Why is the depth of field greatj 7d, z0vznh3x dpmc9(er, and the image sharper, when a camera lens is “stopped down” t(d09pnmdz zx7c3 vj, ho a larger f-number? Ignore diffraction.

Describe how diffraction l*mj0eo+*q 2 jze/ qss2+b tlvaffects the statement that the depth of field is greater and the image sharper when a camera lens is “stesmq2oezlj l/+ vbt0*2*j + qsopped down” to a larger f-number.

Why must a camera lens be moved farther fr 9ieurtlht5/ p*8d. 8wmy8yxtom the film to focus on a closer object?t. w8u89yyd htrilm 8 ex5/p*t

Why are bifocals needed mainly by older persons and not generally byat+uvh9p1cv-at/4 f h younger peo -pvh v9uth1+aat4 fc/ple?

  Will a nearsighted person who wea2 eaualb2gbd 8vw (,;ers corrective lenses in her glasses be able to see clearly underwater when wearing those g82u l d(bev2bwgea ;a,lasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted otrjanull,npm a 2478 gs a+z+*r farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or neg t2,+aan+ *lnu47prza m8s ljarsighted?

In attempting to discern distant /p *0k1prcprlh; dsuf)ey,j5 details, people will sometimes squint. Why does this h*f;k r5s )/j1pp0yldcu r,hp eelp?

Is the image formed on the retina uc /3j.kbgd7u ojq: g6of the human eye upright or inverted? Discuss the implications of this for ouo6 g7 /q: ujdkgc3b.jur perception of objects.

The human eye is much like a camera — ye7j9ia zmwzji n;+85u ft, when a camera shutter is left open and the camera is moved, the imagew7+mnjz9jza5i8u;i f will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifieve cuw0// gj:cao) p:sr is also a converging lens. Are reading glasses therefore magnifie0u:j) caowv// g:cep srs? ----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 usuallyl m h -.xqbm-ayqw 9ieed,0g45 produce images that are colored atqi 9m05bxle4ewy q- gh,ma-d. the edges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equally reel85qhp2b7 7zu4d7p whzs 2by the two surfaces. If a planoconvex lens is used to form a rzr7wzs7 bp72hd 2pl 5eu8e4qheal image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a si mv/- sl4g. iu lp17l(i;lixsqmple lens are not present (or are greatly reducesl(1gu .sq7;4p l/- liilxvi md) in the human eye?

Explain why chromatic aberration occurs for thin le tn z7rq6en;-lnses but not for mirrors.

  By what factor can you improve resolutivmvl4( pr89xex s i6x8on, other things being equal, if you use p8vx8l(6 r9m xev4ixsblue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors fp q*u 900 (+zxthalloin astronomical tetfzp0xlq l+ (aho u90*lescopes.

Which color of visible light would give the best resolution in a micr(hjt- hrzb k*-oscope? Explain.(tzjk-b*h h-r

  Atoms have diametersm/1h 79kv ga+bf rac,f 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-sut/r,hm :ig 6tdhetz7v.ht ; +tops 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 141fbj1v .1h2j6 m/z x1-o 9jotucobjza-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports tm-)-ip s/3zh lyu9k9bune (iphat 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 q q(x1 fl wfz65/(quuwtaken 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 to 206:q5yj.ot;sc2 ex snu-.0 mm from the film. For what range of object distancesqn s-; oy j:2c5uxest. can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a diuz.qjvd qadz .-.k 1(p1 s;fokstance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm ;(s.1z f..kaupd1q- joqk dvzheight of the film?    mm

A “pinhole” camera uses a tiny pinhole ii *t+z9l skdt:nstead of a lens. Show, using ray diagrams, how reasonably sharp: i9dlsz k*t+t 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 corre( -uymp5su 4am9eiqs+ ct exposure 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 2r+ 3q ck- ec6,v7cjar 6b2xmwh.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 lenses corrected for th f( : w*ip3u;7( rsobogssy-eve far poin3gossfv;:y-er wosp i7( b* u(t $(=\,\infty)$ 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 /h2 )wnk5jow0( 9tup/gof a amperson 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 point of 14a ux5t1tusy0y-y2u 7ek1b -pz $cm$. 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’sr.217 cc nl:x9og72z6pns ncwor;u wg 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 corrected by jmc(x0 ke o lm0j18ts4a $-3.50-diopter$ 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 sej1 k3u(q cmea9e objects 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 e+ k58lj5ob,,g8jj 3 drb)4 eyrjbwszqye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fou8k 47i,rrq 7dpssye7cal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewing ax9fu7 kss9nl .n 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 iuvce128 e/pr30nuz,mjufb 8has 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 .fwv1afaf on1o/n9t s,l:dn5 of a lens used with a relaxed eye if its focal length ivnno sda.f,w/1nl 519atffo :s 12 $cm$? =    $\times$

  What is the focal length of a, 0p-mdhsfcd2jwcu 6+o.*x o g magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at9 9 38yslexj.. jocajt $2.5\times$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:rf9s;n,c v uzq n5n0q-$cm$-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 viewed wl+q9 tjui;ns cg ,xni 5n62g6jith 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 .vtu0:r)m xl v7ne. hp5.55 $cm$ 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 length of 8.5gflwk) +t(yrj4/ *obkli:hxo aan*nk q 0 .48n $cm$ 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 rate) 5lk jkm1s:mntkd 7v0d 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 telesndnv x3g isd;c)5 vts8w6z-4gcope whose objective lens has a foca5n4x - sztnv86sidgv3)w g ;cdl 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 astronom h*qawxaxe/* *ical 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 wqt6*o qi3l9bjh, n9f gith focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its t ttovv-3 yc bd9575dxmga /ip3wo 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 adjust: +y atux.xojfkwi:- :ed 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 telescope using a rq /vqt;v1 6j 0dkch4haeflecting mirror whose radius of c q tc0j1vk6/hhq;dv4aurvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearsiwiq;.c4x:kco k;ea l) 4a-m z to 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 telescope (Fig. Below) hh +oii,4lbd*c,o-u kn as a radius of curvature of 3.0 m for its obcl 4dk*o+-i uobih ,n,jective mirror 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 focal length of z8 4l0m (cb*i7olrvxw 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 1siw5w- mdrjh 99 w)ss.2.0$times$ 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. oc rfw2)ytpfq:a+ * tbk769ee+1uj rk8-$cm$-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 assuminzl*ho9h* hqq- /xlq)ng that the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length of 2.706 hirf6f55q9da7 dr-qj)i ashk 1iotvjd9- y 8 $cm$, 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 ooi .yyhgq(x,* zk0b*thin lenses, placed in contact, that have*g. yx0yo , qkz*hib(o focal 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 aberratioj3o5;g1ud qw ;kvc.t: :zircen in a particular situation. A planoconvex lens of index of refraction 1.50 and radius ouv:z ec:i; q.gktodcj3r;w1 5f 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 h a++ muo9-q1) ebqjcufor the 100-in. (254++m o)1uhq -cuqe 9bja-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can*-xbehj p0es;jix1d* resolve features 7.0 $km$ across on the Moon, 384,000 $km$ away. You have a 2.0-$m$-focal-length objective lens whose diameter is 11.0 $cm$.
What focal-length eyepiece is needed if your eye can resolve objects 0.10 $mm$ apart at a distance of 25 $cm$? $f_e$ =    cm
What is the resolution limit (radians) set by the size of the objective lens (that is, by diffraction)?
Use $\lambda=550\mathrm{~nm.}$ $\theta$   $ \times10^{ -6}\;rad$

  The normal lens on a 35-mm camera has a focal length o 8zhld69w- 2kjmg/w/p m+gubif 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 barelvf5bak(h3 c 9wy 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 cad kyh2t*dyx4n ;8)nk3v t./jx sw;hmo r 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 separated8c16l c+etczjv bfj ok011q v) 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, lyiqwtv75ui5m02pw .n8k x9jcg- d u i+iing in planes, are spaced 0.2k0 5iu5w x8q iivpcm7nw9.j2iu d-g+t80 $nm$ 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 i.jpwi;6x) z+xg:1kroze w3 ynm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at yg)e wj1z:6 k3;zpro.+ixi xwan angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is observj(w+c, /cz z)ru;k3y dppx3 gaed 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 confg 5h7itlbfu rz+8 e-l0j 07sm0*phwisists of parallel rays. What would be the magnificationig rzf 7ujh heip*0t +7bf0lws-l m850 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 pass tklkyasw484 ,ed toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to chak 4a4l8ts,wk ynge 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), the6lblx :g(ja01k ahq ;c magnification of a camera leh0;x 6:jlbl1 a cqk(agns is proportional to its focal length.

  For a camera equipped with)vt:ct2985 r2 hmyyxcoqd 6 fw 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 hermp9f.2d wx 6jdzok30n y9.f q)yjbyj+ right eye 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 pointtpnuw;-4k.z p of 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 magnifyic0; 7hqjc*jmk3be v k8r/(-q.z 5/i ufwgsiszng 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 using the lenses from/x *bw.2z hb4ls6ml rm his reading glasses. They have bl6hl2zw4m*mb. /x srpowers 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 us su9q69pc +3 )vlrep+evgd89;ttdptkes $+2.5-diopter$ 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 (25 cfseud lbil9qs, d7 ;;xirn 4-;s(h 7e0st el8$km$) 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, exposurew 83g ( bv35 mqrwgmwd15/h+kxi1ekjw times must be increased because of the increased dish /1igkw1b5 kmr+qw (m5e8gjww3 3v xdtance 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 eyepieczq ( m 0h7sdjt nptk-,.:jvyr7e 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 Teley0vvv7e4 e ft8tl 4 rc aqf22h/7jrdx7scope, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distanc dvxeev7 ftr0ljf th 4/72cy2a q874rve 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, one with a)a-kce w;vu, $f=4.0\mathrm{~cm}$ 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 t 6b qr;in-d9rs;duau ;wo 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 pla.b gicj o+2 b62jyki /:ytffz)te numbers. Assuming it i ctyz)i2.jji b:+ofk/b ygf62 s necessary to resolve 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) ha2( cbyukeg)iosn 7s2mvja-; 6/ i0ruqs 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