Why is the depth of fieldv(y873(f urf dbxq +id greater, and the image sharper, when a camera lens is “stopped down”u8rv f7ddyf(qi (3bx+ to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the deptz wivnos7qe tu )3056dw c0lz;m25bgk h of field is greater and the imagec5owwuigsz7m n50;d3lzv tqe b60 k2) sharper when 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 closer cd5qgp*9ml;en qgt 19object?pg9* ce51tdnqml ;9 gq

Why are bifocals needed mainly by 8zn -f s-upm)wolder persons and not generally by younger people?mn8-)wp -s fuz

  Will a nearsighted person who wears corrective lense+1h3*v mk ;sh oidw+nes in her glasses be able to see clearly underwater when wearing those glasses?sw3ik1+;dh h*nvmo e+  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or fars nwb bv-kje,jvld80c081i -gxzar +1oighted by looking at the width o kcbr-8j 8n va0ed1-ixwg,z+jbv10l of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, peoplk5 r24z*n ;i hs4ihlqie will sometimes squint. Why does this hksh2i; lqzi44i hrn5* elp?

Is the image formed on t.vsc lyis2+p -he retina of the human eye upright or inverted? Discuss the implications of this for our pe+ssl2y pcv i.-rception of objects.

The human eye is much like a camera — yet, when a cayjjcblk/v u8-j 16 v6emera shutter is left open and the camera is moved, the image will be blurred; butue6y8b /jkc-vvj 1 6lj when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is a+wnvu 3gwv9ms84 0*g cq sbe3glso a converging lens. Are reading gla3+gg3 4svvgmnbw0 8 w9eq*scu sses 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 produc8g h3++mv(/ nstyar9sfxmv; le73avhe images that are colored 7v8m/vyfsr9sh3xh (gn t3;+m +eaval at the edges. Why?

Spherical aberration in a thin lens igse/.e 6qo 0uew,ee(q s minimized if rays are bent equally by the two surfaces. If a planoconvex g, .q0ee/ eqew(ue6so lens is 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 pr*ch.1y( qtik nenu wn2nm;* r0esent (or are greatly reduced) in then i2t 1c k q*(my.*rh;0wnennu human eye?

Explain why chromatic aberration occurs for thin lenses but noth2gm a5xc*q4h for mirrors.

  By what factor can you 1:keg/ztv5 ryd,u )liimprove resolution, other things being equal, if you use blue light ,vzk1t/ ru 5 ilyd)ge:($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors to7ek-b1dwmq*y :s/ /x9abr tin astronomical telescoy/ :edtbq-twamx7 o9/ 1bks*rpes.

Which color of visible light would give thy k 6vb;:dhke-dc(ul: e best resolution in a microscope? Expuv b(;dkcdhke -::yl6 lain.

  Atoms have diameters 16fm) o mngxckrm1p7iv :.jk 2of about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens h n 3- u (ukqrq2nos4,jz:la:slas 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 knc iirfv0wu+k2.02x*fumw314-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera setting ol 5ncg:3q6az(oaq*vsi/-q( ) d vgfn vf $\frac{1}{250}\,s$ 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 vcb2mrp0 *xx 6is 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 isqcgodgm36nkgn fw+;*2 ew7n 4 200.0 mm to 206.0 mm from the film. For what range of objeccgn3 d2gm6 ww4nokf*gn+ ;e7qt distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishe2nvr6 k3d;wr,.bt( +4s igdm2brseni s to photograph a 28-mtall tree from a distance of 58 m. What focal-length b4,d26rv(n; skegbis 2w3dmr+ t .nrilens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole insteadn34h 8ydcg 8jq of a lens. Show, using ray diagrams, how reasonably sharp images can be d3n8yc jgq 4h8formed 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 es f0/ *js r dw82qu+x(xrixu+txposure 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 2t-w ,gle8o 2r.q ik:fi.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 t8 nzr olsnu)a61rz8/ ehe far poisz z ou/enr86ln ra18)nt $(=\,\infty)$ 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 neu4 ry -5hqsy av-: k;-yec6vwzp tg+t2eded for a person whose near point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point of 1 csb37cuu0)l5m7h cs x4 $cm$. 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 lenk. ) yadqac fw4uy/:r*gth, 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 corro 7xkf,s q2b+dected 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 wa xoo t9ol pnmg+0g*7kofuk tdeq:, -j*7:1yobjects 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 t.u 1wt0yp32491f dyd xfm)0cwvwuiq lhe 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal leoc+ 8crc .f2dtm)s0pt ngth 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 sys 0) zo7ufeamd-03csjqtem 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 h1d cbjq3 b.ap q:zn:-1 i.zbcias near and far points of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens used with a relaxed eye if its focal a:ul;w0xck.j7ahw 5 i length is :xul.i0c ha jk 75aww;12 $cm$? =    $\times$

  What is the focal length rgixlo (b/;8c5w ixla9v,og *of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at w hw gh+/z-wo2 2bl:rfl8np:u$2.5\times$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 .(x-w7uu/rwdi 9)rouh4d y pg,he:eza 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 aly s4l+plsn 5vg;(9si 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 5gvfb oc/n 6az 1qu5k*1.55 $cm$ from a $+6.00-$cm$-focal-length$ lens. Calculate
(a) the position of the image,    cm
(b) the angular magnification. =    $\times$

  A magnifying glass with a focal ldaavg,44m * jtength 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 epfv8me8te2(l0i i h9 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 telescopome fiquyv ( b8;)ccvn+abi3 po+ cj78g h..p4e whose objective lens has a foc8i e(qnbci).v4m cou.p;jb+ yagfvoc8 h 3p+7al 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 astron ,v76 a(h,cqbw (co*pzo6qtfe omical 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 objective with focal leat)59bnqc v)qngth 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lensesxcpegh q 6rbzvip(s5p+ ;e *94 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 adjuya2klsa-k , ;d, st5yssted 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 a+yk.:p vr.mxz n astronomical telescope using a reflecting mirror whose radius of curva +.myxpv.r:zk ture is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be ma5a, vqq8 lgos9gnified 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 r ) f(hlehomil(2r7i jv2fuko,1)y8b madius of curvature of 3.0 m for its objective mirror and a radius of curvature of emf m(8jv lfou2hb i)lrh27 k1(o)iy,$-1.50m$ 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 winejoxo9rg-4j 8 vp6 r6th 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 12begdo91e;2d)meap ( f .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.firai*ta9 -l1d17s,0 jnt evi 8-$cm$-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 i1y:-bkp t.v ucmage is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a comz0uq8(( wvim w2hp v19rp oa2lpound 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 i*h3wcwk fif 05aaprh;7kv; ;b8jw9e ls made of two very thin lenses, placed in contact, that have fol9;be8 aa35; hvff;p r 0kwj*wkich 7wcal 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 partic+p(: +kh.,jft *hd hmf.tys ose,m5rk ular situation. A planoconvex lens of index of refraction 1.50 and radius of curvt d.mpsh kjf +t,, ymh+(:5.ke*ors fhature $R=12.0\mathrm{~$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 diffra(px/mcnc7j bl1r+s70h-lbj qction for the 100-in. (254-lsnp0/j7 7 1jb(q hlmbrccx+-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construcswr: 8f4 gnuo: pz(g(ot a telescope 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-mm camera has a focal ll4wcr 7u/2ff 2qc qc8xength 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 a 55-ry)u +t-pf /s6yib /vz$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye distinguish two car headlights 2.0 k ts4-+1/ jekxkxjrg. $m$ 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 separatey:i,5x* moru4gqn3dx d 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 0.133li 5q3 b2jd*xa nm fall on a crystal whose atoms, lying in planes, are spaced 0di2qj 5lbx3* a.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 0.097 snty nu/v)zfe 46/ m+*tfdxfr) :jcv43 nm are directed at an unknown crystal. The second diffraction maximum is recorded ws6 ) v dfjyxfuv+ )rtzmtf/nn/*4 :c4ehen 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 diu*7*k lj zji8fbap 9q/ffraction 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 the X-ray j.s w,ae(0u.xl;xyksi :k z,o beam consists of parallel rays. What would be the magnification of the,ks0 u syk(elx:. owij,a;.xz image? a the magnification is   
(b) Suppose, instead, the X-rays come from a point source (as in Fig. Below) that is 15 $cm$ in front of a human body 25 $cm$ thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that results. $m_1$ =    the magnification is  

  Sam purchases $+3.50-diopter$ eyeglasses which correct his faulty vision to put his near point at 25 $cm$. (Assume he wears the lenses 2.0 $cm$ from his eyes.)
(a) Calculate the focal length of Sam’s glasses.    cm
(b) Calculate Sam’s near point without glasses. his near point is    cm
(c) Pam, who has normal eyes with near point at 25 $cm$, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.    cm from her eyes

  As early morning passed toward midday, and the sunlight got more intense, aoercr gl(t;9 3 photographer noted that, (t;cr 9go3erlif she kept 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(d7: 1ij8uk:4wqaxwmdq7pd., cu w3k ynrsx6 infinity), the magnification of a camera lens is pro: djn8kw dwrkms,q7qu a wui71c(x4:y3d . 6pxportional to its focal length.

  For a camera equipped wit ,zm zssu )lis1lan7 k0a4;a8t8o*dqzh 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 between 4b u0,vj); (4nnamw pii5 $cm$ 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 o btkv n :)-lk:pwq0o3vf 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 (iq hb.svtj 46of 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)bj)l sol12e u the lenses from his readilb))2s1eu oj lng 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 useo53 p+quw*rvc s $+2.5-diopter$ 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 altitu4y hfrnalr4*b;xhwh4ych6; (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 must be incrmhe-izponnn/2i k .5 fg63z l4eased because of the increased distance of the lens from the-z n2h pzi4en l/k3fo6m n.g5i 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 telescope are spacfa/i,cqp6y1( (naxa zm2hf0 q ed 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 oiac ;e2*kzq+bvrg ;a shd-/f5bjective diameter of 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 near th aqr;ivksgz + d5*;h/fec b-2ae Earth.    m

  Two converging lenses, one b0kk3-8vhft kf/ qb ,5svpo/ pwith $f=4.0\mathrm{~cm}$ 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 hf+ h9fy5lk /.bnhp2opz *rdf1 as a 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 photograph license plaoe 5:0,sfln)p:i ebscte numbers. Assuming it is necessary to resolve points seeec:) n,o ps i:l0bs5fparated 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,e6a4yk ji0 gj4io2wa 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