Why is the depth of field greater, and the imagekjd62mtz3q + .xnk)cj sharper, when a camera lens is “stopped down” to a larger f-nu )qn2 jkx6j 3+t.czmdkmber? Ignore diffraction.

Describe how diffraction affects the statement that the depta*o3jqb9gos ua ;t :f5h of field is greater and the image sharper when a camera lengo9of: 3bj stqu*a a;5s is “stopped down” to a larger f-number.

Why must a camera lens be moved farther jk+jd9tn 5mu6from the film to focus on a closer objecjndj u+6k m59tt?

Why are bifocals needed mainly b:ig:an (mh:6qpr;kp c 1cf2cry older persons and not generally by younger peoplpih:(;:r ccka cq 61pr2nm fg:e?

  Will a nearsighted person who wears correct;-u-n+ a0er*eb5y v/rqo y cixive lenses in her glasses be able to see clearly underwater when weanq-i+ oe/u-xyver*5r0 ya cb; ring 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 bj .ss.pi p6:ay) b zan2+fc5hmy looking at the width of the face through their glassascmnp:z.+5ij.6 y)2ahp fb ses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern difx xbjb )/6 3 et1xhn-;d 2lo: gpd+iupmme:8istant details, people will sometimes squint. Why does this hxxufjl ;:d-) xmpd ih16 gne/b 23i:om tpe8+belp?

Is the image formed on the retina of the human eye upright or /ol8 y6bhh(z8 dq,fcx 62mvzfinverted? Discuss thy z6h fmdqo,/ l6z b8vf8hc(2xe implications of this for our perception of objects.

The human eye is mucicec)5nn3fo6,.cr+x d w cr e3h like a camera — yet, when a camera shutter is left open and the camera is movede cdwf)3xr6i3cnoc , c5en+r ., the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A dge8 r.a,w-bq simple magnifier is also a converging lens. Are reading glasses therefor adrg be.w8-q,e 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 usualr:am,phvyfv7 0vfy/5 ahjy* / ly produce images that are colored at the edges. Wh ,0vj/ ar*/fav75 hfvpym yy:hy?

Spherical aberration in a thin lens ism8hgfec- 6crvt;4b v (1fgsb8 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 m-;8 ( rg8f bhef6vbtv 1s4gccsurface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (dah/4w: g(mqmhvqh- 4th4 1bhor are greatly reduced) g m hvb whqqd(h-1 at44h/:hm4in the human eye?

Explain why chromatic aberration occurs for thin l. p)*hy4 puj-w( tfrmqenses but not for mirrors.

  By what factor can you improve resolution6g6vv1tyva3 r)8w rey, other things being equal, if you use blue l66 yr8t3wy r)1egvav vight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting 7k42vkuvp /*mv d);xi(lehbp svh* 5vmirrors in astronomical tek ;k5 /pv7s) v2 mv*hv uivpxhe4b*(dllescopes.

Which color of visible light would give the best rejfb2 ,rg-xup+solution in a microscope? Explain.gj +upx-fbr2 ,

  Atoms have diameters of about ucrfb0blo(e ngm78 (1 $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangin9(owz*j unrw*zn2sm arn d9tmm 7 lh1h452b d1g 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 ha36bekec +qhe fd ;.fs4s a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports thrb; 8;i6cky .-mu om qpb8js7eat 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 6-qlvr1zdce z ys avp9:- 8. 0*b(q q8zgcscdfis 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 bnb7 -9xkbun 3ae adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be a9ak3xb -nbnu7 djusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes tvasuxw/+9. j)2 m2k m89 m duivx:pfxmo photograph a 28-mtall tree from a distance of 58 m. What x :f2vv9 swm mjd8pxmi x/+9k2ma.)uu 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. Shoj,e2,rt1kcd) efhx-s6 sdcw* 3bn2he w, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In jt-dbdsc,e6f )hx3 ne,r 2 *s2w kec1hparticular, 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 exp) kmut xs9wzrk.; dk0 0dy5oo9osure 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 abbo5- fp,g z.nr.r wud;out 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 person in Example 25–6 wwsd2 s m:0.*e/norc)mxncax-ore contact lenses corrected for the far2n.om esax0ns:c/w *- )mdxcr point $(=\,\infty)$ 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 fccrw 6 /i*3xbpower 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 1x..ncrq6pw mvlr 6v2+f9jm9 h4 $cm$. 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 top23eyo i*gs*; yav uc8 read by holding a book at 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 vs xyq62wc,s pym/ x3kd9w:*yis corrected 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 ;rdjwfk: r)eg*-mw evq; l s51can 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 nearsighted eye indxk5u agx3 ea;d78m(5 mv z4fe Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a fy am0/p k2 z1dhnzyn.0ocal 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 ow l-mf+mo sp 47ba;sd8nn( y(mf the eye–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 np6 :ljbp* (udlear and 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 magnificat w)+v5n ip0y)j pscun b46ety4rj a2m.ion of a lens used with a relaxed eye if its focal length is 12 pyc+ twu4m4p)5 2 v ab j6s0jnyen.ir)$cm$? =    $\times$

  What is the focal length of a magnifying glass 1ul4z/za*bnf *w b/4wty 7gyiof $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated mcy g 50y zy-g28gdb3aat $2.5\times$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 wl m/y.utx0h -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 isoo6q2g8n 5d pf 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 rx0g1m /hvnyp(etc(/ dw . m3z5.55 $cm$ 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 lengthc8uw7bgbo; 5s 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 at ezydlz u(hy.7, f0 ;rx$3.0\times$ 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 astroqjyk hy6ay)l * o-;uf xrg:+0,k6n mvrnomical telescope whose objective lens has a focal og;vnul +6ym0k:rhyf-y aq,*xjr6k ) 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 astronomical telescope is desired to be (+e1izksmu;b 9fv91jy( bnh2 v 5mm (cqzb(ou 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

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

  An astronomical telescope has an objective withq86c1ilq5.mhog hfuapx,k, bh) nn 0( focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenr2szhh86hvg8ov0 0betejgqxxc/tj: hz;+ 6 ,ses 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 relax3aoht(.v ;xer nrp6ym91x3l wed 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 ozj g8 6xwatm69f an astronomical telescope using a reflecting mirror w66xaj9gt wm8 zhose radius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearcmxrl7t6 - ,xts 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 curvatn7aw46p vsl+ kure of 3.0 m for its objective mirrkwlp4+v7n s 6aor 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.-*xtcxwc 8+zg.r:m +fnb evy eyepiece 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 1hkmuu vz 39 .ba;b2;bm+dgr ih57h8hj2.0$times$ 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 1.8q+(ajz qtduy a-hj-9 6*j :aqoxfai04-$cm$-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 located0ah:gapg o7 v7 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length of 2.7npn6yb 8bipl8d4f+oy 4f1f /s0 $cm$, 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 contact, thieuds,77/ lhnyjeqc k,zr82z5; p sn9at have focal lengths q,7u n z yh8ckln9s2iz/jsdpe 7 ,re5;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 aberratiocg. p qs(xauml9n3f.., aa q7tn in a particular situation. A planoconvex lens of index of ,atq..f7px a.3n qm(uls ac 9grefraction 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 resolutio.l0nu/**gkx .9xzxffzbjqd8 wy 69 xqn limit (degrees) set by diffraction for the 100-in. (2* *lx x j.9f wqzqkux.b/y986zgn0xfd54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve featur0z(r hxv f4,wlv8sw x:es 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 lengtvhsxs8.od ,2d2l,3w9viu2m g 2ivwuph 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 barely resolvedeb5nar z9 z0ehw06t w8 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 ac8ckc* .5n tpcar 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 separated by abojn9p z/ mjfiz9:jug 4iqa5 v3:ut $400\times10^6\mathrm{~m.}$ 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 nk54 7ytok.4a.itu 1m; syxs ycm fall on a crystal whose atoms, lying in planes, ar7so .1y.kyu x 5my44kitt acs;e 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 an unknown crysd r)u1lb.6b opo*efa /tal. The second diffraction maximum is recorded when the X-rays are directed at )od6 /lf r.obue1p *aban angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is observed at +.bug tgpa24ysho5 x;*u f0e l$\mathrm{25.2°}$ 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 i/(pn y0-yvcm consists of parallel rays. What would be tpm c0nvyy/ -(ihe 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 mi ln,3yl9kx9 oj+p9kxl dday, and the sunlight got more intense, a photographer noted that, if she kx9p9kl +l ,oy9 xn3jlkept 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 ma x-hdmnhg z42k/tf-5 agnification of a camera lens is proportional to its focal length.h52zfa-hkm dx g-4nt /

  For a camera equipped with a o6(ih+jj ;jzla0vfj 850-$mm$-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 e7pw ;uz16blir ye 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 ofhxhfpb,;1/ zn 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 power of a )t7bm x(n/ulw 1ls,te$+4.0-D$ 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 fq wut/dbt8fu i;o4bhe /0 3/fqw 4:dkvrot w3: b ifd4 uq0ft/w/;keb8uvh4qdo/m 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 usesa o:xwib:2xz +vsn yj37e3y5y $+2.5-diopter$ 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)71ep bhk.bw ,h)teudes (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 ur)*jy r1m.93vg fsznshort distances, exposure times must be increased because of the increased distance of the lens from the film for a fjs.rmf9 y*)vzug r1 3nocused 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 eyepie t ar:u7hc+r*wce of a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2 kjqr 3gy mg*6edk (37y*ojzz1.4 m, is viewing the g md*y j rozj3ke6q(3*k7yz 1gMoon. 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 near the Earth.    m

  Two converging lenses, hjuz,l r,;r n8one 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 ma2m :1ja2 zep2kg zxhvul3os 37gnification 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 plaih d(;cts sr+w *8hnq5te numbers. Assuming it is necessary to resolve points separated hd5*r sqsthi( cn 8;+wby 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below) has one flat surface and thd) se8tym f,fy rz1 *gt7f4n3rm2hof 4e 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