Why is the depth of field greater, and the image sharpem+-:h fo6l jzhz rs/e1r, when a camera lens is “stopped down” the+ rj-:oz 6l zf/shm1o a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of e)iwaq;tz2 b(k(f o0j field is greater and the image sharper when a camera lens is “a( o(btk wq;0izj2ef )stopped down” to a larger f-number.

Why must a camera lens 8ks l5b0kwp9h sp e3fx,nk)a3be moved farther from the film to focus on a closer object8weh k90kla3 ,f3)ssb5k pxnp?

Why are bifocals needed mainly by older persons and not generazfj4m(3b2fztys , bh3-e 2msolly by younger people?b4( hzm2zso,sey3-2f j m btf3

  Will a nearsighted person who wears corrective lenses in her glasses be able 8gaday ,s0u5k to see clearly underwater when wearing tu8sa0,yk5dag hose glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsight)ojf7pd3ajq2b) o3i6f ed ed:ed or farsighted by looking at the width of the face through their glasses. If the persi6 oj)f3 )327dp djed:ofaq beon’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimee5fvc.uq +dg801 9:advec:b y9j qglcm- p0hds squint. Why does this jfde1hp 5 g: dvq0:qag99ulycm e c0b.v8-dc+help?

Is the image formed on the retina of the human eye upright or inverted? 95nh4e u :;vv 3rofhf*gl:vd zDiscuss the implications of this for our perception e 3dforh: v gfvl4 *9u;:5zhnvof objects.

The human eye is much like a camera — yet, when a camujs*1lc 6 ssosps (65hera shutter is left open and the camera is moved, the image will be blurred; but when you move your heads j1shscl656suo(sp * with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lew f:v2uv8wxixa,b.: zjh9 ;z i :65kggmzb-ztnses. A simple magnifier is also a converging lens. Are reading glasses therefobzw;.f: b xgzx6ai5t g-vmz: vh2,w 9k8ijz u:re 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 prodv,lzo*s7 gqzfs;an fr 9, :-hwuce images that are colored at the ed7 gszfs9l:,zr*-,vwf a;honqges. Why?

Spherical aberration in a tgj- iu 2a16h(fdbv1k zhin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagramv11 ufa-zji2b g(dk6hs to show why.

Which aberrations present itt,uf ,tzp 97. ef5dgan a simple lens are not present (or are greatly reduced) in the humaf .z7d pt5e9utg ,fa,tn eye?

Explain why chromatic aberration occurs for thin l4 l/dtot(fq21*zre lcenses but not for mirrors.

  By what factor can you improve resolution, other things being equal, if you use94 /hzytiom36 ri,st h blitotyh ,rs6i/ zm4 9h3ue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantagq+3uwrar6 )8 un3c 4f .eend f)mj:sbces for the use of large reflecting mirrors in astronomical ) jabme:.8c)rcds nnwfu6e+ q4f 3ru3 telescopes.

Which color of visible light would give the best resolution i9x 4bg +h/efbln a microscope? Explain.9fh/4gl +xe bb

  Atoms have diameters 2q1xlx*gnsf9 49w5hxtkxs 8 p 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 hask*o6i7-tokzs 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 lv umh.x g2 xmkg(q03i7bna :vsg2s3 *iens has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports tha p8p:e2*pxb hc ,hj2cfvj s-2ht 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 phoi rt(/j2i/gvm tograph 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 so that it is 200.0 mm to 206.0 m; 3z8v x*b2fd qzi7qjpm from the fq;qx i2z dzb3 f8p7*vjilm. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photogf4c/g i,7cxfjraph a 28-mtall tree from a distance of 58 m. What focal-length lens should be uc,j7 ixfc 4f/gsed 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,kh:.: s*qdtg+ +vvjgv using ray diagrams, vv.t:js+qgk* gd +vh: 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 exph.44ckmuq egl)32 cpposure 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 aboug*)rh*a 4h *ng4jl y (cbywsi6xp l.j2t 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 persc8hjc1 ne s+4hon in Example 25–6 wore contact lenses corrected for the far pointjehsnc 1 h8c+4 $(=\,\infty)$ 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 vib-pl1-s9yi 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 txq irf8v 0t3nz9:2zb14 $cm$. 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 jhpajk30/05g0lkx94 qp ejue 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 correctes5bk)s )gp4mndv.i n7d 4.mnld by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly onlyh4pw n8gvx/xe 9b,vst)*p x ;zdv, n2v 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 ey3tq /3 k:ba sn(emj5bdqyq1z 2e in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsigh eo( ff j(,hx-x 2;a.nebdcri7ted person’s eyeglasses has a focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye)u9cu3w*j6 e qvurp6o–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 and far points ;bbp7e q ot;zi l1t;7df8ld6eof 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 magnificatin8hqkgt 4;ct,on of a lens used with a relaxed eye if its focal length 8h tgc;,tkn4qis 12 $cm$? =    $\times$

  What is the focal length o-: acivhrpd,cc14d1cf a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated aqenkpnkat3 ;;u- hh5i, il*6ct $2.5\times$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/rlyq+uguqg(-lb3 k; . r t9dhing 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 9.cjwt9fg15d-uj)16f iw;,ua sr 1cvau 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 placm6 akoncem8e0j7i x/zl,bn5 2ed 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 len9 k25m,2 gypuihr+tmgah-s t 4gth 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 ratedzpziq3kniys*51z 6 pdf) 2uk* 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 astronomn 5 + hr+e+4mhuhyh9ndical telescope whose objective lens has a fo+ 5+ 4ynn9mh+uhedhrh cal 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 astronomicar.gbnn y8qn: 4l 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 teledoay-zo3: +rgj f-;bqscope has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescopeqbbmp.f *gdq*t*vp62 has 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 redmudm +f y17m.vq *dk;tv +oj.at9-wu laxed 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 astronomica bqu vj3w:kv.n*j2qb +l telescope using a reflecting mirror whose radius of curvankqb 2j.b3+qv: vu *jwture is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to beh7mr x /jt9kspl,nlz;a0)(z n magnified 120$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

  A 170$\times$ astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
$f_e$ =    mm
$f_o$ =    m

  A reflecting telescope (Fig. Below) has a radius of curvature of 3.0 m for e1k*.gae( vleits objective miae1eg(velk .* rror 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 length oneju 7t vi h+vm/l7t9+f 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.d 8b zcdk05 ey0x*qg-r0$times$ 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-) 1vobmu h ,5tcqqd*t5$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the final image is locags3(i/wf5 s8wz5 2vz fba*ojxted 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focdds a;tyx6 4e4l;al lm bv,0+xal 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 mt) ;9wlz-tg gtade of two very thin lenses, placed in contact, that have focal lengths of ltw)t9g z;gt-$f_1=-28\mathrm{~cm}$ 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 aberration084 f ;-/rt-q;4t v shbbxcpdo.pxc wi in a particular situation. A planoconvex lens of index of refracqibc8-;/r spb0fxxpw 4 .;oc-hvd t4 ttion 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 ylks ,+y59 aolthe 100-in. 9 l,5s lyok+ya(254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that ca +flo.3)+ey)2p - lb)qon3tfcntik72nbk dfrn 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 ha +*ld :aw8z c9cszyfj2s 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-yr8-* 9(xz*sosxkboxc.r ;cld l )a:saears away 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( n(y5ls5tq1 qjv/ ulwyj kn4l+- das. a human 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 sepahzdf 6n)po s3zql85r- m75z)cwkt v(y rated 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 atoms, lying in planes,s(,.j 7tqxay v vmq/e9 are spaced 0.280 vmatq q/7(,xy.jv9se $nm$ 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 cryr/do;1ry*p n cstal. The second diffraction maximum is recorded when the X-rays are directed at an any*;cn1orrp /dgle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffrt xm gclp2 +1hj)1ry6laction 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 i9d 8u;.6fz5ni zyifg4) dvz nitoo,2dmage that the X-ray beam consists of parallel rays. What would be the magnification of theynff6zzu5dd8 ,vt. iig;9z 4 nio2o)d 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 kehmzt,dez* z:4,x9h oe57s wintense, a photographer noted that, if 9d,h :kz7e 5 xh*4ztewmzoes, 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 very far away (assume infinity)v:v 4-.:vm fo pi+gewg, the magnification of a camera lens is proportional to its mv:f.vw+vgi4:p oe -gfocal length.

  For a camera equipped with axds(nl1l/kd 7 1xdh3 g 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 betwemgoj-jvp5iui 6-f:3sqm0 slq4 ap- 4yen 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 15 kue9o,dp)f k .w7hzy2$cm$. What is the maximum magnification the child can obtain using an 8.0-$cm$-focal-length magnifier? What magnification can a normal eye obtain with the same lens? Which person sees more detail?
$M_1$ =    $\times$
$M_2$ =    $\times$

  What is the magnifying power of a au/099kiyxm2 ,ex5fg( gv-l rl0dor o $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a 3w5( z/,yai)3p hfcmg3pjsr ltelescope using the lenses from his rcg/hs5 z(jpm3,lyf)3w 3p ari eading 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 wx:ts8 zmvw. f 3fvz1+$+2.5-diopter$ 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 alt 7y:3+n syim4ykarfo i3y)* otitudes (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 sq fl+zq8j,s)mhort distances, exposure times must be increased because of the increased distance of the lens from the fim,zq jf8 sql)+lm 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 tehmj q)f;8g 4rglescope 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 objectic;gy ed2ef, 2dve diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is e2y;f,d2g decnear the Earth.    m

  Two converging lenses, one wi17 rdx(a h4 -qtq.rttrth $f=4.0\mathrm{~cm}$ 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 8.0. If the th ut*7ps/ri4x: ogsm,wo 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 licenxmd-d8mxgf i-i2k q *0se plate numbers. Assuming it is necessary to resolve8*-0fdim-imxd qkgx 2 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 planoconvexhbuul7fo4 *3 o9qq /mt lens (Fig. Below) has one flat surface and the other has $R=18.4\mathrm{~cm}.$ This lens is used to view an object, located 66.0 $cm$ away from the lens, which is a mixture of red and yellow. The index of refraction of the glass is 1.5106 for red light and 1.5226 for yellow light. What are the locations of the red and yellow images formed by the lens? $d_{i\,red}$ =    cm
$d_{i\,orange}$ =    cm