Why is the depth of field greater, and the image sharper,79dsv2-)rxk yi).o(hlwmu 2dgg rl-b ffy j;4 when a camera lens is “stopped m) xolr- 9sydid2jr(vy.h2wgb-fufl ) k;74 gdown” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of fienytn*- i(u9pz ld is greater and the image sharper when a camera lens is “stopped down” to a larger f-numberzun-yptn*9( i.

Why must a camera lens be moved fe:qx-jwhff 3j*o 40,8ghoqz iarther from the film to focus on a closer objec *8hj0g,:if3fj4eq x-ohow qz t?

Why are bifocals needed 7 z)2gdt 5+lhupyanx6mainly by older persons and not generally by younger peoput+ygd h76lp x52z) nale?

  Will a nearsighted person who wears corrective lenses in her glasses h26kd 6() dr: dih)rixyc3f qwl7+u ctbe able to see clearly tc63d+qkrriu) cf :2( xh6lwd) yh7 diunderwater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person yx+:9h,unbe r7k;p- ryu;b zbis nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig,b-z upr e7nxkruy yh+ ;9b:b;. Below), is the person farsighted or nearsighted?

In attempting to discern di )0q l oqxo8e8ru9 mbn9t7ispo v78xk,stant details, people will sometimes squint. Why does thb089r p)v s uoq,oxkxli8n7 7 om98qteis help?

Is the image formed on the retina o3l)/t9f5p 9 1siwt krae)drxwf the human eye upright or inverted? Discuss the implications ori/tk) d1l 9aefswr px)59 wt3f this for our perception of objects.

The human eye is much like a camera — yet, when a camera shutterg;xqqxb6u+ )jsbzd3, is left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you s j,+bbqux)x3;d zs 6qgtill see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a converging d4 by e( s5bzo-i4x0;nz rh2xglens. Are reading glasses therefore ma(nx 42 es;rz4o hgx5dbi-0z bygnifiers? ----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 imagel7hhn,z x imdh;k a u*jw.(-9es that are colored at the edgei,h(*j9auk h mw -l ;xzh7de.ns. Why?

Spherical aberration in a thin lens is minimized if rays are bent equallyx9wm;rb db)7f by the two surfaces. If a planoconvex lens is used to form a rwrx ;f 7db9)bmeal image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a -kvmnfjf*1luw9uh(a. /tooh fy*4 6usimple lens are not present (or are greatly reduced) in the humu4lofv- 9tufwo(y k1j mf*hn/*h.6 auan eye?

Explain why chromatia.yb ihkv31-q6j +2 fxnlsah/ c aberration occurs for thin lenses but not for mirrors.

  By what factor can you improve resolutionlz1 c2 -s4)edpy:s xkj, other things being equal, if you use b ksesp :xl2d1zyc-4j)lue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflectins-1q4uiu ek6 qg mirrors in astronomical telesco6sek-q1 ui4u qpes.

Which color of visible light would give the best resolutiol/mjvccu d(-u*3 zn.cn in a microscope? Explaincc/z-umu( dlj* 3v. cn.

  Atoms have diameters of .-v 5.8;cfnohxqtdq v 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 rangi5l,luxo2s/kqop:e-zl ppw5 x 0pc o. ;ng 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 (tobi6xi jmv*1qpl ,sc;t 0;alens has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports b,;+yvdg glxk8lvoh52- i+/wdma y s8that 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 phot5ie .v(r *t mx)d7m2avozgk g3(sgy)oograph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

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

  A 200-mm-focal-length lens can be adjusted so that it is 200. 2k srk3tz)ii-my6yfoi77zo (b. p xx30 mm to 206.0 mm from the film. For what range of object distances (rkskz 2p 7t-ixfbmy7i3zy6 oiox).3can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to pho/1 rdvkko/ku2tograph a 28-mtall tree from a distance of 58 m. What focal-length lensk do/u /k1vkr2 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 6*y7fzjxxq s xe7/ft8, c:m-.zthmy 7z,gja qof a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole ca-*xt.:/a8 gxysmqmq fx, jy,z7h7cze67j zt fmera. 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 is y* dg mlzi jg(/ n-7,ej0hk.61bijltq $\frac{1}{250}\,s$ 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 a slm6crck/,098 nl fxhbout 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 peu+cely n5,ra- rson in Example 25–6 wore contact lenses corrected for the far pointc l5-ua+ enr,y $(=\,\infty)$ 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 pointe -bp( hx gq kmav,k:5pt0w ro8o5z(9z 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 po8p tlwt2jvf3n; m62buf 2grt8int of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holding a book a;(xm y 2/tvzjnlg 8o/jt 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 x oyc;.a+6nh ycorrected 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 betwt2y/sx2yx 7ndxsvwbt yap 9n//u3 )6ueen 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 7vt ms4tzl4y,than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted perso.+ku-jge02o*auu x upn’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 obje0h:+mv 7 pl50- sxxgufd4hdzfct
(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 and 4j +wv* n -lfhtd5mc2q20.0 $cm$, 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 a7g6hv r 4: i q+umjgly:x;s/wm lens used with a relaxed eye if its focal length wu;6::s/hmgyrv7x g+iq 4 mljis 12 $cm$? =    $\times$

  What is the focal length ee -jzk *gf5 rwnjtc)r-uu3u 8/ri1z6of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated : vj l97dmyn8lat $2.5\times$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 9.0f7vi3 fd1b.l e0-$cm$-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 beetlen ug 2o(wlh4 s64o3kyzborg3, is viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placedir:a)y d74xu(n *ixta 5.55 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass with a focal length of 8.5 -k6hi z) xqnh,rr3 r.g$cm$ 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 ratedb ntfu-y2 2)pbm v2gk+ v6w;ll 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 astronomica-j3hj ym eov8u34 f3zql telescope whose objective lens has a focal length vmq-4zyj3uhj83 o ef 3of 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 telesc .. yg8iyv9c7 0dl8djqr9 0sr pqlr7xcope 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 with focal length 85 p +f3hy qyzed/sp85q( $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lejxlp hn.j w8 5o,qxs94nses 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 telescopea+s. q59z lqiz adjusted 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 astronomicxfajboq( - +/xchyb ph0pk7 1(al telescope using a reflecting mirror whose radius of cupxc/1(f+b a(ohk-xp hqjb7y 0rvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearsts buktr8vbxf(3o2 ok8.9rk n n)1u rc89,bpp 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) has a radius of curvature c*m;mck :p438 knwrqfto7m7dof 3.0 m for its objective mirror and a radius ofccr3wm; no47kk :8mt* 7qdpmf 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 focaltj1;bm i .kopx07p j.u 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 12.710 ck/rfpth)a bs;(j zj:buc0$times$ 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 1.8-l3yyehd7go/fr fo/1 5nt gp-q(t l8; s$cm$-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 locateduy:w3i1fi f(c q1yq2d 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 2.70 (gly2( 3tcaf 5sag9dyz* hnzpl4-c.k $cm$, 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, t v7z-iw z5kza)ub ;/ljhat have focal lengthzv /)kub jzaizw;7l-5 s 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 s.z-chq f ,bprjj*w 9kup) ahq77n t09planoconvex lens of index k hqnjpq )9c7 h7wps,uf tr.9-*az0jbof 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 l.4:epnh v3x auimit (degrees) set by diffraction for the 100-in. p3u: avh4xe.n (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope th*nr 4-0r0lp lerb0d hbq7cw:gat 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 h,cu6fg;u exl1 dcrd(5)p/ma w as 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 q lca7p 8fq:2pucd: sl-u5l/zby 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 distin )j23jgek yrl:guish two car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are sepa5:tvcs vh:r2d+,ly ygrated 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 oafj nl ik76e*,n a crystal whose atoms, lying in planes, are spacedn ji ,fa7le6k* 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 crystar6ybeqy.z c4 z,bg:l. l. The second diffraction maxb y.6g,crlqe4z:.zybimum is 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 diffrb z h,*cca2tvzw4g 7n.action 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 conventionao7d1mizgfs3 8t .;n izl X-ray image that the X-ray beam consists of parallel rays. What would be the magnizmniiz 3 s.g o718df;tfication 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 passed towars;d zz jx9.q 1kd)ty)ud midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she hdx1z z)j; y u9).dsqtkad 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 awa v3py/nlka*vufq3t6*yt :0v fy (assume infinity), the magnification of a camera lens is proportionak n/uytv*qta03p *f :lv6yf3vl to its focal length.

  For a camera equipped with a2;wtz a : bnuh7tsgx5uvb)8yv5 lm)z8 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when objects o74dzcx +ds5agl /) vxte)is: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 1xpih opdov04ma6b 9 115 $cm$. 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 ghu9t dnv//5j6 gfk.x of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains trie 8jx, 6k)uq6gjh bec(8nh plj0f8ai l-s to make a telescope using the lenses from his reading glasses. Tgp80xjhu8e jhq(l6n ib6k ,)cj- fla8hey 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 uses x 9sgop6-i) sjp w*ert/ 6mls;$+2.5-diopter$ 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 extrzeh.(,wo ;bm lemely high altitudes (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short distances, exposure times mu,btt n*t;f +xrst be increased because of the increased distance of the lens from the film for fxt;bt *rt +n,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 je .md( w3v:ydof a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective ,7; 4kfam fe,j batoz fe/8,yrdiameter 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 waf7rfof,at,e;j az m ek4/,by 8velength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one with r g6na3u9 ;.uuv8mt;lcuv5rm $f=4.0\mathrm{~cm}$ 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 magnification120dj9smj;6( x j( u fsgunotk 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 plate numbers. Aqjasrhdl 9381ssuming it is necess 9jd3hqr l8as1ary 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) has one flat surfactrhd- )m /.zrse 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