Why is the depth of field greag )u9ob q)l/vcter, and the image sharper, when a camera lens is “stopped down” to a larger g/)lcuv q)9b of-number? Ignore diffraction.

Describe how diffraction affects t +0pkb4n6e5ht zqout+ he statement that the depth of field is greater and the image sharper when a camera lens is “stopped down n0+eu zhb4pkq+65tot ” to a larger f-number.

Why must a camera lens be movq;yvb;d3ixk /a /wa a3ed farther from the film to focus on a closer objectw;3va qdixyk/ b3 /a;a?

Why are bifocals needed mainly by older persons and not generally by youngeuxh oo .hpsni/z ;:1i4r peopln:o.ozi s4 p hi;xhu1/e?

  Will a nearsighted pern ntljp 5d4(7gson who wears corrective lenses in her glasses be able to see clearly underwater when wearing thos75tgd n4ljp (ne glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or farsighted by looking at the wcx 3p64 a ea+qnz+at( y4rift3idth of the qn+yp4 ra+a6ft a343c xtzie(face 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 dp0cw3 r cn8c bkud*h50istant details, people will sometimes squint. Why does this hel3 *c0w rc0ucd58 phnkbp?

Is the image formed on the retina of the human eye upright or invergk. 4ayo3 2cob(vfiwb37ibt) ted? Discuss the impli3gv otic2wai7bb. )o fkb(y43cations of this for our perception of objects.

The human eye is much like 3qt7h0cb6 ahua 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 0hb7q6u aht3 ceyes open, you still see clearly. Explain.

  Reading glasses use converging lensm7qq u gxnl7 h3 39jx;1s;udetes. A simple magnifier is also a converging lens. Are reading glasses tntsgex7d 3;mlqq; 37u1uxj 9hherefore 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 use usually produce images that a;:p9 kb1 wkwmoylv2(sre coloredk(b ol ykw1p9sm v2:w; at the edges. Why?

Spherical aberration in 4u;.jg c:l2kgytql v)/2hqxni; ex.w a thin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of 2glvl;/jt ):q ;.2xq4cix.n w hku geyan object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are greatly res 1j1mysowds, di kj7hkzb29),u)sv -duced) i) )s7,jb1 m zyhsk sod12wku- svjd9i,n the human eye?

Explain why chromatic aberration occuu, v:l znef6*)qkvj* s*wyo* brs for thin lenses but not for mirrors.

  By what factor can you improve resoluttvflcg;l yz k+5py ,n)+)e6f;q)x3 z -dopgfqion, other things being equal, if you use blue )pqyke)o zx)c;f tyl +5pdgn 3f;6 -qfgz,vl+light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use off0 u33j h.v kbo.qc(y; /nqpiq large reflecting mirrors in astronomical telescop 3uy ohnq. ;qfp.3/vk(0q ijcbes.

Which color of visible light would give the best resolution y8rj:53iwgo 1v ytew-,b0arfleh-7t in a microscope? Explaibr jt0l5aig wh-7r,8 w yet1eo-fv 3y:n.

  Atoms have diameterszol-5 ai go+7 vuf9r q,m-z(re 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-sy)j bx x.d79 lh4glt-otops ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a 1 uz;:lp(lnr*ikrb 4 3h4-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera setting 8.dymny+o unnjr+d 00fu.yy.:+bbof 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 photog7oyx6r h+ qn.zraph 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 se g*0.lgoa cd8xaj(q)o that it is 200.0 mm to 206.0 mm from the fi(dg.e)j0ag l xao8c* qlm. 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 from a distance of 5h;7n8gek,j/w ayh7ga 8 hjh; a7gyg e 8,7wn/kam. What focal-length lens 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 of a lens. Sho5(h*q4p 1 xtqpjn ve/d75 qcvtw, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two(v5 p5/e7hvcx4qqtjn1 pq*td 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 expyr 7+uva)h (ccosure 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 about8fa ;(ep )nwjn 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 pern);0.lrgsreq m 1ck)zho3*1z;yycw h son in Example 25–6 wore contact lenses corrected for the far po*s oh3;l0zcy qy k w)1zr .1mr;nge)hcint $(=\,\infty)$ 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 are0odgdn nb 7,n6 needed for 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 pgi4t e2 )c ej*e,:w4 zvld(xzooint 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 ;wecm zo( yd5*( y2dinlength, a distance of 45 $cm$ away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 $cm$ from the eye and he wants to read at the normal near point of 25 $cm$? +    D

  A person’s left eye is corrected byd)w9+ws nkgl5 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 clea;sgwv;s+3 ddvr lr :c24;leyalf0s a0o *foi- rly 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 th, ; stccj46acbe nearsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted persow(3m.9 s yucoln’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–lens06vk3 dfr 3j sm/lh-aj system 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 and 2gl 2b 1x.x / 6kf wbu0nyye*gcu6x3k+x0.0 $cm$, 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 its focag2d-yj (pqgg hdj)nse4eqi(+ g9f(u)l length is q(+gisqy(e g4-d)jh nje) gd2 uf9gp( 12 $cm$? =    $\times$

  What is the focal le2 +b-vyvi 8tg,tmv 8xbngth of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated axctk, 0 mqkx*,ptpx w,7 tg4r)t $2.5\times$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 2cix-;aofp efi 34/vo 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 vf 0kk;tz,cb5is 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 placed 5.5cej s ny 6ssk) +qa)sl4k-c.r;ei39w x5 $cm$ 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 fo82 )rnlu; cbf tik:sf4cal 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,+wz47 6purlpaoy5pl nu*nw7 )cl ejijl: g2* rated 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 oblog1k gduyn. c wkg 256t28+fcjective lens has a focal len+cg gu6kg5. ywtck 1 2nd8l2ofgth 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 oytb6qeb* xe)e *56pl if an astronomical telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

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

  An astronomical telescope has an od p/:sy *nub22 gcurm3jv30e abjective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spavze nh.w17 k+6 wxzzc h2b3(y;m h1niaced 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 for a relaxed eye isy5-1 mtdh cjz0 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 usingqonb ff80px)lzw)f b83d e *xs/a v.u:j)c)of a reflecting mirror whose radsb0.ofzpu ))x)8*ndb )8a3 /v:wjo qlxfff c eius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearsp s rtac:ex.), 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 cur 3 szd ic-,9.xabo2omkvature of 3.0 m for its objective mio9,k2xbz.ic-o dm3 asrror 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 eye l)keaa: smt hx*67u.vpiece with a focal 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.ep1bl cz 6ty7;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 1lu5g;tf o rp e(,d.1yf.8-$cm$-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 tnpt xzl-*6e6 j jrb(oqla5- jes,u)m4hat the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal le 0nu3 4+nbcy2d/ g*icge i8ekjngth 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 ob1 ke/ x1-blwif two very thin lenses, placed in contact, that have focal lengk- xi1bw/l e1bths 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 vbl* q2c*wg.p isxd8mqin8:/ aberration in a particular situation. A planoconvex lens of index of refraction 1.50 and raddwlbpi 2:8.*/ nv8s xmgq*cq iius 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 difframb5zjo )v0zdpt,9wr0 ction for the 100-in. 0j z0)zp9mbotr5wv d, (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct )lxkr 6wd s(m5/58(r hminzrja telescope 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 camera has a focal length of4k 2b6o 9fe 5fpevlj7r 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 a n e p 0do.u.buuwj7 zb446j0h5glulz0way are 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 humaf xye(4:j lay7g k/yi(n eye 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 are sj)kyg jmp29 q0 o)m+0 yjgscn3eparated by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crystal whose atomsf-a.yt 2 i57uowxdsq), lying in planes, are spaced 0.2802. s5- qxa) i7twfoudy $nm$ 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 crystal. Then ci;5 9utj-ch second diffraction maximum is recorded when the X-rays are directed j c nc5uh9ti;-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 op( s2 ozwiwh0 3he*bs3bserved 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 consist cx sgub6- 3dxp5.34ry+mkd-f:m dgeas of parallel rays. What wdm-dx p+d :uf6m-a.sg x k4gc5y33breould 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 the sunlight got more intense, a phozr:yo5p c31:tjpd m ri7f56y*i 9xjbotographer noted that, if she keprjtfy6 1p i95jy3:o:obmxpd z* r 57cit 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 infinity), the magnifqivp7 l9 5ql2iication of a camerai2 i5qlvp7q9l lens is proportional to its focal length.

  For a camera equipped with :cs uvk;u,mv sh0w4ex 8u. zk7a 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 onw,*echgv 5-s-uhev)lly 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 poi9j3tt muqy3 b:6o5s trnt 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 poocnpax ce8-a9.n7bk*w)6nu cwer of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a tewrtr+aa ge xt(7 dxtlk-5 /f29lescope using the lenses from his reading glasses. They havefa 9akx(r5 -d+e7wt rtx2tl g/ 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 use5y9yns xa 71vj,bd )hds $+2.5-diopter$ 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 altitue/awzxd869 h wdes (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 be i i/+ed it/xyyc9 f7(vyncreased because of the increased distance of the lens fromvfiy /7/i(txyy +9e dc 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 aad1ccuz. o u g7mxf1 )1w6qxh1re spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescop5 s28+ivo nvt 8dl2ot28 ragbhe, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that tht288vn2vh582 baots +dr oi gle Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one ww fx(fsyuysmpp3xhz (,0s29 9ith $f=4.0\mathrm{~cm}$ 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 x3me5okl .or: 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 lic2 b,wb0+w c+x sbdh)ycense plate numbers. Assuming it is 0, xbw+sc)bcydwb h+ 2necessary 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 surw khr )qr(3n:pface 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