Why is the depth of field greater, and the image sharper,mf04y** 6lyq kleueo)7a9zar when a camera lens is “stopped dyyfoa6* e9e4rllm ) 7k0auz *qown” to a larger f-number? Ignore diffraction.

Describe how diffraction affeevkl6* ryyx7 v0c 0bt.cts the statement that the depth of field is greater and t0vxv.y bce7tr0 k6*lyhe image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be mhc6ock5fha8lzncz9:sl.82 coved farther from the film to focus on a closer objecta:f oc885sklch9z2 l6ncz c.h?

Why are bifocals needed mainly by older persons and not generally bh 3maz 75sh5eey younger peoplmesh57ze3 a h5e?

  Will a nearsighted pp vqhrnm dq-yo c43+09erson who wears corrective lenses in her glasses be able to see clearly underwater when wearing those glvp-dqr0 mq cy4nh+o 39asses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted or farsighted by looking at the i7+4wu os3khwf2ch2l 3+u8 x5 +spyb(oltyxk width of the face through their glasses. If the person’s face appearowlp 8xf5hk7u32 o4bics(s2+ l+ xy3k ywuth +s narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to disceg 3lpqnu tp7 ma kpg,:)s47e5lrn distant details, people will sometimes squint. Why does this hel53q7l,k4m t pg)pusap gle: n7p?

Is the image formed on the retina of the human eye,t*9qq*mh n )gyiz.))kg nq d-vgi wa4 upright or inverted? Discuss the i g d4i n9ngyza)). *,qqq vkmht*g-w)implications of this for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter is left v.e3yklg*d9qke1l 9 czd, 07 czam.to open and the camera is moved, the im3la ,e1kzo 9.7c0vdydk9celg q .t*mzage will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses02t2t1w l,fjzrr uo0f . A simple magnifier is also a converging lens. Are reading glasses therefore magnirlu t 2w0o2ztrf0j,1f fiers? ----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 that2x i +jx.nu*mr are colored at the eu2* nxr+jx.m idges. Why?

Spherical aberration in a thin lens is minimized if rays are bent equally ha/ck s)- -edxby the two surfaces. If a planoconvex lens is used to form a real xca dh)ske/--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 tfy)(arf6 t+tpresent (or are greatly reduced) in the human e+)r fa t(6yttfye?

Explain why chromatic aberrationlcvta a*0 gj5x.5yw 19rs ey7z04uxid occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, ot9a0gc q 06rajjher things being equal, if you use blc0j0raq 69j ague light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of largep/ .t)puhu2;ikqs9 1vxjogvot*,k i3 reflecting mirrors in astronomicai3j v,k2k;x/p 1s v)9*.pgiqtoutho ul telescopes.

Which color of visible light wouye*ma +h7 ec0xld give the best resolution in a microscope? Explaye0e7cxha+ m*in.

  Atoms have diameters of aneeq ut /eo-oaz4; owl6 q/8f2bout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stlrx6nu * bpg x4-p0ii:8 vaig*ops 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:s6tgl -jtto + 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera setting of ,v eptdt)v4 /p(l3hni$\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed ph-c snfgju9wt j1*2r;x otograph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be ae;j9vv0-.j ni- bo phe(e24 tyab ug8,,axkzfdjusted so that it is 200.0 mm to 206.0 mm from the f2je ev-. oz pih ,yj0agu xb,8av-b(4t;9 enfkilm. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtaaooo* .r2e-l7ftfu flmt,+, mll tree from a distance of 58 m. What focal-length lens should be used if oto.l,omlfuf+,7fa2*r-mte the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead / :wgd*5usyq65rio e.f opk6q of a lens. Show, using ray diagrams, how reasonably sharp images ca/ ugq55o fy q*p.6:okr 6esdiwn 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 h)sthg.(tnnsz/bw, 88*fa.qcnkl 0q exposure 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 akwcy0)q cm0*v bout 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 Examplef6x5x v3b12rv+vg2; a:yj+ tt pgykqe 25–6 wore contact lenses corrected for the far j yt25tfvv :ba2v kyp6x;1e qgr+xg+3point $(=\,\infty)$ 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 : 7h s;wnevja: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 1p1-px4 m/ xy .gspti7d4 $cm$. 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 4m-1hm64nmifh k )utda 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 is corrected by 6o7znzoe /zd fs(uw91a $-3.50-diopter$ 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 s: uq1;xw wa am/we*szvrqk:: +o q-r1cee objects 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 inphbx) 4l mq+ix3.tjcha)0 z7k Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s e8lc,ugpq;4iz 5wgmz, e14tn0xsf3 g syeglasses 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 d0x10pn- qh;f)s tkn kxv l28zbgw0r6when 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 20.5rkk,wsx rk nmy n+3rk,it -3.0 $cm$, 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 magnificatib2-sf. i p 3wmd-pavs+on of a lens used with a relaxed eye if its focal length i p3b.f+ ma2sdvspi--ws 12 $cm$? =    $\times$

  What is the focal length of a lxh np9lo0)o;o/cc3 wmdl5 8(c4 nwqtmagnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated azd yty)).a(hz t $2.5\times$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.uq;:u a8r0m3yu odi21xc bgj,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 z1 .+ y er (hykvs6in,3bfvvp,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 placed )c im0sw0- zrotux::p5.55 $cm$ 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 length of 8mzcg6py wz op ,v,*20w.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 .ay awef)1.kc rated at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnificati.i- kxynvt4m+on of an astronomical telescope whose objective lens has ani4kytx.v+-m focal length of 76 $cm$ and whose eyepiece has a focal length of 2.8 $cm$? What is the overall length of the telescope when adjusted for a relaxed eye?
M =    $\times$
L =    $\times$

  The overall magnification of an astronomical teleqvv 5 yo1rz.(s3hdj-jscope 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 objoedjn 14sf ;3rw 69qt+r;eweg ective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lensw; z9er:k x.baes 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 p6re*6( dgcosrelaxed 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 wdfu3o wk)7 ,gtb y2r:an astronomical telescope using a reflecting mirror who 2)wdft,b:wyuo7r3gkse 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 magnifiejm, ,acdu+fi1 i: l2 1)1s 4urauwrfzed 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. Belo8imt-+a +ijrs bt**z vw) has a radius of curvature of 3.0 m for its objective mirror and a r+**sz 8-r itvbimatj+ adius of curvature of $-1.50m$ for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the photographic film to record the image of a star? $d_{2i}$ =    m

  A microscope uses an eyepiece with a focal lenvemv:5 g5wczkxzd clo54 1w*4gth 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 12.0d0anb :gyhdwpf768zl r*1 7ac$times$ 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 1.8hdb39j p aw2qt*/us69tt 8vre -$cm$-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 ass ccv.-9j*l wxqqh4,0dtfgss+ uming that the final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has arm dsb 6:.hm e qxs.wz0x8*7cn:riba8 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 is made of two very thi n)- ojqgkad):2rg(eq* mw4g3 6hmpskn lenses, placed in contact, that have foc*4) ka qs- 3pm hdjmnr(2e6ogwgq)g: kal 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. Agp8ij 0 5v.ammo2qr m; +ocg-y planoconvex lens of index of refractionmpg-og2v 5r;y80q jm.ac mio+ 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) sbr2n/z :l6w*oi orrb 3et by diffraction for the 100-in. rbo r23:/w*b l6iznro(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 featu h*we0fr/9ukwres 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 camera47buij kyw1 pf*x0ff * 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 barely reso3b bf/yir.n nu;*b-; ,kvkjc63op srclved 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 di:yl9c a3 ta o1zo(b4histinguish 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 by adt,t+qyd ukr (u576habout $400\times10^6\mathrm{~m.}$ 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 .c,0zbh62ukv+o.v nbk+ bh s7 f.lj etin planes, are spaced 0k2vtj+0f.k cebolh bs+,.vub . hn7z6.280 $nm$ 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 ubj.6-4/ -n9;gdu hni/hmkb1jf yxjr are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are direct9nb h y; 6bmiu/jkrj/4gxfj--1 ndu h.ed at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg difnp*g/ig .ruch6 gp, +yfraction 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 ed( hef+ ;z /nbqab)x(that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnification i +ezb(n/ xe)(fhd ;qabs   
(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 mord vux yc.g,lcu m-0z3h9w4zoipop3)2e intense, a photographer noted that, if she kept her shutter speed constant, she had to change the)puwh vlx3z.o-up0c 9d2i,cog3y 4zm $f$-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 of a cau0s7ol (y2 wr2szxn4 by sus02mera lens is proportional 2y2n u4lrso7ys0(sz 0x ws2buto its focal length.

  For a camera equipped with a 5 5swzd6htx(k; 0-$mm$-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 bet7axm prw 61cx4:nbzqa 2 -mzs1mb5ry,ween 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 of/nv yxb//me*5g*yc dq hz)z c6 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 powemjf87+c mxs am+,g,k ir of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains triw1x9z2oid4x .tlcm 5 i0tnhyakd79e8es to make a telescope using the lenses from hiskx5ny4m0 zxcitao2 8it9 dle.dw1h 79 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 usesbfb2q--urj 8 p+rq be2 $+2.5-diopter$ 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 extre7+ msi x3wy,h-*slzg ymely high 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 short distances, exposure ti/b/j4cps 4rjwd4- y gzmes must be increased because of the increased distance of the lens from the film for a z/wbj- g4s/ pjcy4r4 dfocused 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 spaced 85 r.e3 ,vccqky) $cm$ 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, is u6zj6mb;xo+nv8sn i;u( * y )bizse 2qviewing 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 ux ) b8 mnnu2i6z;jyiz*;s6qo+esvb(Hubble is near the Earth.    m

  Two converging lenses, og k5l89ai6a(53n uinzo 3 ahti*z pc0wne with $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnification of 8.0. If the two lenses ar 0myj8 6sdjrh)ucb* d k0m1nf8e 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 pla6r8jld:8m9/j : zszh js(joblte numbers. Assuming it is necessary to resolve pointsz:8bs s d6lor/zj(8m9ljjj h: 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 fl s wfw:miriovmh( 91/n)f;x,rp jrx75at 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