Why is the depth of field greater, and the i jw;+uomgph 3g:c.vb9mage sharper, when a camera lens is “stopped down” to a ujvg3;:.p9 bo g+wm chlarger f-number? Ignore diffraction.

Describe how diffraction affects the statement thatw2he1 qom0cuqd:)p-p .l0zb6ai*b h w the depth of field is greater and the image sharper when a camera lens is “stopped down” to a la0obpqhb-i2:1 6wce).wp z0h *qm udlarger f-number.

Why must a camera lens be moved farther from the film to f:5y:a au wfb-xocus on a closer object?ba5-:yw: fxua

Why are bifocals needed mainly by older persons p29(dh*m ajp x,r-b;dx nm.4qn h ta7zand not generally by younger peopjznmpd -x x9tqbhn; aa7 .4*m,rdh(p2 le?

  Will a nearsighted person who wears corrective lenql0jtrr wh*pr r7c nmi81c4-6ses in her glasses be able to see clearly underwat7 1rn ljcr 6-pcq whr0mr*8i4ter when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is nearsighted uhm)o b els*0e.rdbl :7.v *lbor farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower throug.o.r b)0 e ul*l7dv lsh:bemb*h the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squint. Why doe m 5 n(ukg2b yg:zpy-n591lbkrs this z yplbm2kuy bn9- g1n:5g(r5 khelp?

Is the image formed on the retina of the humap tg grj)h)kky. - oec7n8/5imn eye upright or inverted? Discuss the implicationsihk) r -jg5yc.7poem nt/)gk8 of this for our perception of objects.

The human eye is much like a camera — yet, when a camera sh l,keyf(* 18xzfuqcx q h4/yl4utter is left open and the camera is moved, the imagl (lz yxxeufyf84 k,q4q/*h c1e will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a conver)kuxujn2gq / +x9mnq/wvb : z/ging lens. Are reakv/ux+ :) qwumn/9j bnzx2g q/ding 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 axs1 q2p gf) uq5,*d-lok6kjnore colored at the edges. Whyq1f d*,62kl)n uq-xo5s jokpg?

Spherical aberration in a thin lens i7) zt1ron;d t75ph -szg3v(yjbub h*fs minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object a5 )ufjpyvr1zhzgtbns ;7(h7t* o3d-bt infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens z fxw2j7u3ba p2 2ri:sare not present (or are greatly reducerx:bjif2p a2 uw27sz3d) in the human eye?

Explain why chromati2kbq dm zld3+6c aberration occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other ebsdmg6ue1r +z5n4,b 4 q wuu0things being equal, if you use blue lig 4m1regsuze406ndb ,uu5 w+bqht ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors i4 .srnt*b p.ol-vpd 02ygm)jan astronomical telescopey 0p )v nlsm *b-.rt.d4ag2ojps.

Which color of visible light would give the b fc)/s4rsx;:9jsl2zh5nc+tfz4prl cest resolution in a microscope? Explais;l59z r+jcp2hfx n)4ctr 4:clssz/ fn.

  Atoms have diameters of aboux+j )lurfok(8:1 yrqj t $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lh;e uba9:l/f,eq7m udens has 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 lenqbghf+xx a2lhkf3a22x5l 4cvm k+9a+s has a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that:d mjwl4f:rbg8o.:gzc (ti rx0r0l b 2 a camera setting of $\frac{1}{250}\,s$ at $f/5.6$ will give a correct exposure. But the photographer wishes to use $f/11$ to increase the depth of field. What should the shutter speed be?$t_2$ = 1/   s

  A properly exposed photograph is tun/ ,bd7 wsg,eaken 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 is +mnw4q u 0rzk,200.0 mm to 206.0 mm from the film. For what range of object distances can itrw,qn0 +z4mk u be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance of q,jxma.1p; u.b k fws858 m. What focal-length lens should be used ifm.kqbx fwuj s.a;p8 ,1 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+9i kdr-my *15kwhlh d3 k9cnz ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In par*3- m9y1n +ki khzdhkcwd9r5l ticular, 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 correctynk02lj (wz,s 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 about j2-tfjhc vx.42.0 $cm$ 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 contac:c6xoq 46f; ,x qihkzlt lenses corrected for the farl6 ;o4:kqx fxzh6,ic q point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person whose near pointem et5 2p6(ljmi6wtn . 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 14 kejkaa k91dp+sn61 br k*5; fv$cm$. 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 t*v 1wle(5qyl 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 isyk1m+ 9j 3 oget0cxs+w 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 a9t.,eym ul,w*:mz9e 3 ajv3rvn8 teuobjects 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 nearsij0ev07+ps.pk jc*tze0 p njgm 83y3k zghted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a;ntnajt.s .3 x 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 o)12scn h dcbgzgu)i i7w ::*fybject
(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 nearrkw ,l 2 b*z /;w)ze*vulf6xzq 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 4f gmsz6vvpu7+ um:/kfocal length mf u+/gkvu47 vszp: m6is 12 $cm$? =    $\times$

  What is the focal length oxkvjiu 6w)6lx/j2b76w9z.- o nslvqf f a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated a.:;pa pmpb )l65zyhc ut $2.5\times$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 usinb29w aq/ykz-n g 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 viewed with a 9w+dr;c1v/ 5 b fzduuy iazzlh 0k):*wwpz6:8o.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 5qbiq/ fo1l 7ppo*ogrlcve(6 2m.84h z.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 le i*qjg /6+-untj2dfs1kiru:v ngth 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 w.uoktsie6r-g4fz*,nb b 8:mrated 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 telesbnz udwd,a 0 o3/9mtb*cope whose objective lens has a focal length odo z/,bt 9wbnmad3*u0f 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 /b)1fr:klq ir fq5w5utelescope 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 c.ffd5.izc+n j3 .jiey8 5n(,j ozyziwith focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its*pt-ug* y4qlwkmz:;r 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 32.8 k l59kwpmjk 9q8+kbko fn +4fjmhh*;2 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope usi:i*3wkpk-bw ;1hy nkb ia-nr5ng a reflecting mirror whose rak:hb*nk rw3-;w5piyb1in k- adius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears qj(2)u.*bbybgo;y b m to be magnified 120$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

  A 170$\times$ astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
$f_e$ =    mm
$f_o$ =    m

  A reflecting telescope (Fig. Below) has auln1(8sz(o9,lo1zxvabsg4 o radius of curvature of 3.0 m for its objective mirror andnx,o9 s(laglzv81z ( os1o 4ub a radius of curvature of $-1.50m$ for its eyepiece mirror. If the distance between the two mirrors is 0.90 m, how far in front of the eyepiece should you place the photographic film to record the image of a star? $d_{2i}$ =    m

  A microscope uses an eyepiece vq :llr+z3m w.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 12.021 kbd3is n*qi$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1.8 q)k/ b,sxyp+r-$cm$-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 thegz u. xmmczc +l8z0 g(ll48un8 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 b.frs3,z ue7m 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 o/fxy 2)ms(u9 bvves4 two very thin lenses, placed in contact, that have focal lengths o(s9yb)o/eufx vv2sm4 f $f_1=-28\mathrm{~cm}$ 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.+l2xw: kpb//z0 otw*hyi g wr6 A planoconvex lens of index of refraction 1.50 and radius of curw wo *yb rlx ph62iw0/tk:g/z+vature $R=12.0\mathrm{~$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 diffrau:2a fd a5po i-v44fsuction for the 100-in. (2pd44i- a:foa52s vfuu54-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve features 7.0yk i5b:b*7qf mqo9u :z $km$ 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 caahdu q6qy;a24 mera 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 rexhcv.la l*rx ukn7l 78 4y/oi+solved 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 d+k90io hki0e rk9gs-eye distinguish two car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separatxg 2 zvs,jou8+ed 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 nm3pcze:row9(0 l x6nu.j 8 kpza fall on a crystal whose atoms, lying in planes, are spaced 0: 6z nz (e90kp3 awcpjxo.u8rl.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 s5*jyzhatv 355q , defu cox9-second diffraction maximum i u av55*te,yqj d35hofz 9csx-s 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 i)f2lrz 7 p;xlds 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 imz(/osxo 7nt ,xp+ph*bzp)( dxage that the X-ray beam consists of parallel rays. What would be the magnification of the image? a thb7/sdhot*(z )xx,+ppx oz(n pe 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 intensejd 8y8f4 j b7er.ohc1s, a photographer noted that, if she kept he4ejjfo 8hc 71b.8 rsdyr 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 infinity), the magnificationi4 1 v w2kfnq)m3t4e3yi5cf yt of a camera lens is proportional to its focal lnwv2e 3 fm1kftqc4y34 iit)y5ength.

  For a camera equipped wm2iewnda04v - ith 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 betw7g*(p)x c2 nue -ifpt3kuz.i oeen 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 15j*ig . -itos3u $cm$. 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 of cm,f yrod8i8a+;x / bpa $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a telescope using the lenshqre b y)etq( gq6(1a.es from his reading g y(eha6 g)(bteq 1q.rqlasses. 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 use x fwx*;u.glnpxipr y82*7a:ms $+2.5-diopter$ 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 altitudnicv,nw7f; vti+f 8-wa2 fsq7es (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 shor;z3 xety7nld6b4kql y + b)8wct distances, exposure times must be increased because of the increased distance of the lens from the film87nwxybky3c dlbqt6z4+l;)e 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 spaced2x/dev -u-esxu2ar(oi 0/ unu 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, is viewiegzs t (yn1 2dgt0zr:( -,hdbrng the Moon. Estz( d1het rbrsn td0-zg,2gy:( imate 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 the Earth.    m

  Two converging lenses, one p ql;+(* d8hyggd+)ac7tqz 5:twi pkjwith $f=4.0\mathrm{~cm}$ 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 aq/.j fm d*+zdpwo7b 7of 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 photo-niyz4dc(6 z v62yjkj graph license plate numbers. Assuming it is i4kdc26yz(yjv -n j z6necessary 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 surface and the otherr7+ij eh ik/4r 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