Why is the depth of field greatb c; gouxj4)8yer, and the image sharper, when a camera lens is “stopped dojgo8x4c )y;b uwn” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth of field is greafl . vm 86wd5yfqzl77xter and the image 786f7q.xw m5lvfdzy lsharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moy6bvkjfbmwt: d42w 11 (cg4 )bf+12b mqhrtmnved farther from the film to focus on a closer objecthr(w4m d +1 bfqbcj:2g 26vykt4 tmn1bw1bm) f?

Why are bifocals needed mxp;;h :sv o kz7ll11naainly by older persons and not generally by younger peo:akxl;z7 lv1sop n ;1hple?

  Will a nearsighted person who wears corrective lenses in her glasses be able /xx m0z*.dcl+ sugue 5to see cle/ dc 0mgu5*sez.lux +xarly 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 nearsi y b)*z/j5 fm-j2k.owho7jrqr ghted 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 f*of/2y qk )bj7 - ojjh.5mrzwrarsighted or nearsighted?

In attempting to discern distant details, people will 5sf9mnr ndwzfwa 1.2 : jd+) m-o4hzflsometimes squint. Why does this hel9zdmn5jz)owln1+ a -d.fw4:fh sm f2rp?

Is the image formed on the b3+v0maxq6 sy-f k8r zr56femretina of the human eye upright or inverted? Discuss the implications of this for m5+6x06me vyrz - kfa3brq f8sour perception of objects.

The human eye is much like a camera — yet, when a camera shutter is left g0uz8 :crw8oxopen and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explai80 c8urzogxw:n.

  Reading glasses use converging lenses. A simple magnifier is aln ey.1t : fsv+te6 pug6wc8;r/k8 qogdso a converging lens. Are reading glasses therefore 8:pd6oetyfv 1 ; gnek/cqst6+r.wug8 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 pro1r0 4ig3s nwqoma rwh 8cvpn -t d;f7t3v;99zrduce images that are coloredt9s- 84v qo pd1;mhrvtn3wrz0 3 g ;9rniwfca7 at the edges. Why?

Spherical aberration in a thin lens is minimizedig1wx e:(h gs/6ky-sr 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?:igsr/hk x -y(gse w16 Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are g8rut3fhx7d k 9fg7qr .:p;eugreatly reduced) in the human 8p9x;td fqu7h. ugrk3 re7f:geye?

Explain why chromatic aberration occurs for thin lenses but not for mi2b( sh-ul 0rz+so4ctc rrors.

  By what factor can you improve resolution, other things being equal, if :* che/t: 0d9nffu89, jd p cxpkbnkn4you use 9h4*xn9j f: /k,tcuen0d:b 8cnf pkdpblue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for theb:i23eeskt: pjjfmf/ 70 )t5l2xmll b use of large reflecting mirrors in astronomil)j:/p 3t2iml xe0b2s5klm: ftefjb7cal telescopes.

Which color of visible light woup l4vy8 z:vl3sld give the best resolution in a microscope? Exp 3vszypllv8:4lain.

  Atoms have diameters of abooht-9kxyzq:tpq*vl / ;cb, vekz6()out $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-s 9 i2vv8srm8v miy-b(btops 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 l r3pb3v ilt) sqz:g+t6ens has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reportr2ni cobcf)(9) mr5j os 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 ph u1iy7a ,zas8yotograph 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 20(n0;qj(4 itlev9gvg c0.0 mm to 206.0 mm from the film. For what r4qigngve j c;ltv( 9(0ange of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance of 58u5cz; *udzg n0(wnce: m. What focal-length lens should be used if the image is to fill the nc0( ;c ez wu*5:dnugz24-mm height of the film?    mm

A “pinhole” camera u8iehl3k) ukh0glz x 98ses a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can 0iu3h l9gxzlk8)8h k ebe 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 exposure i(es9 cu39vyjhkj rr-rvv/b-, s $\frac{1}{250}\,s$ 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 2.0 i .hu+xmie,e. 5eyo)p $cm$ long, and the pupil has a maximum diameter of about 8.0 mm. What is the “speed” of this lens? $ f-stop$ = f/  

  If the nearsighted person in Example 25–6 wore cod1 )w 69xxy9 fpkcnizd 62vje+ntact lenses corrected for the faryc6zvjd i2x9d9k6)f wp1+en x 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 person whou/+v;7f oo:e na azh: tmd0)75dlgxecse 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 poin us-sqsi, 0a -h:q.vdnt of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holding a book at arm’s length, a distance eh lueo qdc8.+s u/,9xof 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 corw;e,bikc t 4t6rected 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 oo70 sv6/ek edsa5:ldmbjects 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 in Example 25–6 than the 2.0-9fi2a am k w. alppa27jn;zl- $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses ha lt u:iwfp0ww-xzw8f 0*b9 :nks 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 viewing an obj;jn lb81z reai0,s u,iect
(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 and 20zbxf6 armw i*-ks)x(mjd 0 9j4.0 $cm$, 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 tu4q: slw)gq d tvu69*nk312uu3 y nuiif its focal length iu4 t 3y 3uw)q6un vil:k1*g9qtnusd2u s 12 $cm$? =    $\times$

  What is the focal length oflv0ho8d kja--p8 zd 0j a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated h:46 )/-k ent:v ghd;neeyzfuat $2.5\times$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 usj98x*beoh3b0k5ky 2x6ywfajf9 p,aring 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 n4f a9bfp0zovb 5 :t7qa 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 plaw w7(rg*h -3fbp;h(g:d sdub3njajq.ced 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 with7-cvzoa0 fus 0rszy6d t6 0.aqga)d.r a focal length of 8.5 $cm$ is used to read print placed at a distance of 7.5 $cm$. Calculate
(a) the position of the image;    cm
(b) the angular magnification. =    $\times$

  A magnifying glass i bg4c7 un*(mo3:mgoezs 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 astronomical telescope whose objectikiy5 22z:likjdgsy4 lnfc(wrm4; 24 rve lens has a: g2 yrwk;lijcz4yd2r5slkf4 4( 2i nm focal 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 desirji1cvrne(+st1v rs ;5 ed 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 has an afml cct85m,+dvrru(7 b+lrwzz*5 l5objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescopgn. e zo t8mjeq0 5m0kfq:v*(we 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 adjusthwh,4sfa4mp eb*ss( ,,1 niehed for 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 astrom-rvljeu/g5 cy 1 um8vwje*5q.4c -fonomical telescope using a reflecting mirror whose radius 8fgu q-m/el1meuw 55o.-c y*v4jr jvcof curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified 120k3cc dn ;iv/1b$\times$ 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 ra4vao mjxx*.b+ba. nh*md6zgv 1il:tj*6 cma, dius of curvature of 3.0 m for its objective mirror and a radiudtj+** 4h6,:av oij.ba. vm6*nagxc 1xbzlm ms 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 len68a608be.v)v ta dcebf xsgc. gth 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 1:za)3s:k . /04 /uutt g wvd9vookjfyvy6y:rp2.0$times$ 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 1.7hvp/se0syf7 b ).iyg8-$cm$-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 t)i*cmcw1 8+swdm *xg 5a*tuog tr.-5orxkp2u hat 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 microscope has a focal length of 2.70n mls2uua99jww+4 ,alyj 4t /s $cm$, 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, ths3ca.sjbvig er 4*:h+at have focal lengths o g3b:sa +s4*jvherc.if $f_1=-28\mathrm{~cm}$ 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 particulaxo-;6o m:mh 0x9xcdci r situation. A planoconvex lens of index of refrx: 6 ;90dcmhi xcmx-ooaction 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 diffractf6 dbhftbj /x5:e7 a,0lc 2cos*spu,cion for the 100-in. (2,lf0bj/:s 5th b6,s2xpe7cfd o ucc* a54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can rex5m j3nqztr8wm-)9ww r km*m,solve 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 oze9ontg ++9j has 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-years away are barelyd4 en)p(vg p4y.awrwn pf 26.n 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 distingu knyvk n30w0h3unb/ ag4 m1xq:c2rwj)ish 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 a;n hitdb0ln dk ,gh( t ,ne9u+j.n3k0sre 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 0.133 nm fall on a crystal whose atoms, lyingm.tzf89sl )v n(cawp6 in planes, arenlczvw6 tf) (m98 spa. 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 crystal. The u/xpjq rev-83a (:bw)9xikz :8fd vi wsecond diffraction maximum is recorded when the X-rays ave/f-iv:(39xua w k)biwdz8 j :8r xqpre 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 obs4r6h.jvs7a5b;k jkomhv 2z a:erved 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 imrhm +*/k2oz yoi. -rfsage that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnification.*h- 2rr osio/zm +kfy 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 mid2 vkepeds*xac2d6 v)ed8 4j l,day, and the sunlight got more intense, a photographer noted that, if she dsx2* 2 ekd6p4lj,vve 8de) cakept 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 magnification x snw6bo 7f1o21bxwv3 of a camera lens is proportionxbo vfoxwwb 26713n 1sal to its focal length.

  For a camera equipped with a rhqih6xijt x*e2nlq3k4271 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 n :7kl*l:vftgwmznrf+g0 t7 od3tv. 9 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 *;dar+w7 x);pguy5 if ,uvdlcof 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 j- ub7ala3l:kra.dldm3ro(r .+ (pkn 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.tt)v6v)x3.avou8uufo 3 m r+- j 5z4pcmhcdc a telescope using the lenses from his reading glasses. They ham)vxoc jv-)hct.5ac33 um6d +.rpuuvf 84zot ve 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 f6z2o nkzhqj4mk(rln; 7l1 szl g42z) $+2.5-diopter$ 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 altizzp6zl 6 ca*ucr9 .km/,vc of)jm3s9t tudes (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 timesi/ zivmf/+lf4 must be increased because of the increased di/fzmi+ /l 4ifvstance of the lens 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 sip)/4 ovwo.u(d2v9 dcchch(.6cyne 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 2.4 t3zal8e6 dmp6 m, is viewing the Moon. Estimate the minimum distance betweet83 6zedpal 6mn 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, onb xb8eger5fpwsnx(+l3 )cg 8-e 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 8.0. If 8m2: l/ 7tw5/me bgakzy b-jqvthe 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 pj lvvcd4aezqnm 0y;y0f u) )7-late numbers. Assuming it is necessary toyv-4nfle0)a7 ) mzvjc dqu0y ; resolve points separated by 5 $cm$ with 550-$nm$ light, and that the satellite orbits at a height of 130 $km$, what minimum lens aperture (diameter) is required? D =    m

  A Lucite planoconvex lens (Fig. Below) has one flat surface andn63y 7hoom zzz:2chw3qfa z0 4 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