Why is the depth of field greater, and the image sharper, when a came /2yh:8 z5hnk7alxc ygra lens is “stopped down” to a hxlc8zh k 75: ay/2ynglarger f-number? Ignore diffraction.

Describe how diffraction affects the st3,bpojt+6r -ggd fd2w atement that the depth of field is greater and the image sharper w-3d6tw2g+ b pj f,rodghen a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the fikwjodtgl e1(g3n 3;.w 5wj 5 hcko/kk:lm to focus on a closer objecw/cwn w;(j. 31g:kkljtk oge53kohd5t?

Why are bifocals needed mainly by older persons and not generally by young*-nuv 6d-iv ak*fpx3 zer people?p*knv-* 63ix adf- zvu

  Will a nearsighted person who weer4eq: o tonw: wz1k(1ars corrective lenses in her glasses be able to see clearly underwater when wearing those glasses? :w11(wr e4neooqt:kz ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a perte. 3 q. bjb7ul7n 2g:tizxls1son is nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face.e7:1g .zbstnli72bu tq3j lx appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern dif:qh :*; c;0 d,jx,5el xhzpxdqlwm6 zstant details, people will sometimes squint. Why does this e6 fz; ldq*h5jh0:xw dxq,,pmx: lc;z help?

Is the image formed on the retina of the4m ir8xp5pn c3 human eye upright or inverted? Discuss the implications of this for ouxm p53i8rp c4nr perception of objects.

The human eye is much like a camera — yet, when a camera shue) sr2 gicokf)mb+/9utter is left open and the camera is moved, the image will be blurred; but when you move your head o/c)gmr+ 2fb9)usike with your eyes open, you still see clearly. Explain.

  Reading glasses use converging le:5s0.0q be6i mj+.k+r nn pza*dfwfypnses. A simple magnifier is also a converging lens. Are reading glasses therefz+5k.mb*+ dfy: .jrq af60spwniepn0 ore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s u vgk5883cnmu8 ojd7yckltx c8ow8 *pn-2 r1e ase usually produce images that are colored at the ev3m c n2-8ja7g 8nl*18o eptu ykxwcckdo 58r8dges. Why?

Spherical aberration in a thin lens is minimized u l ak8d++yb5wif 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 sh+uykl b5+wd 8aould face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are greatly : mbsk8 6jspu6ekm1fb ,nm5h5reduced) in the humankj 8ms5 knp fs6: 6mbemh1,ub5 eye?

Explain why chromatic aberration occurs for thin lenses but not i jo/a3/b(e ysfor mirrors.

  By what factor can you improve resolut*9 ,jnb6xc dopion, other things being equal, if you use blue* j69,ndxbopc light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors in astrono+sm/ dpcsm1)-n0 ko ce ia6,sfcj(pu(y 9(cznmical tea+knm9m/ ((ceios01) cfcz,sud(js- p ypcn 6lescopes.

Which color of visible light would give the best resolution in a microsc )qr9jvwfju(;qs f /l9ope? Explain.;q)q jf j rlw/9su(9vf

  Atoms have diameters of ar0g4qsp33 4lmut n9mrbout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops ranging fr 7hpnd:8jx8ycrq28a hom $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lki -c-j,jtmj *p*u-diens has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports 4;f3s y i04fg9rh .;ft, fewcmmvah9bthat 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 photoutav . )9 a-j*riw gnunb8r(i;;qk mh4graph 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 lensdzu fi6 .ne (mb385 )ssibs/kx can be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what ra8m3dbu5ixif )/kzsb.6ss n(e nge of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishe; 8oj3kx0zc in *gff9qs to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be kj30z * qofigx;9f8nc used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using raoud 2s 5w9kp0x-:poedy diagrams, how reasonab u9:dox2e05p-w dsopkly 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 3q fzw8.gcko;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 alm p78poy6gl :1b xb,k;gq0sfbout 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 le-uvpkp4 fmp*y e pey 9a5 .z4am4yc71jnses corrected for the far poi4m . k fyy7pa5yue1cp -am 4e4z9*vjppnt $(=\,\infty)$ 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 qssn7v6s uk nu3kxz :eh5f :5u;-dh imq*lg5-a person whose near point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point of 1n t6sr s;60kiw8t ao7i4 $cm$. 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 tl*wcsk5 * ftf:x(lltprukc9dk/sq s ny- -., *o read by holding a book 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 covs7rh1or3u0khi43 f 1* q svq8t2ky yprrected 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 ail,li eoo 3, 1p* wvoc7o6+dwobjects clearly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Example xkhpb albp5kr7 96y)-sq .z6u25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person8txs:f wwsis n;kll:q3k+v;m:e( ct* ’s eyeglasses has a focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewing an objecj d/lwew2d3 7: d kfh6wyjwa+4t
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has near and far points of 10.0 av39+jd lh8 yjhnd 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 usedm0cdt+ljp (h / with a relaxed eye if its focal length isjld+t/mh0 pc ( 12 $cm$? =    $\times$

  What is the focal length of a magnifying g ux /n;flt kdu6i/5iot s2j1d;lass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at;x6 n:ckp7d: i9; .6yvppmk mcp*kbin $2.5\times$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 usingebqho)gs.o e1(g5 y 8i dv8+su a 9.00-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle is q00;gr /ohfb4vc zsz2viewed 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 5.55y h7z08xk e :sws; -bq)e2nnog $cm$ 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 fznxjqcedt) / d,vh9 /sm 03l*focal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass is ratep.)6 y0z-wlfwxj hw 1td 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 astronom,qlebg b 1 6kv2lsa3/bical telescope whose objective lens has a focal lengvb l32esgk6qbb/la1, th 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 telescope is desz0by w;aun * ufz: 02megpo/v-ired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

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

  An astronomical telescope has an objective with fo3l232 icc5 vk:7f0ci (c hhr vhj8qnnccal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its)dl)am;l-kiy j( p;em;gh0up 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 adj5-zq; 2aflah busted 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 reflectev8mvnmd fi2tk0k5,s+v0k1ij( qm k: ing mirror whose r1n2m5k,:+(stkdf v0 i kk08vmvi jqemadius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be3isxn;dtdd,a) hr 2qc8;se) w(j: kat 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 r a2,0 ot 2 *bjv+qga5ijfvh(qa radius of curvature of 3.0 m for its objective mirrog 5j bqtjv20* 2orifavq+,h (ar 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 1.4ehb no+ao -+n)0 $cm$. 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 121.bzhg).p8; i5j(iokv ov j lm.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. y nrwaxe :s.n ,,u/fc/ryc)(y8-$cm$-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 locatedb 9vis7d8e-gm 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 2.7bc/rkc:o(y q+c5if oo3 q2e n80 $cm$, 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 haves/qzkrtz l0kahh)nm6 / u3 u+* foca k lk6/hau zs 3muhrz/*t0q)n+l 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 sphericalmtu4 a;p1z6 x4xf s5fd aberration in a particular situation. A planoconvex lens of index o6f;pfs4x 5zdxamt4u1f refraction 1.50 and radius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (deg pw9 itatv/1i-rees) set by diffraction for the 100-in. (25itp1a9t-v/iw 4-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a te73s cc)di, h*onq(3,acnv oznlescope 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 2-na 4*lxsnyv camera has a focal length of 50.0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years away are barely resolved byk:u3 46vq rgnk 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 eye0b djiblk.:/x 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 areub,tt s*f y8rk()hb1q. k3nth separated by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fallb jb,kd- h syo7+kdx+ (*1uthb on a crystal whose atoms, lying in planes, are spacsddb7buhky+ h*+- 1bk t,(joxed 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 at an unknown crysta q0guvwuk61w +l. The second diffraction maximum is recorded6wu+qg1 ukwv0 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 diffraction is observed agd6 lnk4ly0bj2 dzm+7dcs7 e4t $\mathrm{25.2°}$ 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 consists of paralgt 81ug;( esn :.j7cmstznvv;lel rays. What would be the magnification of the image? a the magnificat( 1;t g7 :mznuv8.n;gts vecjsion 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 thg : v.hhrn3m;gv:nn l2e sunlight got more intense, a photograp3n ;h:n 2 :nvvgmrhg.lher 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 infidv9;a e 3ls686ykds(:wt e k)sva7xdznity), the magnification of a camera lens ik;(6 s8d ew vletz3avx)dsa7dk69 y:ss proportional to its focal length.

  For a camera equipped with a 5gr rbmz )0toa6(,hu +k0-$mm$-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 he ,-o f8f.vmx,,qsymaqr 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 point of a.hoj fsbp,2ki4 c 5cx*di- n915 $cm$. 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 power of 4raf6oua;pd1zi c+ik xcv-t x/98znj t0q, ,h 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 ljj ftzyf+t e-;ev179o enses from9tj f; ejzyf-tv 7o+e1 his reading 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 usc14 gp9 ow,xv0irfmta ;yl 8u:es $+2.5-diopter$ 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 (2hbb +y2),1 y7jpjis pt5 $km$) 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(- r8aisrl r5 xe(9l *x(qvmik, exposure times must be increased av*m lrrq -ir( 5l(9xske (8ixbecause 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 spacedttv+(- dg cm6q 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of -bsjk c)wgk3;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 tw 3k bkjs-cg;)he Earth.    m

  Two converging lenses, one7uvhhz l, i+h/icr x+/ 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 uyy/-of3 y:nt28 $cm$ 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 numbe js( km+ymts6wo 7b()hw4 ln8krs. Assuming it is necessary to resolve points sepao+ksjmlkb)7nsm8y( h6tw 4(w rated 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 98mmudo-q t/w9k k* ncflat 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