Why is the depth of kfo/gn hj r7-6qoe 4-wfield greater, and the image sharper, when a camera lens is “stopped down” to a laro4ne r kqf7-o/hwg6-j ger f-number? Ignore diffraction.

Describe how diffraction affects the statement thxky ;ndb8b ,v xj 36/:ydxvr:hat the depth of field is greater and the image sharper when a c/jb8x x b nv:h6;kd3yr ,v:dxyamera lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focuod icj zm-md-f9c4m79s on a closer objec9 9ccmdmdzifo4 7m--j t?

Why are bifocals needed mainly by older persons and not generally by yav9v q5 vx,c*zounger people?q5xac9zv,* v v

  Will a nearsighted person who wears corrective lensf f)fk)t9j1ruyat6t) 5* ugftvqri+4v d s-.ves in her glasses be able to see clearly underwater whtf+5 ) ti)kf* vgsf .d4jf9t 6-uqtv)uvayr 1ren wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nexfyo 2u-,5qh38mpj) a.y co tsarsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Belomaq s-.fo2h yc38u5,)y tj opxw), is the person farsighted or nearsighted?

In attempting to discer5o/f -qgkt womgc*)j+ n distant details, people will sometimes squint. Why does+5/gqgctfk *wjo -mo) this help?

Is the image formed on the retina of the human eye upright or inv5 6w beo/z u)ne)4teoaerted? Discuss the implications of this for our p /ou6e zetn)e)wb5oa4erception of objects.

The human eye is much like a camera — yet, when a camera shutter i +sg;z9hp(*yr2rq csfs left open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you stillhs gs;( y*+q9zrpr2fc see clearly. Explain.

  Reading glasses use conve mc-xvx9. y6ahq p9xq5rging lenses. A simple magnifier is also a converging lxh5 9.-c6x xqavmqy p9ens. Are reading glasses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for childr6fr/-y v: epflen’s use usually produce images that are colored 6:yff/- lprv eat the edges. Why?

Spherical aberration 6fuxddf)7as: in a thin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is u daf fs6:x7d)used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or are greatly reduch.mr* kl 3 w8/bpn5l7s avjk(red) in the hu l8lhk 5r.r(vspwnk j73*b am/man eye?

Explain why chromatic aberration occurs py jsx-1qvmg(vs:7 .efor thin lenses but not for mirrors.

  By what factor can you improve resolution, other td6n ris)c,)7yryihl2 hings being equal, if you use blue light67s,l)2y) i hrndciry ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflectvkre7 *urmys4gv 9b1(ing mirrors in astronomical telescopy94rvs7k1rmgu * bv(ees.

Which color of visible light would give the best re tqw1o ;n0rpb2oj- 8ogsolution in a microscope? Explain.1 j; r8obonqo 0t-g2pw

  Atoms have diameters of about6 q6hp7e :if3cw(xcbioj14ibbs.)b k $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has,audr(nl hy6 6flc .7x f-stops ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a 14p73mu4e6 vdf v7 gf)kzms u53u-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera settxfz1 cz//+wg ping 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 photograpuiba cg,10bwzj2n+6 0wr1fns h 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 beojv.uma)+mhp1ae* f+n 0*b kpq xu4z: adjusted so that it is 200.0 mm to 206.0 mm from the film. For what rangzm+a*vb jup):0a k4q.n*xufe pmh+1 oe of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishe+oas:eh/ g, fqs 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 height of tf o+/,hqga:sehe film?    mm

A “pinhole” camera uses a tiny pinhole instead of a zki.bim9q 3 a.lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider twii3.b9qkma .z o 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 exposu jv pw7e6+y6/:,sy 0ypxxcdbire 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 2.ha )d p8/gzci+9 pmr2tuet)b80 $cm$ 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 wor 9j6w7makxp,y(e-p ekj.h-lse contact lenses corrected for the far po x-k.9em6 -pae,sh7kjwpj(l yint $(=\,\infty)$ 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 needeqm1kvpb( i-l;v.1thtd 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 poi u(e -qrun x:gzsln035nt 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 re d1q(sgnl-;xmywgvdr0r8s, 4 ad 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 isc7ce7xgew p*+mro6s62vu:l v 7dm)mc 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 can see objects clearly only if they are between 2.i:hqu.o/5lq0.wofr i6kjtw5 $cm$ 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 nea6mg)btqx 4y(;sng d2n rsighted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsightet6 du;p 5cvo2jd 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 viewing an object in bj om,qp51eq/-8ua
(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 andi ky(5zbd f*b) 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 magnification of, 4 8qz+r vir-jvawhg-w +xdp, a lens used with a relaxed eye if its focal length i-wqrd i8+h-v+, g jpv ,4azwxrs 12 $cm$? =    $\times$

  What is the focal length of a magnifying glas0xgp/sq *g/na s of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated s+v:p/.n aj 2rz w8ko/hwrff*at $2.5\times$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 usingfr1obdatijo89 k,,8c 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 iyienh4 ha4 6l(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 placedk,t.q lfwymivho(m7/xi57/ q 5.55 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass with a fof9 bz:/j3 atjmcal 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 is ratn(dj3pck1uu8ul qw+5ag9 rf 6ed 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 ast71p4 ;g oeif-;y8mgtvw /xnq zronomical telescope whose objective lens has a focal length of 767fp1 ;t 4e zogv;qyw/mxgi8-n $cm$ 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 oee2jxk5*oo c :5rd+fbf an astronomical telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

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

  An astronomical telescope has an kjpfma7m0rr+9y, cw 0objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescon rm)voa;+ se5pe has its two lenses spaced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relaxed eye is 5m-bud*a6+sih wra e832.8 $cm$ 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 telesc/;zxy0h v 5jej9kiap2 c0sbt/ope using a reflecting mirror whose radius of curvature is 6.0 xj e/ /y t0;i9k zs2a5cpvjbh0$m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magyei3-ar,-t mv nified 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)ocd 5g(hmnp5:ui mrmj29s0j kn b91b. Below) has a radius of curvature of 3.0 m for its objective mirrorj5ubn2g :m5 0b9kr n(hm1jiopmc)9sd 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 9pf ttqi,*- b-s(zokdeyepiece 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 16fb. q*ar2p)ads u,ai2.0$times$ 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 1.8g/ qmbydyu 6/6-$cm$-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 25 yz6hli bl3 f20h5 euc0$cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal lengk,3ad rvz ably4;571h /typsrth 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 ).ebsvot-2 y pcontact, that have o)-y s2vbetp. focal 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 particular situation. A planoconve(c dso.*wtj)phjw;h 1x lens of index of refractio1whh.( *j)oct wps;jdn 1.50 and radius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction f6::i :rika6cktjr6mqsaf 3 p( or the 100-in. s:aifa6kprj3 6qtr :cmki6: ((254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope m6zg,n;ekzc 9 myu-c3 that can resolve features 7.0 $km$ across on the Moon, 384,000 $km$ away. You have a 2.0-$m$-focal-length objective lens whose diameter is 11.0 $cm$.
What focal-length eyepiece is needed if your eye can resolve objects 0.10 $mm$ apart at a distance of 25 $cm$? $f_e$ =    cm
What is the resolution limit (radians) set by the size of the objective lens (that is, by diffraction)?
Use $\lambda=550\mathrm{~nm.}$ $\theta$   $ \times10^{ -6}\;rad$

  The normal lens on a 35-ha(z4gs)h-i sz60evn ht f97mmm camera 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 bag9o;k m05cw yarely 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 disqs ikx1* dtx2 cdo8l3wkg3w id)q94 g9tinguish 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 se jrjq24(h+ak lke c:i7parated by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fall on a crystal whose atoms, lying in p4ree 1cnlk j6982pqai r:ftv 9q- fd2klanes, arqqvc rpt814f9j id-a l:k frek9ne226e 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(s av)(x/ 6i 8uteacko nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directu)a8a (sc(oti k6 e/vxed at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraci :o,;q4 im b3 e4zwe)j6vn1kxu8kirbtion is observed at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that uoj.u ou7of;kxdy-55qb) mzt 2;j f z(the X-ray beam consists of parallel rays. What would be the magnification of the image? a the u5 fz ;-jobt2xuzqd ( k.5o)fj;uyo7 mmagnification 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 zhx9mbfy 3lov( 8h7kaq p,p(( the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to c( ykz phpmq 3(o7x8,(f9bhalvhange 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 ofacymyv67ktod 3yl +g;0o4* ll.puxl 9 a camera lens is proportional to its focal length.cd+yl u p;v xomygl.*y l03t76ao4l9k

  For a camera equipped with d 5kofki ,d/owwi15d(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 be0p.uvzqt q6y v-1r o/+qb2ecutween 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 o6rht0hsm*v*l f 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 ofzs1yeb*84q i)vncnlz :x cmx+:eiz0: a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in tlt(n0bs/3- ;gbvhdsfvw:t i2 he mountains tries to make a telescope using the lenses from /gh(s :;nt-svdb iw0l b2f v3this 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 use674gb4sw w:lcs kzp.as $+2.5-diopter$ 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 a*r,n y+vu*otw ltitudes (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 must be inh :egfs++yyf;om s tijx/5*s 9creased because of the increased distance of the lens from the film fo59x fy ms i;th:s +yfose+j*g/r 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 te6f 2albuzh,jy(01 nqiz*wujzi9 95t xlescope 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 tsov*h q(wa*k3g)h6 ;nc5v ou, with an objective diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that t 3wc k*sa*hq ohg 5u(t)v6o;nvhe Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one wfnzd0ero0cw2 i8- ;: spi-senith $f=4.0\mathrm{~cm}$ 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 *h.t8z)soknsb 8ug :w magnification 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 photogra;w(v b:gm9w zkph license plate numbers. Assuming it is necessary twz( mvbwkg9 :;o 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 sr04-wfq3jvfov ,2pj 6lk y i0x12md qcurface 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