Why is the depth of field greater, and the image sharper, when a camera le.mhxx.xtm93gdllsz2,v( u8 xns is “stopped down” to a larger f.m(z3.m2t 8 x vulsld,g9 xxxh-number? Ignore diffraction.

Describe how diffraction affects the stawfnr 7gcz(/-utement that the depth of field is greater and the image sharper when aw7ngu / z(rf-c camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved fa y8tbq.10rzkd3t78rt r nqgd*rther from the film to focus on a closer objectdkrnrdbt7 g1 3tr*08. t8qqy z?

Why are bifocals needed mainly by oldbz /kzp0d*7bzer persons and not generally by younger peopb/*z7d zz k0bple?

  Will a nearsighted person who wears corrective lenses in her glass ,t97(rf xjeb /wnlu.ees be able to see clearly underwater when wearing those glas(nj/ w rlx.u7e9fe,tbses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person3z1 0aixnf,ak is nearsighted 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 ne130nzaxfa i,k arsighted?

In attempting to discern distant details, pez5xloqaik o/xs*w9 u+ m s-)c1ople will sometimes squint. Why does this help?slwmcix+5us1zo x 9- akq* /)o

Is the image formed on the retina of the human eye uprig n*;4j. bmaz7b -evbjqht or inverted? Discuss the implications of thbnqzjab mb. ;e j4v7*-is for our perception of objects.

The human eye is much like a camera — yet, when * lcctk8 b(rv*a camera shutter is left open and the camera is moved, the imaget8rlc (c*kb*v will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also adg21 qjztat 392u y(3aha9/t1 kmrujxdbe;(a converging lens. Are reading jbzt /9;2j3d2turameht(yg 1x u(1a 9k3 aq adglasses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s use usually produce images thatk /9hg3c;z cul are colored at the edugl 9;h /cc3kzges. Why?

Spherical aberration in a thin lens is minimized ifye tn s f7d-9u1u mg,*w:md)toj/bq, x rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image ofnus *7mtxd- me9t,jug)qwd: b /yo,1f an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations prhm(ifoxamplp 29.8 jb4jmf) +esent in a simple lens are not present (or are greatly reducem. f+b8jfx lami p 9mp2ho)(4jd) in the human eye?

Explain why chromatic aberration occu/qru;1-3n 6i(kjpvc4 v7ehwd h. ma qcrs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other things being equx kvr3y.l(u ja52s ip)1li3b irnq*4e al, if you use blu .l* ir2ulq3s )e34ivj5ikxn yp1a (rbe light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantage22e)0ufvnufgo2we* mu9t 9bqs for the use of large reflecting mirrors in astronomical telescopnouuwe uv292bt0q g*)2 ef9 mfes.

Which color of visible light:a syg-q b4 lu1- -hfd)aezz4e would give the best resolution in a microscope? Expl-)qz1ey-a:e4- 4fub lh gda szain.

  Atoms have diameters ofi9:,e zh,4 bbi;whdn h about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangi7vamd: ug45y5 kb* pmung 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 ha*a ): )o f7grfdbwe8rns a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that ahnfcskufwm-cm,0ib lwb4 ,4,27lea * camera setting of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photograph is taken at d5z89 m:b-j b76slue9ubkb of $f/16$ 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 rxignkifx;69+p4;j oq4 i.vsto 206.0 mm from the film. For what range of object distances can it be adju 6n fr4qi i k+.x;j9x4sivg;posted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtalr(2:zz2zq +vg(w2h smkv ch -wl tree from a distance of 58 m. What focal-length lens should zh m:szc( ghr2qz w2+kv(w2-v be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, using r)f.wny.jsx fk8v /h2 1el 9kriay diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, e2x)k./fr l8wikfs19vy .jhn 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 expg( a8sjqzpd6-osure 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 abouta vhx 34uuls5+ 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 wore contact lenses corrected for 6w1s 9w jcoov4 gb+yh;the f9 hw+gosj c4v1y;b6owar 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 whose near point is 115 wrv01 n8xw.ip$cm$, 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 3jnj z+7u4t ww14 $cm$. 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 adgy 2*x8cttv7c 8 ngr3a vrk04t 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 corrected by aaaj j 8j1/ rn0c hwsk,-2ygjy: $-3.50-diopter$ 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 objectsm.xxkg5guk*0gm1 -tf 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 Exf(+cvo nnun- ,p+2ws uample 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal lenzub5)g8em 9wigth 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 sysv;zy t1k ;lcc jq;ek-:wo4b )htem 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 of 10.0 and 200vt/t9.un;ddb 9a6j ph+ immj.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 a3f4yz61eu**(k8kwz b mztk sw relaxed eye if its focal length is 1wf(* 6z8kys zewk m4z3kb1 ut*2 $cm$? =    $\times$

  What is the focal length of a magnifying 2;4;alblb;ao xthaw g qzd;(+glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated (sr + 7vkl22ul(6qcv5 nrvp pfat $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is using a 9 k gy mxreg car(qg87:/f9wc+..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 withs- qw+r7 foq8w80vu nf 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 5.55 jno8rnt+f : ;3k7dqqfa.l/hk $cm$ 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 lc4/yir ibu;0 *s)b rgnength 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 abn2d o)w:9(u0iqt7tjwp8a2 u erylg *t $3.0\times$ 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 astrono, m3 ysw1eof97)fkmonmical telescope whose objective lens has a focal lengtwyfn,o m7s9 o1k3 mfe)h 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 telescopgu2elu,pyxz96 zc u s v2lz202e 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 telescop,sdc* 3z f7q6jfr5o71rjjq eve has an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 7vqgyd( rrqrf(;d x451 5.2 $cm$ 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 fo i(, i)szq/fwsme:p w;r 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 astronomical telescope u8uusrud b /z1tv,9yj7sing a reflecting mirror whose radius of curvat1/ jbu y7su8 9,zrtudvure is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears tixln+5 g4uqxht ae0*wexw h6.6fk.( co 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 curvature qdb lg: r-4mnf d0*6bpof 3.0 m for its objective mirg0b :pd*f -m q6rldn4bror 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 focjip 8 ort4h7 -,7kaysdal 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 120- nx9 v6:yuk;ty lbql6y,p5k0).rg cqcqgme.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-:(pq+ kiypkcve()o0p $cm$-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 iskp os:j+,jmu 8 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 2expc:un7v 1x76gd ez6.70 $cm$, 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, place37 i)dvcb8b rod in contact, that have i cb d)orvb873focal lengths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particularrh-im lxi,f9f0rv k+( situation. A planoconvex lens of index of refraction 1.50 and radius o+v-r(fxmh9 ,rk0l ii ff 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 -p u .ztzd9cja42a* dsr09umfby diffraction for the 100-in a du* tfpr 4990.csz-jmudaz2. (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve features 7.0d +(p hbx0 phnh3hrsd 2)l6sw1 $km$ 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 l,g*- dj lg t*hex u+9u-nz9dmcn2gym7ength 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 resolved by awrg7wm+ ) 8-,iki oioy 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 hu)+n 0+sq:ivpi*qp rf0tht 4dmman 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 separated l, -8.y q2e.wwjqmmspai)5 ab 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 whostx6txkv0,vzy 8fbq f /0 0otz,e atoms, lying in planes, are spacedbf,x f0xq00 ,o6tvtvytz/z8 k 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 cyn 4k934*hauu) a pgfya27weorystal. The second diffraction maximum is recoaf e4y*owku3a4 uy) pgn7h29arded 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 observed at7 vn3f 4z3 wg,zfriyz3pu:-ci $\mathrm{25.2°}$ 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 ima(z esd-fbto/ ,ge that the X-ray beam consists of parallel rays. What would be t-s( do/zef,bt he 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 towardorjr f ;a1nt:6 midday, and the sunlight got more intense, a photographer noted that, if she kept her shutterr 1 ao;nf:jt6r 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 -(/i k/dcoysz3cp . izlk7h,efar away (assume infinity), the magnification of a camecp -/o dci7y/l.,e s(hizk3 zkra lens is proportional to its focal length.

  For a camera equippedzp / he9p/ws m8/n0u/pcokj6m with 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 clearlyhadr70;jmlio: h-k 8 yhaia:+ with her right eye 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 poizt7i-pfa) uf92s qpm-. 2ynjpnt of 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 powe nq6 8,pzkku+(w*zpmf 9zxtg6 r 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 lenses f :ubplf9wjl 2:rom his reading gla: jpl2:wb9lfu sses. 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 usesskhhq2od 3o,1u4by *f $+2.5-diopter$ 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 altitu+j6wm 4f;zc .qo9dqpg des (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 times mv6+n ,i.wzdf/(k sn9 cqs(lq just be increased because of the increased distances+s.nl9ikn6 dz(jw/ qf( qcv, 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 a ;n4,o-u1lf oqnb yk1ctelescope 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 .fjfwk5( zfw8m(a5(b 79wjn d n+hjty 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 neafhd jn 7w5k y+(ft5(bj a9z8( wm.jfwnr the Earth.    m

  Two converging lenses, one with zdf 8 7 ;vu195t.c+mplty+bkad:odse$f=4.0\mathrm{~cm}$ 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 two ll*mo3 noek +7qenses 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 pho,ppq;xx7m4 q x;ps4 ewtograph license plate numbers. Assuming it is necessary to resolve points separxqp;x4 ;wpsx4qemp 7,ated 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) hxu fa,11m eln7as 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