Why is the depth of field ojxeb2d 5y ky(p5 +q/sgreater, and the image sharper, when a camera lens is “stopped down” to d s5/keyb2xoj+(5p q ya larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of ms,f6 bwb b50tgm8iz p hbz( s6s9-)jpfield is greater and the image shar6 b bzp8ztw9g s-p)m0ih6sfb,b(5 msjper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from th4v9t3 zh.w/bqf,o knse film to focus on a closer object?nts k.f/bo z39v4w, qh

Why are bifocals needed mainly by 9tb goalmv61s+e 8p 0qp ,zr8dolder persons and not generally by younger peoplel qm6+ s o tpa08,d9zrv8gp1be?

  Will a nearsighted person who wears corrective lenses in her glasse7b41:ppze pp es be able to see clearly underwater when wearing those glas41bze pp epp:7ses?  ----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 at thp)ep0t5d) ozzta5k :*lu 6de he width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig.d*ktpe 06e5z )p)a5: dlh zuto Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will soms fg) 1gtg f:h64ngp 9(ltgq,betimes squint. Why does thpg q9nt1 4(flbg)sghggf,6 :t is help?

Is the image formed on the retina of the human eye upright or inverted? Dtjqhu m4 n8;e)iscuss the imputmeq jnh; 84)lications of this for our perception of objects.

The human eye is much like a camevlo:itq4wn 2dob;/dn:p 8 u0w ra — yet, when a camera shutter is left open and the camera is moved, the image will be blt2:w n4o wolbuv dnq8 d/;:0piurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simg3r(r nowtc34n:e(tr s.zm3zple magnifier is also a converging lens. Are reading glasses therefore magnifiectr34er o(t n33r(w: gznz ms.rs? ----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 thgy6i;wih+w(ud : vh 1uat are colored at the edyh 1(h:vu;+ u dig6iwwges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equally by ty3 sxrg0x+lm6 he two 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.gy xlx0rs3+m6

Which aberrations present in a simple lend;tkxt 13vv9k s are not present (or are greatly reduced kxdv391;t tvk) in the human eye?

Explain why chromatic aberrationj) /vg s;nrq0u occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, ot4g bq9kxn .nz uu6(vdsqr j653her things being equal, if you use blue lightsg6 zjkq54 u3(n bd.6vrx qn9u ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large refleccsrd 0nrs :wm(:+0kobting mirrors in astronomical telescopes:0s(r cbr:ksmo0 wd+n.

Which color of visible light would give the best resolution ibsrlyzo pd32*s lmz839q4 dw2 n a microscope? Expdqls9p * zs24y3r w3bo ml82zdlain.

  Atoms have diameters of aboutax jo1(e: .yfz $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens zkfc4)xi(vz2is:p cdg8 ) wv9has f-stops ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a 14- )2nhj:/i, 6 cyz:lli 0 epx8-gzdkyxx$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a cam ot816uhpv1 ;se x6ghle/h7wnera 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 taken at m0nzc z99vfm- $f/16$ 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 ao3:ojf;hwum)o:j ,o cdjusted so that it is 200.0 mm to 206.0 mm fromm;uwh3fjoo:o )c :,jo the film. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance o w*u,a0,er iik-;q xmlf 58 m. What focal-length lens should be used if the image is to fill thw0,q*,;i ar exu-lmk ie 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using ray;d;)yz;nx l e a(2 l)lx:jxqli diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider t (ajl;)x zx l;d x;eqly:2ln)iwo 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 e4mhsqpf*ac ds +r/e .6q/prf)xposure 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 abo c9h)mukz-5obb w0n-tut 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 pe60hwgw(x x08fwjrtmhv/2q4 erson in Example 25–6 wore contact lenses corrected for the farvhqe 6 (x080w/2wmg4h rtfwjx point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person whose near point is 11h1zw(f tm,r f ev :trjp1j2j,35 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point of 14hm 4 pq8;wj9r.g.ubq ea vw;6m $cm$. 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 0l(l9jkoy6, gos8 uqylength, 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 cortxxdb.;wtpn8dw g/6 wj1z o1 .rected 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 between6 84lv*jm( ag+nxfduh f n6bj2 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 the /.6vyl6slyb0k w4jaq 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal5 9tgtthici.g:/g g q7i-vr,z-5zwf r 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 syshy)o 8o0 6 vmhf61epentem 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 has near an4p, *z(oxp2cbtyie p )d far points of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens used 4 j;hrbw1qu0rr + 4cjzwith a relaxed eye if its focal length huj01zc rw+4rq;b4 jris 12 $cm$? =    $\times$

  What is the focal length of a magnify2+jo3dr c74fi n.javding glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated2bmricz lho)0krbp0-um /9ns d ff84 0x/q,xb 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 using a 9.00-:)m;8z:x yu 9oj4w/-repbin nchx.r w$cm$-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 vyw2) ks l+syd0iewed 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 5.5g f9,5)vfq:z s)qpg9 ray pkh.5 $cm$ 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 length9*2 c)fs8ssc,mmj(f2 .jhjoox p zhe1 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 rated md:4/z g7kmxpat $3.0\times$ 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 has yk/id24o a ih(a focal lengia 2hd(ko/4yith 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 magnificwhv ,kkbow*3v .9jbif5x p8 d-ation of an astronomical telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

  An 8.0$\times$ binocular has 2.8$-$cm$-focal-length$ eyepieces. What is the focal length of the objective lenses?    cm

  An astronomical telescope has an objective (7x (uhox(lyp3qm7oxb k2m6xwith focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75n7jq l wz 3av2zs*5 qtg5s7b*j.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 adjust/a)i8fe(pj4dlk wk :red for a 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 telesjbhws.:k q93 tac.cca:hsi56cope using a reflecting mirror whose radius of curvature is 6.0 c.t.wsa:ha3 h9 cq5s6 k:icbj $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be:ra -a0n7ho ci u/n2qdpyih.* 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 telescope (Fig. Below) has a radius of curvatu.uf/qunhdr48 )l7 gjigdpk 6k/tb: d-re of 3.0 m for its objective mirror and a radiugu /jdd r/d.n-fku:tg i q6lk)h7p8b4s 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 an8bdfh2 z02 yn4zt*lennr *yi , eyepiece 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 1214,5 9ytkc)d r lult5gklls3c .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+cn6 up.y /q4c;66bq 2bl/dluuf b on1yvh0lc.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 the final imag 65dinxl 0/7oi0xhvzve is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compoundz+fx d d vi7-* 4tcwj61xkmsp1 microscope 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 very thin lenses, placed in contact, that ha)p+yz-;,zi m k-jb2cvt x gc)b;lj3s jve focal jpt+ yx)lc3v;,g ;km ) cz2sijbz b-j-lengths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular situation. A plano*id /n,qwr / m2rnne1zconvex lens of index of refraction 1.50 and radius of curvndm zrrn*//in e12 qw,ature $R=12.0\mathrm{~$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 b8qsvl 3vt 13uresolution limit (degrees) set by diffraction for the 100-in. (2q1usv 33t b8lv54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve fea; dxjk ;vg(0cltures 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 length 3pxsvkp8i* fg,2o3 upj x vd1em0r w4.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 barq,wci:25i 2hvl7jg9onm al + aely 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 headlights 2.0x o(t,h1i tuc505t qr2heg8rc $m$ 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 bznx+xr7de/do oe 0s rxs9-7,cy 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 atomjxe7+o e/f8j b-2osa vs, lying in planes, ar 7x8vofjo2b- s/+ eeaje spaced 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 ;9zrwwt(;a: 8 b xhwc4 dgjj y5qk*3bwat an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an ang( bcwjd;krxaww b:;jtwg yq 3zh9 548*le of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is obs(dx/yicg wi42erved 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 Xvj1 td85ef3tif+(5v nuaqtf/ -ray image that the X-ray beam consists of parallel rays. What would be the magnification of thjfiv8 f/5(uat3 vf5e tqdt+1ne 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 toward midday, and the sunlight got more idabi*q0.b) gt5h+ hf intense, a photographer noted that, if she kept her shutter speed constant,hdqf.*bi b gi0a+ 5h)t 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 a .9 zeb5*y psar2tnj3bv cy7t m*4oyq *:h6vziway (assume infinity), the magnification of a camera lens i 9 tyrzjb6qm*c* vtv*3np ayh iy.5szoe24:b7 s proportional to its focal length.

  For a camera equipped with a 5 sg4qgh.8mi fg17roa0h 0/mwv0-$mm$-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 ey7lf*jq. qtbm1wnem h;j7 rl :(e 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 1:fd hf 2e9xr7 qoc26vd5 $cm$. 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 magnifyingy l-g,o0-7e fwabdt9x 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 tele0q9ools 2: c.jlxc rd;m*pv/ rscope using the lenses from his reading glasses. 9rsx ;dvmqolrc/ l 0:.2jcpo*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 uses30a 5 hlzzwmy1 $+2.5-diopter$ 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 ads.e fgxuke)x,a p9/ 3)y2y qhigh 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, expoi2-wt id* +qbysure times must be increased because of*d+-b ii2 wqty 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 fq6xy)o vxg.j51m2m+ 3fxtpnr4mt 2a 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 objectiveopx5j8 w0 rw vow-,qa( diameter 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 wavelength 550 nm. Assume the Hubble is near the Eart (pwx5v- o8wrqw 0,aojh.    m

  Two converging lenses, u 5a,yx5kotx, o*wb voax5(v* 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 magnificati(n b ;b/idjh+)igbj e33om b)kon of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license plahm)osa a9uh58f o2vh6 te numbers. Assuming it is necessary to resolve pohh2va8uo65h9f samo)ints 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) has one flat surface and the other h6 pf(usv .x.ez;ab eq:xp7 4y pu2oar1as $R=18.4\mathrm{~cm}.$ 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