Why is the depth of field g+ gw*ylh3da, mreater, and the image sharper, when a camera lens is “stopped down” to a lg*wdy3am+, h larger f-number? Ignore diffraction.

Describe how diffraction affects the statempgf2 ffdnc-6ro+mue* 98- qhsent that the depth of field is greater and the image sharper when a camera leogf*pf + - ns9fqehc8r-d 26muns is “stopped down” to a larger f-number.

Why must a camera lens be move 914nmh)efggsq 0pt+x d farther from the film to focus on a closer objec40) sfep+g g1x qnmt9ht?

Why are bifocals needed mainly by older persons and not generaz 0*8chqaa2melly by younger people8z aaeq0 c2*hm?

  Will a nearsighted person who wears coev-e2e;ol -sw)v3v 2map3u ibrrective lenses in her glasses be able to svw; ve2-ib3 o-up2el3 sveam)ee clearly underwater when wearing those 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 8ggi238dpjrkd8ty r,d, z(+l p w1vj xwidth of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsi3yx +vz28d r p8g8(jjwikd g,,rl1tdpghted?

In attempting to discern distant details, peopl1i8(vce )f f-.j-nfjo4y0qon tcb ji3 thu9g +e will sometimes squint. Why does th8qvj0cj-1j(f9h-) igoic yt f tennb.o+ 34u fis help?

Is the image formed on the retina of the human eye upright qls+nb(gp8l81t-ny for inverted? Discuss the implications of this for our perception l+ gnnfy-1 spb88ql(tof objects.

The human eye is much like a camera — yet, when a camera shutter weo yr0w pmxs*3t93a6is 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 ce3*astmw09wory 3p6 xlearly. Explain.

  Reading glasses use converging lenses. A simple m1xp nnc :q h:zgi5ax1i0 bqms,h6*dn-agnifier is also a converging lennn5 :xq:i mzg *sx b,n0qc1ph-i61dahs. Are reading glasses therefore 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 are )hyobte+0 +ti.egr :zcolored at the edges.tz+.h:o 0+) ebt yiegr Why?

Spherical aberration in a thin lens is minimized if rays are bent ;z4gp+hs )g8u, 6z0uhqcfqm x equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should facec0pg+u,zg 6 hxh 4q8su; )qmzf the object? Use ray diagrams to show why.

Which aberrations present xb3sbbs /f1)bihg+wn 19c c0ein a simple lens are not present (or are greatly reduced) in the humaf0193wbn 1sshc+x/c bb)beig n eye?

Explain why chromatic aberration ocdx o+,8h,3-0ol jho qorzr v7zyv /w/ncurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other 6)+v,o xy8q fumwv, fwthings being equal, if you use blue lfoy6)8xvwvwf+ u, qm,ight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use ofd- 8vovgr5 rn8kxv27a large reflecting mirrors in astronomk7-5ovx2vrvadr8 n8 gical telescopes.

Which color of visible light hjps0emg 7c m.e,6x7; 9purci would give the best resolution in a microscope? Explarch x7, .p07jim;me 6g cuep9sin.

  Atoms have diameters o qrg/;t(dhms/cnn4 (pf about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length ljdb i5c9s99( fx qs2h8h3jfhpens 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 has a67zbr0aemj*d-d6 r q;u3g bv8vxruu* 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports usrn53sn9dn.q0l d vz j,p2e/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 takel 2g,gioxh,cubjcud7kb91- 6n 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 ber n 1i;avywvw;bc2 jciga/8on h 6,-a* adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can itaog18;2an ciw6wcv /-n ;a ,jvhbry *i be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer ok kuhr x 6,o7yze: 3mk:3pxwb,u5ba7 wishes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens w k:7,xe 3mb:upa3uk7zbxkh5,6yo orshould 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. Show, using ray dd2,b )s4kbuull1p9y9r9 b8pgbk (zd 4tb) jbhiagrams, how reasonably sharp images can be formed using such a pinholedytb1z)bhpul 9kk299b b8l 4ub(,p jb)s drg 4 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 exd1 4n+ihc9i4l )ub bbbposure 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 qv0jl, sh8.qk+jyuk5 y bjt07gg)a (v 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 personi *z v.ezxna ;cbqx4p5jf:1m (qc34ap in Example 25–6 wore contact lenses corrected for the far p(*3e zvcpmxz ca4 nj5q;f1ix pab4 .q:oint $(=\,\infty)$ 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 whm9q5g rl(bey3dn61poat power are 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 point of 14 ntxnev05 asl7/:o d5fu-f:ir6 bx23lq: sapo $cm$. 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 td4b(/i c q vtj3h7fmdnq +/7tat arm’s length, a distance of 45 $cm$ away (= near point). What power of reading glasses should be prescribed for him, assuming they will be placed 2.0 $cm$ from the eye and he wants to read at the normal near point of 25 $cm$? +    D

  A person’s left eye is corrf12w0d-i /aqjqpjz2 bected 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 clea;po ref7b5r hp- mgy(f00o pdp9o.h2arly 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 nearsighted eye in Example 25ju-viw ) b -bm/i/ 8o/pgshei6–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fonrbs 4;0/allecal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when viewing an object 9 yq*4hthi z0c
(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 po2bkdxl u q*/+ ; xieis)ur*2m)iar8vkints 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 relaxed eye if its focal le ,mb 1zian/ */bbx pn0;*pfdldngth xd;i/pbm0 l f*/d *nnap,bz1 bis 12 $cm$? =    $\times$

  What is the focal length of aeqj) -rg:vxj,8jbkug z3 ,pr3 magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rateds*q x8c4q -sywk; .fv41 baobi 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 using a 9ep4q + s+ilkyl(p (y/y.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 witww8,dw, dw v9(xwct(nc .ke+jmy5da*h 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 place )9kjy*;dlv(e3 (n tjgsz3sj ed 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 lemk8x6- ifa7mjngth 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 ratexhg sig6behz7,aj63 +d3ng/t d 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 objective lens jumi ze1 41qz*/*ep mihas a focaeuim 4/e 1zj*p*1izq ml length 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 as1job fhzyf.2 l+c1;bijir6 s1tronomical 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 hasesef):k6tj 3(a upku) an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses space7phs5kv v4 5x8cbbb*ad 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 fi4dw 4k;xwt* ior 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 astrono9a;4 dk umh2hrmical telescope using a reflecting mirror whose radius ;h9 u ra4hdm2kof curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears) /crt1htfx;kkf*wi.pu i43 b 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 telescor3 7ws7a q*ifwpe (Fig. Below) has a radius of curvature of 3.0 m for its objew*7q fsr 3wa7ictive 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 focal lengp2/dx be*1jjfth 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 12ei 4cf4:0hf 4yyqi+k ,vxb3nn tk4h63w 8wggw.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-vfr5t3ws1qp +$cm$-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 assum1 as) hp4(cd3k pew;lming that 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 microscovrr4e* sow+m3y*tj3x pe 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 vercmpd.kdok/n ud6)7q keg yi07;m 8h, cy thin lenses, placed in contact, that have focal.c;md7phk d/de)m7 k0i, yo8cu6 nkqg 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 aberration in a particular situation. A planoconveu qxa qqzsrjl-22h3:0s fj k5,x lens of index fqsl rj xqz22 3s0 k5ah,quj:-of refraction 1.50 and radius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular rhf) fuo8be x 7f5t4ka(esolution limit (degrees) set by diffraction for the 100-in.f5xf ue8 a)o7 tf(kbh4 (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to cot i+0 2jfaoc5p46vt pdnstruct a 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 ixnmj8c( i:tv q84rt5zx+ p0j focal length of 50.0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years away are barihk tf,mu 3 ad/7o4n1xely 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 caryxz4d )+uubn; 5x:u lg 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 pxdss3o ynl ,ql(+w1* separated 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.q:ygfp ee 6ik8s w*.5ycb wf 6-*jtx4w133 nm fall on a crystal whose atoms, lying in planes, are spaced 0.2 ke j5*6i :bypc*s t.y8q xw4f6wwfge-80 $nm$ 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 a4 q:ks(foly i5d8rs -gre directed at an unknown crystal. The second diffraction maximum is recorf sgr8qdo4ks y5:(l-ided 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 diffraction is obse0 u y*cm0y0q9jammawgx,qvlh (6 0 uz;rved 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 ib- pso p(ce31m /; ml* iqk5sk;me/drlmage that the X-ray beam consists of parallel rays. What would be the magnification ofekc( qd ;l il3rb;5p/*mmmpe1sk / s-o 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 8cvb, 48h b+8 tg1jzfcyw5eenphotographer noted that, if she kept her shutter speed constant, she bh8nvw+e48 g cj185 etz,fy bchad 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 (ass39/lj q89n.xhftzo yg ume infinity), the magnification of a cam93tz.y/l9 jo8ghxqfn era lens is proportional to its focal length.

  For a camera equipped with+:g3 uwe2+d :hlvo vluhn)v5 z 7za(db 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 h h,,,i ckz-mpeye 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 sr2w.9x.cqlg 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 magnifyi7znx )/qhv c8pr7r bg* u a-3zagbwc/-ng 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 make a telescope using the lensl,8yg6 c;voih7vuyk b) zso8- es from his reading glasses. They have powers o, uhz sg7y8yo bo-lv; c)vik68f $+2.0-D$ 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 useevbs5j..0yu0c . 3rqmv p2hud l+h yu:s $+2.5-diopter$ 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 extremel*.lmbx8hkbzq amqt8 ia u08+-y high altitudes (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short distances, exposure tjcx(7j.r 5u3nyssd k t9i*m + dk:6sggimes must be increased because of the increased distance of the lk .k(tygi3jns+d ug dss6*9m7 jcrx5:ens from 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 are space0u7ry uzz bmehqr wv::;kt :qb)e8.0dd 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 m, is viewincz y-3+fh8 5m2tqy5ge cu*3 x7cwsfhdg the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light xthfg2y+-cdy3*shqf8 wm zu755e cc3of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, obq nhv4lln2d,i- i6j e935vntne 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 magnification of 5pca4baiz ,/ iacx 2*z twsl dh()yx198.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license plate numbers. 9 abw 75ep6 m(llrodj3Assuming it is necessary to resolve points separated by 5 5 l6m 3brjwd7p9e(alo$cm$ 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 , xwaa.r b8w2dthe 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