3hjlkqvmpa+6*rz;n is observed 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 co o8mc* 2plk3qsbm0ml, nsists of parallel rays. What would be the mag0sql*c8obl mm km p3,2nification 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 towar s 9benrn1tqvh-yw-n5g o7w9/ +j eer6d midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she h5y1woen+b v- grqs-w trn6je7 /9h9 enad 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 of a xia* 1ou4u3guz i6v.xcamera lens is proportional to 1ua46 * g. zxvox3uuiiits focal length.

  For a camera equipped imyfk /.:gp4c 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 on9 mnfqko05po c2x k3h6ly 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 kxb 1tcxk43k6,l a:xp15 $cm$. 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 magnifyi ziy 6e.y/, fz1q4g6j qzom-tfng 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 telescope usi nn): wq;ggq818 xkhefp:, tiwng the lenses from his reading glassw wg8f gp8i1tek;,nn h:qx:q)es. 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 ucw aq cte(ky;l+z,s;59uu+f $+2.5-diopter$ 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 extref2z2e 8ae nqi-mely 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 inc 7poorsgi/y5e 9)jtas;1 v-bvreased because of the increased distance of the lens from the film fo o-1/; ygv7a5rpevb ot9)sis jr 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 anp3,o e4drr bu oq5q,q36, xlaad 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 diametj os.y4i, klr5er of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wav,.io 4lks 5jryelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one wiw-qefk aqm99f ja3 ao-- m)g,rth $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnification of 8.0. If the two lenses are ln8 p;ysk+2 lk7s wh 1oq2n/xc28 $cm$ 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 u lobls.h/ 8;5 gb ,n8jp;nfwnnumbers. Assuming it is necessary to resolve points separatllgob,bu.pfw;8 hsnn8 5j n;/ed 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 ii 0 x6r4 ap.oqsp,xi((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