Why is the depth of field greater, and the image sharper,:2 j7afkii e*m when a camera lens is “si e2j*: 7kfmiatopped down” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statementebf,s y.h(5yjo k2u:t6ug+gq that the depth of field is greater and thy ubg25+h(,fu.y gjq et6 kso:e image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther jwq 57ph/ xlxb-0y2yzfrom the film to focus on a closer objecz0xyw 7 hx/pj-q5yb2lt?

Why are bifocals needed mainly by ole5 y.6ce f8xneao7it*der persons and not generally by younger peopl57*yeea n.o fcxie68te?

  Will a nearsighted person who wears correctie - q24.xo nlbmisv9sl5bu8ju n xx8tz :o07u3ve lenses in her glasses be able to see clearly underwater when weai 2 x3jx-s 0 vt qeb8u:nbs8l9x uuznl47o.o5mring those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or +w6 i-h3t7co9pv nwiofarsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the gla3-w w9t+ov6 cpiohni 7sses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern dist(q4c1exs e8,pu p3i e/b0xw jiant details, people will sometimes squint. Why does thijx/ beu xiq,iwec48p (pse1 30s help?

Is the image formed on the retina of the hu) ehfa;zd, s*og 2fhd5man eye upright or inverted? Discuss the implications of this for our perception of objfdo5zhag;)s f *h2,deects.

The human eye is much like a camev)/vrjndt : hcvs5p4o 7 5u9vgra — yet, when a camera shutter is left open and the camera is moved, the image will be blurred; but when y:uthcv7v5 go/j) r4p 95v dnvsou move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simpl-ygw3re58yz +ddv( zce magnifier is also a converging lens. Are reading glasses therefore mv5y d+ewz3 gd(-crz y8agnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopv.f -q w9:hnooes for children’s use usually produce images that are colored at the edges. Why? 9wqho -:n.vfo

Spherical aberration in a thin lens is minimized if rays are bent equallwyoj7y*nsl;5 xf hx ,t-yd6b(-mvf , ly by the two surfaces. If a planoconvex lens is used to form a real image of ahfb6-d( xty - ynmfl s;*o,7y v,xjlw5n object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations presh;m.(;jegw zkent in a simple lens are not present (or are greatly reduced) in the ;mj.eg; kzwh (human eye?

Explain why chromatic aberration occurs f;jhml lk py(,uye( +2mor thin lenses but not for mirrors.

  By what factor can youk d,dqi)tty ,iv/ paj,0 +dqg- improve resolution, other things being equal, if you use bgqta,ditjpy+ d,-/qkv ,i )d0lue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantagu h/+;fq+mnopes for the use of large reflecting mirrors in astronomical telescu pom++n;/qfh opes.

Which color of visible r z,7t3* yd m,uguv+atlight would give the best resolution in a microscope? Expl,a g,dytz +trm*u u7v3ain.

  Atoms have diameters )d1swew) ud l,of about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops krt5x 0+ 4f*kznijui vmq65 p7ranging 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/fhcuh lsm)6ia-ew+uq ( *b khl8y d,: a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports /dtij897 ytlw that a 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 photograph is takeny k3/zun+-x 3n8wwzh-qpz8x w at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm t nx0kuxavh47w.v3u c0o 206.0 mm from the film. For what range of object distances can it bec0uxw hv4a. nkv u073x adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtalj2q4rvk6 e-;rwym* itl tree from a distance of 58 m. What focal-len2ry kv46e*-mq rwj; itgth lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead oqxo9 8 vj29;m,w/a3lj6z 1lcwodmg pxf a lens. Show, using ray diagrams, how2l,x9 oj wm d8m1/voa69x;q cgz3pw lj reasonably sharp 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 exposure :*7ut dcx/ be o;n f2u3tc 7bmw.4ftjdap90zvis $\frac{1}{250}\,s$ 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 abou zr2exji2:q; w 5pmm5nt 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 lek/ ,m , +imr5; hzc1iu7bzoilz zb/h6 81hykionses corrected for the far pointc8 z,1;h1r o 7lo,hy5bzbimuiz6k/+m/kih iz $(=\,\infty)$ 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 p r3h,ahc 6vf: xr/fn7loint is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point ofa 4cw-j6qka (y 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 lengu.mvihmd +*q-sz6i ypq 5ta,:n8 kd q1th, 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 s9d5,jyatgw mkb 228r 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 objects clearly only if they are b8te jm 6. 5ab46jqotonetween 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 s+h/z j v )8onif7lmm 25-uwfz25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a f/h/b ul 9w 0zmm//ptzpocal 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 lengfq)wfag1go / ob 7-0tbth of the eye–lens system when viewing 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 hadw x0jw flua67,* pofvo84 e7as near and 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.y0qa)q/rd7 vd bjz z6 a relaxed eye if its focal length vzy.zq 6q/r0)7abddj is 12 $cm$? =    $\times$

  What is the focal lengtho qxh:rpdvu d;1r81g7 of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated 5lt9 k n7wu8jnat $2.5\times$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 9.00- v7a sf+8blj4z8lpf;b$cm$-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 bqz6,b yqncnv/ 5ey6: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 5n:yjq;8fh 5it.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 4gw1co n (o*. uouzdyk7*5z lvfocal 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 i7gs: djc;ztb) s rated 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 magnificatisyhtos,5 e /(s6d+ feig:,wgnpc/p-hon of an astronomical telescope whose objective lens has a foc(,c edgfh 5ingso,/:p/hssew- 6+ ptyal 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 a9has hl tyyofv7 8 jha9j3021rn 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 telesco zvc,yp pn4;4m)q; 2 fzf7auaape has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has it v0w7qvd5p+l xs two lenses spaced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relhf*tvqh 7 dxd +)z1c9gaxed 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 usiywoscr4i3j 9uo,(g1 gng a reflecting mirr,r(cy94oji s13u oggw or whose 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 magnifcx5db2z6l* p*6y h yhjjim+ 3p3f6 /fvu;wgaqied 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 curvatu q rk1amcxx.)w4.e d/rre of 3.0 m for its objective wx c.1dar 4k .)em/xrqmirror 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 eyepiv4vktl2j/b 7n j)y1uk3r4z6a0r di yvece 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 12.0i ro.e)ktx9u t6n,tx 14fcmi/ $times$ 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.aofw5j8mw;4 tw0 4d dd8-$cm$-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 l1n qn.og6 -(x zo6ocqxocated 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal lengt8f(b2 pglc9.m mq 5zkdh of 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin lenses, plac5rnqx1 :bm*qmzcy ha+h1s:n s(9rbw(69 j wzf ed in contact, that have focal lj5 rqh91baw9zw*fr:zb16 qm c :+s n ysnhm(x(engths 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 scgry1 x 6f81gjg s/j;jituation. A planoconvex lens of index of refraction 1.50 and radius of curvj/18jy6cgg ;grs1fx jature $R=12.0\mathrm{~$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 (qp 3 cfr,fcsbr3 iq4+,degrees) set by diffraction for the 100-in.qf, +p s rq4fi33brc,c (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telest-hg b 7sp;r)s)wgau 5ia*yc+;nh0k (vykw3xcope 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 fe1/e 8koe8n ( m6s)ytsi ko3gbocal 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 1tebx46*btd w*9q zyu gu.xd*qt 85obare barely resolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye distinguish two car headligv,wq +p n/28/ cls uz9zflcec+hts 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 separat bj/-z a17dwyx za,ji:,95n,fnwvg 4taq r 2xged 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 cro+5ovh y w3/kjystal whose atoms, lying in planes, are spaced 0.280o+ k/owjvyh35 $nm$ 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 0.091bl:1g jk),,rjxpbo.g1 tgd p73 nm are directed at an unknown crystal. The second diffraction maximum i11jgbd g1 orp.)g,x:l tkp, jbs 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 diffradz0u0s 4xymz8ction 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 ub16u01m *jnh i c ,81tmeqnh h4urke*X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificeh he uqumthn6r4n 018*ki11 mju*bc, ation 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 mi)fe+h;s7*c t y;gn*l 0smj8)xdy +qv7gikgmkdday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed const*) ec)mv lxgk mtj;qy+87f;7ssgkh 0 gind*+y ant, 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)xp su2j(o (la7, the magnification of a camera lx7ao(p( lu j2sens is proportional to its focal length.

  For a camera equipped x +2ukhi6*6o wriqf7 jwith 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 x)6hr1 x)y 7k 5bv28mypx gv6ixwhn7veye 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 o y;0ull3 2* xzmrlhz8bf 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 powerp8k)h7s*,kb cjip nm) 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 using the lei:u0 qd+6olesk 9)hqinses from his reading glasses. To huq0k)esq+ i: d69ilhey 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 us0,.l1e .wajv wptucb7;a x8jves $+2.5-diopter$ 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 (25qa5 of z/jiv7 6) tk3prtu7nr-n8mzc5 $km$) 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 dazbe6:ou;bns kbw fxn)93w( 6istances, exposure times must be increased beuk an b ;owx6s:w63b(fz)e n9bcause of the 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 and the eyepiece of a telescope are spaced 85 hq/-w5ehef/ a$cm$ 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 viewing np 31eae(xpih,wk..; lg kbp* the Moon. Estimate 1 (eei3hp.kxp,k *lapg.w nb;the minimum distance 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:: h-eznwzbz6-fwa c0xv z:6 w, one 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 8.0. If the two lenses are 28bk8oc;i z +i/w bc;u0d $cm$ 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 /w,/f ill.iqhers. Assuming it is necessary to resolve points separa .w //qhiifll,ted by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below) has o*rebh,(: oe8wm u: dcjne 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