Why is the depth of field greater,b l.xsj xy)8c4 and the image sharper, when a camera lens is “stopped down” to a larger l4 )sjxcyb 8x.f-number? Ignore diffraction.

Describe how diffraction affects the state y38uh*zkr r 2ec)dx(iment that the depth of field is greater and the image sharper when a camera lens is “stopped down” to2c u)ykhi8 xer( r3*zd a larger f-number.

Why must a camera lens be moved fartpf e2+5x z q1w:jw;hn+ rw6vlvher from the film to focus on a closer objectf6nq we p+v1l rv;w:5zw 2hj+x?

Why are bifocals needed mainly by older persons and not generaew.d0kje+ukr ( (3qa3w( g h94gsy vuqlly by younger people? q0eukahwg 4 egds(wj.qu(k 3+y93(rv

  Will a nearsighted person who wears corrective lenses in her glasld:riu *ld3-yig wb4d)4 5tsmses be able to see clearly t:s wgulid -3i dr5)44mb*yl dunderwater 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 look fnf8 ldr56-nvb9x- vfing at the width of the face through their glab rdv6xf89n-n-fvlf 5 sses. 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. W3t2zlvwcs* id h 2o9v(hy does tliwc o9td*vz22s 3hv (his help?

Is the image formed on the retina of thuifhz,k( z.3jbe/a2q e human eye upright or inverted? Discuss the implications of this for our phu, eazj/qi 2.k(fz3berception of objects.

The human eye is much like a camera — yet, when a 0bsentuv*xi ) ubz/ap, vu9(q 4 c,9eacamera shutter is left open and the camera is moved, the image will be blurred; but when you move your head with yourp0 (4e9 bu)z9a/ u,ue svn,t v*xqbcia eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses./kq5bjzqlt*1geltwbq q 192 ; A simple magnifier is also a converging lens. Are reading glasses therefore magnifi wbtj51 9 /zqbqkqtg* ll1e;q2ers? ----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 that are ;9y: gl5tepve colored at the ede:95gvlet p;y ges. Why?

Spherical aberration in a thin lens is mi9so7u:f60uuc6 klym enimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the o6sfl6e7u0k um:o9uycbject? Use ray diagrams to show why.

Which aberrations preseyx ;d*tubi,4j nt in a simple lens are not present (or are greatly reduced) in the hjt4;udixb*,y uman eye?

Explain why chromatic aberration occurs for thyn.wl/g8,ve vin lenses but not for mirrors.

  By what factor can you improve resolution,x6 5)mu8k)jsw *th)a8zdnze/ fkvm y/ other things being equal, if you use bl)t8nus/jza )y65 v wmf*kkzhxd8 em /)ue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two adva.fg ll(n4vmy,ntages for the use of large reflecting mirrors in astronomical telescopes.l4lm y(f,v .ng

Which color of visible light would give the best czannx-z7 1.rf, v-dvresolution in a microscope? Explain.cd-f, z.zvnr7an vx1-

  Atoms have diameters of a(b9 ofr4iv1v;rxw) 4g m ta7qabout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangincp; ;s zv- fs5w;miol i+u(n3vg 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 cmrq:02xb, yjvk z38lw:*vv c 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 satddx+ 1 *l9skpcc;vs x 0r cxv1xh-8,0v*bryetting 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 photograf).n dep 2;jvc)c k2oeph 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 tr+wpq wldo ,e5*4 dng*c-a6d5a*p wvzhat it is 200.0 mm to 206.0 mm from the film. For what6w p*,r5cngd lv +zd5awp*do*q-ea4w 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,m*ajaua 8oxp5 lfr9- a distance of 58 m. What focal-length lens ru ,jalx58-9o mpafa*should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole mdto-;7.;yga zh rz.o instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. ;.yoh gd zt am;-o.7zrIn 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 exhv/bbmjk audf(q(:gr(r m0* 4posure 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.e 5-ht* e7src7gctw):kh1ifn0 $cm$ 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 codkpl,p 1if*zf4ja lq;)65rel tw n5,antact lenses corrected for the far p r6a,)1n5lwp5t4l* z, dkapel ;fiqfjoint $(=\,\infty)$ 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 isfoz / zmxcwik/a)6h7jubb7y(2:txkf+0 4v g d 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 poz;hz y-c1r 5o,tx1wdhint 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 bo-3cx 4;tu o.sp5kem:q /pjlgyok 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 correctedx4 nhidxcnno9*6s5lq833j t v 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 aremp t y(1;ihld 1e/he6zvjv.3 b 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 th*ft m x5t2+/vddl gfr1an the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fo dk9of5najt 9c(rtu 4,cal 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 vz 4lnug1-tgr4a b pd1-iewing 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 pw bvk.i7, gaz.bp 2u5r8n0qscoints of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens used with a relaxed eye kzcg 031+2ond)jp qwt6vz 6 wjif its focal length iq3 kv) o c6+2gwznp jw1dzt06js 12 $cm$? =    $\times$

  What is the focal length of a mag2ekwb0bpt hz 9e,pwal- fju 63v:-jx3nifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated a4c cn)ln1r mb/ol): 1kyw qjeg0j60mkt $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is using a 9.0 )oeiyl*n.mf )l-88-)mltgr ex(pgm o0-$cm$-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 beetl4 xkyt6 j/eo :to4;zfke 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 plakcx 2y.eenp.j*zi7a : ced 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 lengtmb ecim.9,iex:o5 i,j h 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 ra sv: w+w/(. knf9od1leukv)a a0cdy :kted 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 objecterp+ q3a42:sx ay p7boive lens has a ye37+ap b4pqo sr:x2afocal 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 astronomical telescv 2+ tw2yhqrdl) w4m7mope 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 objet u:i9i/yd j(uctive with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its 1iyx zy,d*qoabsk4 i-j)70 qc7z.bortwo 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 as9.wt h- sdid: 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 telesbio+z0a 2hpf 2 j t/daotr-;n.cope using a reflecting mirror whose radius of curvature/-raoznpjd o02+ai2t.;ht fb is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnifi kj )j7l 3jhli *;icv9p2wkng5ed 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 iiyowyw) za-euz/)e2- : gv;jof curvature of 3.0 m for its objective mirror and a radius of curvatureze)eyw;yiwv--aioj/ u2g) z : 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 eyepievxew*e7o3vy;2p ym/d ce 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. iic(xm4/(6d2eyv;o a 9v3mrs4 msft 9sq( rju0$times$ 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 1.80jkklpv k7(kc/stj (. -$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the final image is located 25 qcu: m4(v wj)b$cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length of 2.7q x(;2/hqtuwy0 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin lenses, placed in con:vg,9htw xy8b+qs*bf tact, that have focal g:9 vh8btwb+ fqs*x,ylengths 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 pa66:(2f/ wgygnek**ugci pl snrticular situation. A planoconvex lens of index of refraction 1.pg gk: nl 6*/26*ncywie(gsuf50 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 li(;7 qh7*sshm .uzi devtakc77mit (degrees) set by diffraction for the 100-in. h*t 7 ;usv7hm7(qicsaek7d.z (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can revj2y+x4 peyzhst8 ;1/rx u2 ntsolve 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 xb7u2 nep+gu7 36 rwpjfocal 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 barely resolved by a 55gz1:mr0,1pnm * vr usn-$cm$ (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 ) issl u.40dqdy4d: zka human eye 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 byq(6nke bk n4p: 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 cr1zl/ jkoe(+pjn e2 o3bystal whose atoms, lying in planes, are spaceojezekp olj3n1/ +(2bd 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,4iv.rcd3i qp at an unknown crystal. The second diffraction maximum is recorded when the X-rays are direct4q vi.3 rp,cided at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffract-gmgx v9gi1ssh 5dj /a7td.6pion 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 convent9ke7d3 1jkb23u0mt /p qgcyxoi r8+ doional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificati3mjd +08cd u2 o9/ 7yk itq1ekgrobpx3on 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 more intenseu9zjp9 xkbt+ ea;j)*c , a photot9p)acz ;bx9* u +jekjgrapher 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 very far away (assume infinity), t/v-pb) *w4-4e1zjhl scrfy ku4w g zu6he magnification of a cameeruf64luzcg-w41v hyj - ) zbw4p ks/*ra lens is proportional to its focal length.

  For a camera equipped wo sm./(pwtmozx* ea6(ith 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 :eyh;c35n;gpx7d glo 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 off 0vxhdpvj7f; *rwo32 yz+ h6j 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 magnifying powcla wct6 0vb 1xxq,m61er 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 usingyyzs-3mbip3 *pf z) /t+a ut3j the lenses from his rjz tp*)m3tsziu/ fp +yya-3b3eading 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 use jtp c94fv1cn,-pz+0 zo3 bxilkb-7 tgs $+2.5-diopter$ 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 extremei8r)z k 5obyl1rrp )u3ly 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 incfxk+ef/, m dmw, z8jt2reased because of the increased distance of t/,+2fxzemmj,8wk dt fhe 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 oftpxl 3w 88tzk; 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 q8(i,a/judw zq 8p y-eya3q) hobjective diameter of 2.4 m, is viewing the Moon. Estimate the minimum dist -)a,iuy8qew/y83qzp d(jq ha ance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, o) p8qs:: bqssrne with $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnification of 8.0i424o2kd2d/i lgx0n ohb ht 6l. 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 numbers. Assumingxiq5/r-rne) j it is necessary to resolvjn-q i5)/er xre points separated by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below)go-44 :5 zz8x:h4de zgr7ot ee l elc1kqx/q-g 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