Why is the depth of field greater, and the image sharper, whenps k9u7o3zpnsi,7p.cck*q d 7 a camera lens is “stoppe9 in3*u7pd 7cqsp7kpo.skz ,c d down” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of ficpo- r6),xr s c:tm3queld is greater and the image sharper wm, xrc:s-tco u 63qrp)hen a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a c(ipn6(egh gft. gius ;y9ne- 3loser object.g3 ng-gy;9tui ( nep 6sh(fie?

Why are bifocals needed mainly by older persons and not ge i;gz7byu.h .agkyq k3+4agt/nerally by younger people?qb/ggay3ykhg 7t.a kiu4 +;.z

  Will a nearsighted person who wears corrective lenses (*/9 mbf8zh bnewrx8d z0fpw/in her glasses be able to see clearly underwater when wearing those gwb*0rb m/f8wphn /dfx(89zz e lasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nsw:):5r2xvwaonqck 4kp4y bb )tyr (5earsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsightap4:(vko: 2b 5k5t)q cwyxs)br4ynwr ed?

In attempting to discern distant details, peo/;z;)slpmzt a ple will sometimes squint. Why does this s;z ; zmpal)t/help?

Is the image formed on the retina of the human eye upright 9wbj la+,+,cbz po5rw or inverted? Discuss the impb5cbz ,jww ra+lo,+ 9plications of this for our perception of objects.

The human eye is much like a camera — yet, when a c/.n/ x)6 4k/p/(n nj1rvmnys2lm .kaard hx skamera shutter is 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 clearl1( ) 6kyssv4n .r///nlnxman.a2phd k / rkxmjy. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a conves u)ez+e7nd3,em ycs mnp)q)9rging lens. Are reading glasses )ce)p qd7+mue,nzye n)9ms3s 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 imagesym+1b7k+r31 cv hbye v that are colored at the ebm7 k1yhyr vc1+b3 v+edges. Why?

Spherical aberration in a thin lens is pxi4b6fqxe-bjaj* .hkb i*)( 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, wh fb xj*(j abkp*eq6-x.4i)b hiich surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are greatl n up(+a9b;twly reduced) in the humalubpa;9 t w+(nn eye?

Explain why chromatic aberration occurs for thin lenses but noyo qish xl8 z)bruw:x91; 3nn3t for mirrors.

  By what factor can you fcc5j3z 7kie: yx5 :luimprove resolution, other things being equal, if you use blu cizx7l:u35jk:e f yc5e light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large refle 0wz()g/n5li1 w zcok9zjsw3a8 :mv hpcting mirrors in astronomicalzns)gv30(15m/jww aclh:89w o ipzkz telescopes.

Which color of visible light would give tn)(zja u 0hpehfolb+;2lu.;nhe best resolution in a microscope? Expl2unza. ; hbof+nej )lpul(0 h;ain.

  Atoms have diameters of abo gg.r(ly7i4 n7gnhk: mut $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-sto3m86)o dg obrlps 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 4atm /hhl)/vfo l07aiwru9g: 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 camrc +/edoj 4t1 3twi .c q-ypoo5oc70nfera 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 plb7ca;: jt1sd*/h q4s/ nzx whhotograph 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* llv 29)s wd-ehl:jgk 206.0 mm from the filmlgl )ldjv9:h*2wek - s. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer 8feq w ta5sd-,wishes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm heta,dw58sqfe -ight of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show,zaa3: wtg;/vs using ray diagrams, how reasonably sharp images c/;v aza:tsw3g an 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 expos z94pp bn v(9qw7rfhwt0pbp;,5u tdl +ure 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 oq/g jq d:y yz,qy, mdshl0;5*,bmwp(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 E 0/xf1)/z rez8wt) let3xvf05d 3jeyqb ;qfri xample 25–6 wore contact lenses corrected for the td8 f;)izfex5b et 3verz103w/ lq )0rxyjf/qfar 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 power are needed for a persowatb 7 qkwp)v.xl+a66dni pn42,h5wr n 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 pox1ax;x; a z)hgint 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 holdin)ne b(rba 0m lcq00:)hgxomhq9(rw,zg 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 is zm+ ,a8e 7jxvfcorrected 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 only2w e3w8(r g e 0cm6lwno4he0mrosi0p* 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 eyea5mna.e89aoz l zj5g t3zd l:1 in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted ycqjp 9z:)tw45:uvvr 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–lens system when vie;4nty, edcy*c wing an object
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has near and far points of 10.0 andg tvl;o aftg8;5gu1(c2m3 1crrs-gfnav . 6rd 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 0thwv3 0pyh 5eof a lens used with a relaxed eye if its focal length tvh5p 0 y0wh3eis 12 $cm$? =    $\times$

  What is the focal length of a tf1zc8adepy6tc/8yq m5 -;) le 8.x+cdagjtxmagnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated atjh)ua-6edwaygtdrx-n 63; c6 $2.5\times$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 usinga9;di -juwzy-jc l4 +u 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 ib a**5wu,em26qqalff *z wuv/s viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placed 5.5g( +yk55kbywwlh s ce w-49*zl5 $cm$ 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 lengtw0h07kyth ip5h 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 isyqdup.8eqierv )7d 6 6 rated at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnification of an astronom tfbl/i.7au00pml py,ical telescope whose objective lens has a focal lmfyl07ap ,l0.iutb p /ength 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 txllfo2lb2-s) g o4e+8ji k i:ao be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

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

  An astronomical telescope has an objectivrxv(r,ry 6saxpbu /4v.-8 xpz e with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its twms-dbx.bq+hqfg *q3f60 8qir.b /n se o 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 relaxed eye is y)jpdl(8 1xy l32.8 $cm$ 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 astronomi7df4cu ;ejv5qamtg6lg ,8 1zs cal telescope using a reflecting mirror whose radius oft6 4s5jf ,8cg1ez;v qlm7 ugda curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be+;shd z/y( bdm 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 curvati; y;xsgaawv;jr 4z9h c*8romm::v)f ure of 3.0 m for its objective mirror and a radius of curvature oisa:;jv; 8wgr9 m *ohyxv:c) mf4ra;zf $-1.50m$ 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 hee(yeu4p.sn1 hn;p*e -fz+m iece 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. gfu:0bcs5*pe 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 jsr:0*bw kuqx37 +hl lib1cyrr4i)qa7f2p6a -$cm$-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 located*/sczjv8q g yn:9jl i1x ;j 4kqzui*0x 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compo:f. c*yqn yu o*vh,lk-und microscope 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 very thin lenses, placed in contact, that53vj +** sklq;cr6p ch2k rzqb have focal lengths;vcrp523k+cr kh*s6qbz q *jl 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 aberratinric**w+4 r n0 tsy:eion in a particular situation. A planoconvex lens of index of refraction 1.50 and radius of curvaturei i0c nn+rs4w:r te*y* $R=12.0\mathrm{~$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 res8*ip :e g-:rvxk xy+tf0*o*f6xsvquy olution limit (degrees) set by diffraction for the 100-in. (254i+x:6qk yux-sg* fe vxy0 rpt* v:o8*f-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve featu cd 8wq)/ky n,wkhmm(6zq qpa/ a1zo77res 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 len5p .w9oyy3zb1uz5ti e-q xa+ jgth 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 bazb m /it)p8,p x;mjsy)rely 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 disti5ngupfk) vnufgc/q4 t 7d2f0)nguish 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 separated by abougki5z: mffr+9 d1hb-nt $400\times10^6\mathrm{~m.}$ 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 *iev a007o x-s4j e5tutynl e.on a crystal whose atoms, lying in planes, are spaced 0.7x00ea-. u5 ovleetyi tn4 sj*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 crystal. The secondk:)h;hn)l qr:;tdiw g diffraction ma)d hihq)nlk:;w;rgt: ximum 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 diffraction is obserwqwf q41d1 5 k 2o0-hmh,haamyved at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image ncd)z e l5q+0t7 wtc;-duin+ ethat the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnif wt+5d7c0 ;n ti -zd)lceq+neuication 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 sunligxdu c8 h834opmx j*l 25b*v ldws/sk3vht got more intense, a photographer noted that, if she kept her shuttco 4 lvwm38 dhku* b*/ls3x2dx8jvps5er 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 im f4hzbx,*j 2vv;mm:f 9lu/qq nfinity), the magnification of a camera len2vfxqf /; v*q:u,jlhm m 94mbzs is proportional to its focal length.

  For a camera equipped withrc)q-0jj5c vusv- ioji1 q)b1d79xq f 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 eye only when objects are betw7o m18nrk6pm+0g 2 zvduk77p (lubeideen 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 1i2eh q97rfo71o gac 9s5 $cm$. 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 po 4gpm4cu02n,rf*jbn (ezc mvt3z0a4,)gzbq mwer 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 lense, :r j4nyp0v2,kopvi us from his reading glasses. 2:ouinky,j 0rv 4p, vpThey 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 1hou*:, q6d.asr 6zfc2mxcr9 gj3xqt $+2.5-diopter$ 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 extrec4f xgysa 9/d0mely 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, exp6c0t 14-qlg;fqvot ojosure times must be increased because of the increased distance of the lens from the film for a f04;6qt v fcjqgolo1 t-ocused 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 eyof pi2cd /)wgcz7lo;s xh n)5+epiece 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 diam1hui- l bp3qacaef9b12/) -cdm e7jueeter of 2.4 m, is viewing the Moon. Escb-/uulq1e7-a1 3eda p f )9ice2mh jbtimate 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, onm8(z trb -1o rtx,yp1(j4vvfhe 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 ofgs3g ad f;x6 vu7t;1yo 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 satellh os0a9 /cevnrk7v ( n-g;3 ha;ug8kppite to photograph license plate numbers. Assuming it is necessary to resolve pointsp 9p/0no3- ak7gvv ;ghse;auh nc(8kr 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. Beltvla (6u.+ hz* .p6qhzrk5n ehow) 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