Why is the depth of field greater, and the image8 t3rrm sit/a( sharper, when a camera lens is “stopped down” to a larger f-number? Ig(s tit3a8m r/rnore diffraction.

Describe how diffraction affects th;j ,v)rhx ki)le statement that the depth of field is greater vlkxhr);i, )jand the image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focum u,chzo:+g q.s on a closer objectoh:qz,ugc .m+?

Why are bifocals needed mainly by older persons and noc1.ltrt+n 7gk- l/8cnucy8m ft generally by younger peoplul8-l8+n frg.ccyct /k7ntm1 e?

  Will a nearsighted person who wears corrective pst o n-se *jp-ae.;3omye8;sw+t9k f lenses in her glasses be able to see clearly underwater when we3ns;pkw*o mjtp+e8 toe9y-s-f. as ;e aring those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person iso*va( qc*o:0qzf w5oo nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower thro*z5oo w 0f(aq:qc*voough the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squi4 b1iqe jqyh1*nt. Why does this hqh1 *j41iyqebelp?

Is the image formed on the retina of the human eye upright or inverted? Disczt+x .eu22g oox2q:wn*s ggw+uss the implications of this for ourqo2og+x. eg+n*z s2wuw:2gxt perception of objects.

The human eye is much like a camera — yet, when a camera shdpztb+hr jf-f 4s+x/rfz.a3 w *n6zi)utter is left open and the camera is moved, the image will be blurred; but when you move your head withta+b6*fj+r. iff n4 ws)zd /p-xzhrz3 your eyes open, you still see clearly. Explain.

  Reading glasses use ) f6ispt2 yi0 a) xjyl:wqeu28converging lenses. A simple magnifier is also a converging lens. Are reading glasses theraw:sf ty e08l2 )ij2)p iyuq6xefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for chd) b+ :kqyry0tildren’s use usually produce images that are colored at the edges. 0qrtkd yy)+b: Why?

Spherical aberration in a thin lens is minimized if rays are bent equa 3d1uqp*kc3x ally by the two surfadqp 3x3k *1cauces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens vf1 l1ckyfizx8a3 cxn42 tp 6;are not present (or are greatly reduced) in the human epcx4nla xv tk1fz;3f1ci y 286ye?

Explain why chromatic aberration occurs for thin lenses but notq) qn7 q p-bba0ph.p8t for mirrors.

  By what factor can you improve resolution, other things being ek .c5i tnejd;;qual, if you use blue leijn ;tckd5 ;.ight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrolalvq yd*0toawi 7 xx ;*9yjl(x.:r f*rs in astronomical telesc:ai*y7xl .*lrwoxtf(vj 0q *xda9 ;lyopes.

Which color of visible light would give the best resolution in a 11cpd*vrmgp,microscope? Explai,c1g*vd mpp1r n.

  Atoms have diameters of abouf7e j- 0h1gim0xo6lzut $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length vr**++ji )in +jjuqhxuf(e 5r78b lawlens has f-stops 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 hask 8 zc/r,2kc0ftw tt7( wa1vdp a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera setting of r:) 8i tcm*gvgf+q- as$\frac{1}{250}\,s$ 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 taken at xjekous,6 9q0.l7rv a$f/16$ 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 cazp:54mxq:,r fmrh-bua hyf)2n be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range h-) p2qmy5h4z,rf:fbu rmx a: of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer bh6wuk v6g :g2rjgu.o7 (h + :rwg4jsr o)-ivdwishes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the imavr7vw(h 6gs2:oo)k jdbi w.:gu-+ r4g6hjru gge is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a :y6 r a,am lbteb-ypu1)u8d5i tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed usint- m5a6bidlr1 byeu, )y8a p:ug 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 exp4 q5vlb)voc( qkbf-.v osure 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 about 2g:viz oft)u6 *v6sv)d .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 cor.ker b og sfdipt3(,d 42yb7*ryqs0 g3rected for the far pointdsq igp7y(0, db4*tr yb3or. 32kgse f $(=\,\infty)$ 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 poin ( +h;ibhk.x+ggh-( pmulrs 1ht 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 poie osf 0ze3f..3 ip2lvont 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 eq-e,- qq5o f vdjp((bof 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 b j2w;gl vcteyl2 *d/g;y 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 canonbg2je4kb8)s xlkdorv t0( 8 h z(i-+ see 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 the nearszz-j.wfx- it p6/bbs*ighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted u /xaiu9axj 7j6-uhm 6person’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 eye95hdsz6t2 os c–lens 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 andc.n ;;uwvrkz)j* /t*lyqwk g nf2:vi / 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 of a lens used with a relaxoj1gr ajwf61tmd )w 4.. 2txawed eye if its focal length is 12 ).xj2.w wawdg64m 1f orjta1t $cm$? =    $\times$

  What is the focal length of a mas/q2 ygmf1 c 4tohp8j*gnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedra,f.s4u8dz kyymtf8/9n0yw*3j - bdr qp r3t 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 us j0 wcbz7(8gdaing 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 viewed with a bou8 :zvralab0o(d;w:g4 .nz9.50-$cm$-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 placedrtu/; r8ycn-wei w 9)v 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 f uu--cqbtlm1/(y;59mer b qr nocal 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 iwhy cx5n nmm5x*b-p5a4 /*pjat $3.0\times$ 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 astronomivlpq m),d0ro qa(8, 2ukd7ku jcal telescope whose objective lens has a focal lengtoqq,2uda)j p0uvd(k 7 l8mkr,h 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 astronomi w 2:b0l)mo,+ mcmzstical 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 telesco lh 6tx/fxtb12 7 z+dh p2jcu*e(oqq)kpe has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope 3klz1 .a8tnu l,r)pa5u vo,wihas 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 for a p*cn;xnq sg*, 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 magnifyi -f -jl*3(y90ffui k sa*vmckzng power of an astronomical telescope using a reflecting mirror whose radius ofci-jy0u kff3m fl*v sak(-z *9 curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnig 9.ck(rjk5dz fied 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 3nrzafat ivygb6 ss20:an,e 25 zu )i58.0 m for its objective mirror and a radius of curvature ov 5 a 0r 86z2)bgsy nz:,iatisnaeuf52f $-1.50m$ 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 eyep+vx0u q+a: e;-+ e,kwlauvxpiq c;e;piece 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. ;p n )e7ah1waceivrd,q9 e 3g,icn eax-c;9/s0$times$ 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 1.8l kxej)cto1m k7(f +6p-$cm$-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 fuhmpv2 q -8cw a6-f,voinal 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 foca* qg/qr0(vtccn qj+7:q0s qaml 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 thin lenses, placed in consp:b f/(2d xrwtact, that have focal l:s w2fb/xdr(p 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 planoconvex 0qyydr4+hbycq9 spt * 6 nm69rlens of index of refraction 1.50 and radius of cdsy *4p0r69yqn htc b+qyr96murvature $R=12.0\mathrm{~$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 tht- a0:zkfd) sp1r q2moe 100-in. oqsp a-tfrm02k1 d)z: (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that pl, (my81p 4 ov9cjdkw:. ltuocan 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 lern(z-ux3cgk 6 ngth 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 vdhj. /7 lqi-zn 5mzq5are 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 b*, tsod/.a ftlxdd0 4/lko+ptwo 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 separat gcwu2,wyj5) ;arhakomcx 733ed 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(flxj1*,b7tba bz /mi atoms, lying in planes, arez*7(xm/b1 bfbj la, ti 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 directed at a hb93fa18l;qjtiwjuf h ;im67 n unknown crystal. The second diffrafi ih1wj 96qm;jlfh38u ;tb7 action maximum 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 di c)gthbu5s9;s ffraction 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 con995a, j6kejcurc+mg uventional X-ray image that the X-ray beam consists of parallel rays. What would be the magnification of the ic uc9m jaruk9 +jg65,emage? 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 mlj,lnn6n d*g a1lax5.fa4iri7o ;a,/-p gzfbore intense, a photographer noted that, if she kept her shutter speed constant, she ,p bjl7la/fnr,n;aglx.dof4a ai5 n6z 1gi*-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 ss/; mtm0s4ve (assume infinity), the magnification of a camera lens is propor ts4;svm0m/es tional to its focal length.

  For a camera equipped with a ,l)dqoc834 kcu mofbjc6 )cn6 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 heshib2jp x5 lc70msc *p-/vgk-r right eye only when objects are between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near point of 15y qktz23itiq, qe)h7 4 $cm$. 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 powe;xzwsr;f/ *zl r 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 telescope using the lenses froyst;dw0ot5n7 :q(e4l , bcf loeo 7 qyc,lot(d:nsbf wt40; 5lm his reading glasses. They have powers of $+2.0-D$ and $+4.0-D$, respectively.
(a) What maximum magnification telescope is possible? $M$ =    $\times$
(b) Which lens should be used as the eyepiece?    D

  A 50-year-old man uses uxv prx; q8eup 6mutq.ox o5:l22z* 3q$+2.5-diopter$ 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 altitudf*+x9e0o;6vykxqg g lx (yc6res (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 o 19aq env5/oabe increased because of the increased distance of the lens from the film for 15o a9oa ve/nqa focused image.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece of a telescope are s/ h h4lmtt.)ospaced 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 objectivrdi h+zg aj-2)e diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can disg h2)-i+rz djatinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lense86 y28k bq iic:kslvz3(b 9pxos, 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 telesc,+5 ta8btx1qhci,yy.q sy8lrope has a magnification 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 tyv*a 6q 2e0ouplate numbers. Assuming it is necesso q 620uy*tevaary 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. ;o.sp3g 3r)m -zptyteBelow) 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