Why is the depth of fiel/p1bbh 4ycnniwe:(r5bqq7t ;d greater, and the image sharper, when a camera lens is “stopped down” to a l;(i7p ebb15qrw4 b/ntnq :cyh arger f-number? Ignore diffraction.

Describe how diffraction afj/r7:ms-b aim fects the statement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a laras7 bjmim -/:rger f-number.

Why must a camera lens be moved farther from the film to focus oo pesh; ii+z1)pq1d)rn a closer objecth p1i;1p+)qz soe)idr ?

Why are bifocals needed mainly by older persons and not hz82e yp- xq.f/2qk dygenerally by younger people?dqqe8 /yz2f.hxk p y-2

  Will a nearsighted person w6i3gi8xq hx:vho wears corrective lenses in her glasses be able to see clearly underwater when wearih: xgv8iq3i6x ng those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearp: yk 0-:pslqhyyk2 z ey7m+)zsighted or farsighted by looking at the width of the fapk-yzq m :27yph +k0y szley):ce through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squint. Why doeel yqcqjl rj)o76g9i b20q*34wniv. bs this heq*ve.92gi jl4 0rqi3 q7 6b co)lbynjwlp?

Is the image formed on the retina of the human eye upright or inverted?wrl5mo7yb k.5g)n 4 gj Discuss the implications of this for our perb5o7rgm5 gnl.j k w)4yception of objects.

The human eye is much like a camera — yet, when a camera shutter iloa.ui 3jo o;6s left open and the camera is moved, the image will be blurred; but j 63olio.; aouwhen you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converg 08r7(c9oiyvhkf p 2gcing lenses. A simple magnifier is also a converging lens. Are(goik vf92hcpcr 8y07 reading glasses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscoposufy/op)5*aw-i g 3 jes for children’s use usually produce images that are colored at the edo *o- )yjuf 3/igspa5wges. Why?

Spherical aberration in a thin lens is minimized if rays a+ z ) d;mejr3 (6h-ndkijm*dnore bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which sur3e+io-hdrk)j6z ; *d nmj (nmdface should face the object? Use ray diagrams to show why.

Which aberrations presen7ov i,-9+. iqpip(y-n4v w oxlkp+cgnt in a simple lens are not present (or are greatly reducedn47-g-nvi.+wol9p,iq +p ic xp (oyvk) in the human eye?

Explain why chromatic aberration occurs fr h+(6sqgm2dqye7it+ au,o0ior thin lenses but not for mirrors.

  By what factor can you improve resolution, other things being equal, if you usjurj n)(ke) 2(ayo-vbv/js6 le blu) 6)- n(ejlj2yas uob(r/vjvk e light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirroujwk;,g:afy+kxx p;(b4 r d2urs in astronomxgx(u,+4p;rkdf;:a u b2k yjwical telescopes.

Which color of visible lig+/hzoei:w9mclvwu 2 o:tq 3 ;q*q9chm9epi)n ht would give the best resolution in a microscope? Expl pmq ei oucqwq99;2l:v:zce)o miht n w+h9*3/ain.

  Atoms have diameters :w7wbg26q pl+suthn1b0 uet / 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-stops ranging f63oaft, k y t)7da5wtyrom $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens ):a ltndr, 3ephas a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a8 v.wc y1y )e -de qxd4 f6nwpxeiky:w.j8zf(: 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 8gho)zks 5;riis 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 200.0 mm to 206.0 m gr yvx6v.,wg.s 6an3exz4428efffy mm frv n y fer4ms2a4x6ggf3we zx,v6f8y.. om the film. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree froe1 t)s)/(yav9)fa)xi kyxxd x m a distance of 58 m. What focal-length len tk/i))x)xaxyxs)f(v1dy9ea s should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny .y -i3b s2u0-nd iwx xe ks+jz9o,mi,ypinhole instead of a lens. Show, using ray diagrams,xuyk 9m-+e-.bdnw 3 2jzi0os,,isy ix how reasonably 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 exposure ivwt5h q9ns)fg fph2whahb ja u,+9,:2s $\frac{1}{250}\,s$ 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 s3i736 ebai-/irnafz ; ;wnah2.0 $cm$ 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–ggqwou :p/1+.5o;vd7y - dwt+rs)5vv d husxy6 wore contact lenses corrected for the far +pq gsd ur;v7dx5odsw-vyvg 1y. :)t +uow h/5point $(=\,\infty)$ 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 fel:b2(0c x cmp ivk jdx2x8far(+9tk.or 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 qzcv)ttslie3 :+g e n2qt:6n,:w4bsy 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 distancajp j:g /cvwu+-r53w ke 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 c-j, j th.sz;q ajjg0)dq+gm +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 sesv+p5cu- sz 4ne 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 q4/2g yarv;uhthe nearsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s ey6jhks 2esqrz*co4hk 4o, my2 7eglasses 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 sfrqrzqqb*4 vn ,7-( esystem 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 sk elql)2 m3e.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 9eix 2; 9/bgxrous+93c r8im ee)colp of a lens used with a relaxed eye if its focal length 9+xseb; c3 92rir pgmie9coeu/8) l xois 12 $cm$? =    $\times$

  What is the focal length of x gy4ipx;)y1q a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated : iq n88+a9ob yjo.os qxjo6pci*dx,-at $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is usingd.* a nbf24r8 gd.hnfp 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). 5u*xsssm 0n(dj4dpf .ds tx 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 plaa2b lan 6zq 15nqxl5c m135ayoced 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 :mqvsfef* 1+r5r;v gp $cm$ 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 rl( p-7/ m/f myn.u:ehupkam9o ated 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 sr( fhx u(x)v,k fput:;t8c l:of an astronomical telescope whose objective lens has a focal lext:cpfsf( );rvxu(,:u8l khtngth 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 e75k,hs 4q-arkn g io/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 fbcqv 43x8u81tn3p ng:s;u ox $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope hasqu 484 4;v3yomtzt wv*9q tn*jkmirxg(h)di + its 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 adjusted forrfs uqrre m641yx2 :7m 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 pow1s t;24rnzmower of an astronomical telescope using a reflecting mirror whose rw nm zr142t;osadius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears t3*pp wp x)kj8to 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 -hf:6)lhb fol(Fig. Below) has a radius of curvature of 3.0 m for its objecti lfb h-f)ohl6:ve 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 focahv7tx/ qj6ibzq:6 1+rm s0i9ms2 jcqyl 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 12z15d i(bh (m4c-xlyk ;aki+gk .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 1.8-zmo/a: icygwp97 u; s:7g3ga8vcdl k2$cm$-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 thsi-ssqx1d.vc v x*: 9 zo9oeb5e 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 +viljy ; :.0 bthl4tnj2.70 $cm$, 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 inn.gheu06j r1em (up* s made of two very thin lenses, placed in contact, that have f.guumne h nj10r(e6*pocal 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 aberrhfwcni 34 t: :y5jk0f+ggb + okwg1fx6ation in a particular situation. A planoconvex lens of index of refrac0yf5 xj6wtkfn4 1k:g+bf+ gc3hoig:wtion 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 (degrees) set by diffraction for the 100-incyv)ivn mv:b;1 ev, r.3rm.g x. (25r v:cmber)v1v;g i,..m vyxn34-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope thag5/d9/8trl m 1zcxfont 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 camergwe) esov7b+ 2a 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 0,yos8t1 yi ,. igorbpare barely resolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye distinguish two car headlights o 6g0cgdui x-82.0 $m$ 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 separateq :ib -mxot03zzktqyi +.52lid 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 v4,u fd/pm9ik0.133 nm fall on a crystal whose atoms, lying in planes, ar vfd,p4u i9/kme spaced 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength 0.0973 nm are dip 2.ps*udh usyoe:/i0x7sn0a rected at an unknown crystal. The second diffraction maximum is recorded x:u0uh/y27spn do ape. 0*isswhen 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 diffraci talc750n jvd+ xwtf( t jqg/8k71bv*tion 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 thj)5 nwxln04vg e X-ray beam consists of parall jgn5nlw0v)x 4el rays. What would be the magnification 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 toward midday, and tbn2culd 3 2o9xhe sunlight got more intense, a photographer note3o 9 lcxdb22nud 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 ver+.s3dhmze 2hp4k2-dosb 1 dx/* urimey far away (assume infinity), the magnification of a camera lens is proportional to4ou-p ds . e* 2bezxd/hds12im+hkmr 3 its focal length.

  For a camera equipped wi 7bit1 ji-t(7rbhg3o. uy9er tth 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 objects are between .air-wmr xtisraoy e:13 5;m3 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 a 3yz4w ky4:bql9b( f1h qcq9fof 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 magnifyie8cd (2gthri)- f(pi - p+ljnang 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 mn3 shzh3ivezxn .e)81 )+xfhk ake a telescope using the lenses from his reading g)1 xf38vi.3 ) ne zhnh+hezksxlasses. 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 uses5jvu).o bh6ul $+2.5-diopter$ 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 hiv, n7; b+b f0 mx-yt6uca2ousdgh 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 sho1, zy9lnq/ py4xum2 rirt distances, exposure times must be increased because of the increased distance of the lens 4 1pqy9/zniyu, m xlr2from 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 eyepip7a)- a+)twpux(l ukz ebip h*r )2ea8ece 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 d+o++s dxaa d7riameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objerd7oxsd a +a++cts 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 lense yjn1;lxyl s7.36zlokc(*j 5xubcu h5m*aqt,s, one with $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magniff7* .0ll)b 8z lkxvy j-ov-yb(xkyp b7ication 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 num rzk(fra3 ;r74+rq fqhbers. Assuming it is necessary to resolve poikr+4rqfa qr 7h;r(f 3znts separated by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below) has one flat surface and the other has8s1) p whc4fsj $R=18.4\mathrm{~cm}.$ 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