Why is the depth of field greater, and the i qmt h,dwkgax8xo70 a8 86f1fumage sharper, when a camera lens is “stopped down” to a larger f-number?uhd886 ,t1a 0 ffkwox7 am8gxq Ignore diffraction.

Describe how diffraction affects the statement that r*xjrv3 :k.g);ittqo l: bkg,the depth of field is greater and the image sharper when a camera lens is “stopped downb iv3ktgxoj t;,: :r*lg.kq)r” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a closer on0qpck(n h-u l mw57 guejr()3bject3 ncrpju5mkq- (h e ug0ln)w(7?

Why are bifocals needed mainly m3uf).y kthn 2by older persons and not generally by younger peop.m n3fhu2t)yk le?

  Will a nearsighted person whom nd zqyw-g5b ok g5od2c;n)+p/8* bqf wears corrective lenses in her glasses be able to see clearly underwater when wearing those; o mkqo b-/)y *cw5gf+bdqdzgn p2n58 glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsigoa 70 w:)fssvtz:nn 5mhted or farsighted by looking at the width of the face through their glasses. If the persons:znonw sa0f m57 :)tv’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern dis60vytkdcvwvr 2w8 vqq6a -+a6tant details, people will sometimes squint. Why does this helpa2w6 c-k vv+tvw8y06qv da6r q?

Is the image formed on the retina of the human eye upright or inv6qwu(e 98e;g 7mzjfb eerted? Discuss the ijm;7 ze6gfqw ue9(e8bmplications of this for our perception of objects.

The human eye is much likenqz3*u ckys+u6s;c b 8 a camera — yet, when a camera shutter is left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly6u+k3c*sncb ; szuqy8 . Explain.

  Reading glasses use con) i n pido. ;gtik3+nei+qoa2-verging lenses. A simple magnifier is also a converging lens. Are reading glasses therefore mao aiki e +n+)g2q; -.niodtp3ignifiers? ----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 :ogirx*wb(4 0rz cep:)jfd v+iee7y 0 usually produce images that are colored at the edges. eebr0 +r f c0i)v wz4e(:yx7oijpg*d:Why?

Spherical aberration in a thin lens is minimized if rays are bent equa fb r1kx+ fyhg/nbne3l0:61hklly by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, whicb6f11xbn/l+rkh 0yn gke3fh:h surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are greatly redazmo1 +xc.t.jt d 6xo/uced) iot6jtz./ dom.c +a1xxn the human eye?

Explain why chromatic aberration occurs for thin lense1+gj qc 5iuw-as but not for mirrors.

  By what factor can you improve resolution, other things bou7 zr03 u(js-e l(vdzeing equal, if you use do r0us7uz((jz3le-v blue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mil:-;6 u+wiz hx)-x lf5t vyzfyrrors in astronomical telescop uxw x;zt-lh -yfzyiv+f):l65es.

Which color of visib44d5kz vvpx7k okv )cwy,jx;/le light would give the best resolution in a microscope? Explavz/kdxp;v5 v74c)j y 4 kokx,win.

  Atoms have diameters of anp4nfnnq m,url*)f)- (w0(gkyo )elz bout $10^{-8}\,$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 frox1etlte8o -7z + nvue(m $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a0i )u ;ckpwe(y 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter report c*v lrou7+:lper*4vps that a camera setting of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photograph is tak/ qnfwwmo951lhi bt 6y4dj, pj(05bxq en 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 k4uhbtnf8b7 + adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of obhk+t nf8 bu74bject 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 oj u*qp7f77r rs(d4 hief 58 m. What focal-length lens should be used if thqhfr7*s4rjiud7e 7p (e image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, usinrh*c8i -/zc rq( a4f0op gncxaw*2c;pg ray diagrams, how reasonably sharp 8o4*;rp-a/* 0n rhca igc(qcw2fxczp 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 exposur qq- txl/v 6* rgdhe6dff5cd+/e 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 abo8 -vx9ra4skd:o em* afut 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 lenses corrected for thq 1 wu0(otj3i(8sndy4*r f bzde fq(1dot f i0z3ys*b rd84nw ju(ar 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 poiu(qbj 7nr0/pcc / v 5s:ik13bqc ld ck;;jitn.nt 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 pointdq.f id36j i4m/ :hncp 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 at arm’s length, a distance o ; tiwqbp r/iod-d41w0f 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 6pfxx3if snmpcc ( h1(ls3p7 by78q v8is corrected by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly only if they are between45 cc r8mhxyr- 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 3d 1qr dkhbq7 )x;,xuoeye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsigheca/90j:ls3s eq4f by ted person’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 syc jo). 7 f77jjboj0jexstem 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 and far points of 10.0 au( n s4oj8e ;zkckh8r6nd 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens used with a relaxed eye if i8u vs + lk3(bha,xdzvyhk 6j1(ts focal length ishu+v 8z(6 xjklhvab k3, 1sd(y 12 $cm$? =    $\times$

  What is the focal length of a evn(v; lwv/+t magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated hf/k6 e kkscpe0 -.g2rat $2.5\times$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 usingwrm 7mf4c4a 0 c.8zjw7jy3gqb 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 viewen*5lk 3nsu* svd 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 bt sod(wau1 3q v(s,;q5.55 $cm$ 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 f7z l 5m,eymzb-(b(a tnyg3bs.ocal 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 rated 1x:q)c6 iebej 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 telescope whose objec:q h)y*est :hkx.: pa/8 bfvvve yxd3(tive lens has a focal lengfva ::yv 8e(q.e/:hdvbxkpyht *x )3sth 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 desired to bj:.s ,9rtq v*3 srqlbw-o8fsle 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 fgxcmk8m1yypz )c) q2/xyo.h -ocal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses space* r8kqzug8 ykxym( 89qd 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 adjuk n ,:tbx-4af:mgf2cjsted 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 reflecting6 gqvec 1+a8emui/8oj 2arz7m mirror whose radius of curvature is 6. u617a +2vr agem8izjm/ oqe8c0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears tvw1tqna 8lvwt3rpd l/ 3e/ xpykh9+2s 0.dl,xo 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 of 3.0 m for ui t:8rl+oxe3its objective mir 3x t+olue:ir8ror 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 )v(1*oq t7uj.ky jkayz4r ro7length 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 12.0u(a/,c68efy vd kx*gw $times$ 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-wo+fz 0m a7rf* *wpn7dgkc /j0$cm$-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 located 25 :/exx7.ypr vem s;oh:$cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscw0wdcq qzh(j+(t4 0g cope 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 thinr/v jq9;0 tl2mfrprt4 lenses, placed in contact, that have focal lf92trjr 04 rlmtv/qp;engths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular situation. A tc*x.ydd0p dr4f, q2fhb ,ue. planoconvex lens of index of refr f0*2xdf4p.,dru .beqy dc,htaction 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 l6,8bfq e5d.)kapk pkt imit (degrees) set by diffraction for the 100-in. (254-5. qp6 ,f)etk8 kdkpab$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve feajoe; 8 d 6mvhyxb05hlgcx912euc4 b5ftures 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 foc j ,6/zm;/lnu wb18r dp7mjspoal 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 rdgo-7bm qdtr cf 6;j49esolved 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 disvk9oprw6)6 9v5q pfcvtinguish 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 separatef/8hrv e3ft /)spe.w xd 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 0.13u1n;kq c(lt lm113osh-,apiei g;6 p h3 nm fall on a crystal whose atoms, lying in planes, are spaced 0.281hst,cl16en 3pi(hkaqo plgu1; ;im -0 $nm$ 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 crystclp0j,;vq+zk6k*t dj al. The second diffraction maximum is recorded when the X-rays are directed at an angle z, 6vdqjltpj*c;kk+0 of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffractiemv4rrfbq:r f.wm/n u,1*h 5uon is observed at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that the X-ray beam consists of para mngw(h*g/l1 g.n g;rbllel rays. What would be the magnification of the image? a the magnifi. 1ggnbng; /*(rmghlwcation 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 )mhzvq5-2 : ,yz5gc ife bs1 ugk-bx9bsunlight got more intense, a photographer noted that, y z15bx,uvsm-g9qe -c ikb)zhfb5:2gif 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 ve:mdw/gddn5 b :ry far away (assume infinity), the magnification of a camera lens is proportional5: /m:ddn wdgb to its focal length.

  For a camera equipped with taz9 igo8h9)b a 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when objects0 f2exdekf3zb49z 2vu 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 poi0.fhfh r+uik:o; ,ilf nt 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 magnifying power of ncyf3.fl u.6 q09*kwbft p4kwo1ri 5)acd - cla $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains trieei su5n uqm):xpxamnl93/b-k/i:6yss to make a telescope using the lenses from his reading glasses. They have power- x n9mq: /ibs3u6ukm s5a)ipnye/l: xs 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 5b hq1nksw)g-7zld - c$+2.5-diopter$ 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 high4 bn/wn k*d1ew ,4unax 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 must js(ek0obtlg8 cua18 4be increased because of the increased distance of the lens from the film for kt(0 841jesuboac 8lga 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 eyepieceka3fizdk pm(0 a p*.s5 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 Telescope, with an objective diameter of 2.4 pw3on *z6) 4(iobsrxk 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. Ass6( kx*sr)3n owb4zoipume the Hubble is near the Earth.    m

  Two converging lenses, one witip, p,1ny udn:h $f=4.0\mathrm{~cm}$ 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 : 6ojmbdv1n.h;pd* bmn+e ;vv s-s 1nw8.0. 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 p +,jmo f(: s spug4ysn;g5tss2hotograph license plate numbers. Assuming it 4t5pgn:+f g (2yssos, m;sjusis 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 (b-j hk(x3. )xb6j 6ffr2bzsjf Fig. Below) has 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