Why is the depth of field greater, and the imagfm mw 5bh,u8(t/ ee 23zn8dkkge sharper, when a camera lens is “stopped down” to a larger2 eb(m38gthme 5 zwfudk kn,/8 f-number? Ignore diffraction.

Describe how diffraction afoigzkl, h87oj9* vhdsf19)ncfects the statement that the depth of field is greater and the hkc1)n zgol,*os79 ihfjv 89dimage 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 ouom539f n.xf a closer object?of.53ofm9xnu

Why are bifocals needed mainly by oldecf:jwc (jgq5ak2*b :,qlx z+:tdfir-r persons and not generally by younger peoq z,gd+j b5:cj ax-2:* (citfrfq:kl wple?

  Will a nearsighted person who wears corrective l w/c8mu4mbkq 1/;u-ajsp0psm89 xwqlenses in her glasses be able to see clearly underwater when wearing those gja/k8w 9mlcw u/p1mu qm-4 bx 0p;8qsslasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a 0k:xl 17 4itksgnp5muperson is nearsighted or farsighted by looking at the width of the face through their glasse 7xl 5g m1kit4us0n:kps. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern i,(t *rgt ypalw2 a;6wdistant details, people will sometimes squint. Why does this helpw26w ,p yal*at;tgri (?

Is the image formed lkdx bmkuio.nuit000v2 i 12sx2(bl 5on the retina of the human eye upright or inverted? Discuss the implications tbl50 o.bxnmdv skk20i1xiuui0l22( of this for our perception of objects.

The human eye is much like a camera — yet, when a camera shuob 53+7isrqpltter is left open and the camera is moved, the image will be blurred; but when you move your healribo +ps73q5d with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simplesb4 oyjb3c:p/ wpieh2s.y- : r magnifier is also a converging l b yrhj.:ossyw:32/ebp pci-4 ens. 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 children’s use usually produce images that are col fv. 6tdwrt080ui(y zkored at the edges. Why?68k 0 rtzu.td(iy0vf w

Spherical aberration in a thin lens is minimized if rays are bent equally by th 9a i-poro:f81z/r(6yss k1gdnxp l b/e two surfaces. If a planoconvex lep1opzasr - l9xo/ / rgbfiy( nd61sk8:ns 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 len uzy.1woa k)s/alntdu:1; cy2s are not present (or are greatly reduced) in t wy:tk1 d/nuuls2 1za;a o.cy)he human eye?

Explain why chromatic aberration occurs for thin lva0,t8 o+ xwjnenses but not for mirrors.

  By what factor can you improve rm3nm/ja y6rf-pionsp35ga ws4*x b 0 9esolution, other things being equal, if you use blue ax/ r3*wnmay9s-poi40n mp3jb6s5gf light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for -s9ol8 8qzyt qthe use of large reflecting mirrors in astronomical teqs 8tlz8 9qy-olescopes.

Which color of visible light would .yc ad;i/k. ujtpn+s3 3wu9yagive the best resolution in a microscope? Expl.t9yja;k w dnsu u +3.ycp/3iaain.

  Atoms have diameters of abhksj +6he0nl6 pv* 5ypout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has fp*h bismw hs.e7iw7l(4stznux f y4iu,l-/6.-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 hatwl; juj) *h;7t d1xyms a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a ca;eo4r+ xokt5ai:f h f(mera 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 photop.5 t59olibr ograph 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 kqf: e,bb *x04rvq4jzbe adjusted so that it is 200.0 mm to 206.0 mm from the b0qj v,zf x4r4q ek:b*film. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer5d3jv xpjwfikw(/ r1:r) gfo1 wishes to photograph a 28-mtall tree from a distance of 58 m. W gf)r31rjk xv ijw1w :o/(pfd5hat focal-length lens should 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 ray diaiayp9n+y (sk 9u.c* st.qpp*t grams, how reasonably sharp images canctkip.*y*tps9u(sa +9 n yp.q be formed using such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct exposk;uynvu. n5(ijbp u40ure 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 aboutx 70 nyt9-n zdxghh053j)cveu 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 i9 fn j- c3;gsrly n)ul/8cdmy6n Example 25–6 wore contact lenses corrected for the n69rsc-nu/llg mc 8 j)ydf; 3yfar 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 7 tcjq8au* 1pxkfvc0b) gpt,7near 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-df)zec8mxno7 rfv ) u)y;ucv0f) ,ar4 $cm$. 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 lm:mn1 )yyq3p**l iaxyength, 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 corre r/(ns:(acwm fcted 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 objectof)tsn;:lznop m6j(3 nrpt/) s 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 nearsighteduwp10-6r nf :8ch vo;n;abvrnn7jr l) eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyvgnq+; lr) cu6eglasses 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 whe ga;;zwx6x z4rn 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 ohtd-9j d igj 785ixnx92ev(guf 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 im7y j*6f ttge*hc )h*jf u j,tk(op34wf its focal length is cm4*th 6ept fj*3k *tgwj (yh,7 )foju12 $cm$? =    $\times$

  What is the focal lewfxdyc42pn 4-m jo f2, a66c6x/pkdzs ngth of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated60pfspz 1 zxqua9e- /o5ib b0s 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 usi*jbrv ub:e4j2-bek /t ng 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 viewetteuw3/5v g*l w1e 1wed 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 place+(hid;l gctb, d 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 m j)r:uqc xtkn +26y,sqq6cw4dxp.7v 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 is ra,z-gvitq)ko/ce 0 d2 ited 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 8 jo+k lgk)av hs2b4a5astronomical telescope whose objective lens has a focal length g+25v8khls aa )b4ok jof 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 g0d c zay. wnykyg+9 b5l1emh c0-aq;.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 objectivefvjr+ a v*n2z..8biz j with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lensmvy/lmpn: x he7a+:f 7es 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 finn+/0jh :dp jphs6.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 astronomicalemy pc 1ee9:5b telescope using a reflecting mirror 1 mc:b9eepe5y whose radius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be m3kh ,n/dv jtm7agnified 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 b4tp0 *vkxm,t6-hsw,ohif l7 curvature of 3.0 m for its objective mirror and a radi h sf,*i740o-tvtl6kmxw,bph us 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 anu.ekw/ n4ids)og.fq y1 nu b86 eyepiece 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 12g hy-dyn uca0 9d33g mttx8h9*.iq(ht.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. i72gxpg fw-9q8-$cm$-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 the3h , avw;sbavk64;i*mrraxlz w*:*j x 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 nqp),n7wp qutp- y97ufocal length of 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin lenses, placed in contact, that hagztt 62 rxg2m4ve m42x6 tt2rgz gfocal 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 abelgvtw. tmye q tq+75 j982rangql/ (j:rration in a particular situation. A planoconvex lens of index of refraction 1.50 and radius5a 2r/ .:qynet(8mjwqlg qv79j+t ltg 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 diw+ dj4lwt o;7rffraction for the 100-in. (2todj7r+ l4ww; 54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a te 5t(j5 ntk9 khk2y3amn,fd lg/lescope 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 fota/hguik5d7 7m3 3h 5edy/apwu*+my ncal 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 bm0x6q) i bv/ hn4o5kymarely 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 distinguish two4d,7q;yt k tco car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separated by abo.fk mi(iow ckv (-h3lqwb70/o 9,myljut $400\times10^6\mathrm{~m.}$ 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 atomw/yzvdg u*s g jaz:8zu5 6 +nuz,kkf55s, lying in planes, arek 6 5ws 8 zf ,:u/gz5nuakyjug5vdzz+* 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 second l3t3 aw7.yyig n*q2nndiffraction max. ywgytniqn*7anl33 2imum is recorded when the X-rays are directed at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is observed t y-f8gczhol,8d7yxfp;9 (rgat $\mathrm{25.2°}$ 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 thek:gdmptrr; -1 X-ray beam consists of parallel:g pr 1tkdm-;r rays. What would be the 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 toward midday, and the su77,mfas lyr( a8j7bnsnlight got more intense, a photographer noted that, if she kept her shutter speed constant, she h(a s7rjm7 fsn,7y8labad 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 ofk znli g/1.p(j+ itxm77imv2y a camgi ivyn7p7 mxi l(/.+kmtj21zera lens is proportional to its focal length.

  For a camera equipped with a 5k6/1x05al/8hezmcf / dzo c rt0-$mm$-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 bbqt0 j /9 rmle99i/ofgetween 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 po5g;d6igj1eny, w (c nyint 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 cbn6;kf j/da7hy 6) /bcg/pnwpower of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries tdist,7 )8c,xdek wzid6at)t5p(/ s uto make a telescope using the lenses from his reading glasses. They have pc7kix,,edu tt5 sd( 8dp6azttws)i)/owers 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 usesr 6/)tcp85//ui6ygt bs cvk0 yk3rhrj $+2.5-diopter$ 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 5-n+tb:mf0)gafz+we x j8nzwhigh altitudes (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very shorlyb7 o mx,+-mgt distances, exposure times must be increased because of m7+xlm y-o g,bthe increased distance 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 tiz+e15s5h. sz yz tmkcr9884m 9 qnhvjhe eyepiece of a telescope are spaced 85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective diameter of 2.4 m, odz1+k,jm4al,xpl 1j 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,,lj4 jl1oz xmk1+da p Hubble is near the Earth.    m

  Two converging lenses, onecyc:t5f5 og8 x 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 telescbyu :a,w6g;v j wjch(i(b8+xcope has 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 satellx7( ebnb( p js kfkhf4:se x1n),d2p5site to photograph license plate numbers. Assuming it is necessaryb)jfb 7,fsep52 e4x dnn:k(ksxp1(sh to 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 sur:zmkk:oa,b( z1n0p jeface 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