Why is the depth of field greater, and the image sharper, whfp8qexff, j7e ;cp03 hen a camera lens is “stopped down” to a larger f-number? Ignore3p c, 8x0e ;pfefjf7qh diffraction.

Describe how diffraction affects the statement that th5svboj vl,8/z e depth of field is greater and the image sharper when a camera lens is “stopped down” to a larger f-numz8 bo5 svv/l,jber.

Why must a camera lens be moved farther from the film to focus on a e+9r f6okpeibns7m7a3, q;vi closer object?i 3m 7bqfepo,6rek+;vai7sn9

Why are bifocals needed macu3 f,gbymc yx0,0/sl*w xykddo 4n.5inly by older persons and not generally by younger people?0kg* nyduc ly5xb /0sm4,xw yf,cd.o3

  Will a nearsighted person who wears corrective lenses in h v,vxa2fun4i*kup y1/ er glasses be able to see clearly underwater when wearing thosey2* /u, apku iv1v4xnf glasses?  ----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 ap)rhjt67w uk/ t the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or 76wr ukph t/)jnearsighted?

In attempting to discern distanaj6;bpa ea5 ir4p(-,,xmzvikv5krzzb/m 5 /s t details, people will sometimes squint. Why does this hev/e/6 ,rx5z4p ,a5z5m(bisk-kbv;maj paizr lp?

Is the image formed on the retina of the human eye upright j.g**l0 th0( gz q iu(*xpgnukor inverted? Discuss the implications of this for our perception (u .u igj lntp g**z*0qx0k(ghof objects.

The human eye is much ,t qxwxw;*8oqpd :o fgvwf9-17jkr h,like a camera — yet, when a camera shutter is left open and f gw, hwvr;fdokt198 q-p7: ,xxo*qwj the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging len;b 1 kg 5hyrreh6 uu;2v*pjuq:)nuv9pb9un7c ses. A simple magnifier is also a converging lens. Are reading glasses therefup9 nurhk6 yn5jhbugp;u:q v)91ev 7u;c br2*ore 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 usugx5d(,s 6hrww j:ihtfa - 2-fkally produce images that are colorefaw ix,fs--6h5kthdr j(2wg :d at the edges. Why?

Spherical aberration in a thin lw) aa92v z8mslens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show m9lsa)a 2w8zv why.

Which aberrations present in a simple lens are not present (or are greatly rede4l sg 6-kfjf;uced) in the huma-;46 sjkfgf len eye?

Explain why chromatic aberration occurs for thin lens48t /jnn(hs:lc k u3gbes but not for mirrors.

  By what factor can you improve resolution, othajbuw+ w. z;30/zoi ixer things being equal, if you use blue light (wuobzaw; i0+ ./3izjx$\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large refl6ku3 aqlbwf36o0kc u9ecting mirrors in astronomi3660 kk3u qubal9cwf ocal telescopes.

Which color of visible light would give the besb,((j*isnpx1 bytm0p t resolution in a microscope? Explapjs(*x ynbt0pib1m (, in.

  Atoms have diameters of abousj1zv- br z-mwu9rjy(b+mjk ,z-vi :,t $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lense; 3wf+io,3) f nw.eprks6q dy 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 lens xax1 ro3x::3rypj07w zsn 6anhas 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 camefhpn69 ht8w *fra 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 photogra l8z5f w 0v:bee pryn(n36yo.uph 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 a j;ky59z)w+xmj9jqis djusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can j5ki 99z+symxjq;)jwit be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mta +5qun4ov:fjqbqz )qyd ),bc 4ll tree from a distance of 58 m. What fc d qq4 )u)vbn:+,54q byfzqojocal-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.sle:t li7gyg49t;h0y ,tucf7 Show, using ray diagrams, how reasonably sharp images can be for;elu c7gs,tl9 t7:0yf4ht gyimed 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 correy(l-x+h ;ddw u bxol*-ct 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 2hfib6*ny-zeus /)p* ) ohj wo:.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 t i)ciyt/jt,-u)e8 fwlenses corrected for the far p/tytic- we u8j, t)fi)oint $(=\,\infty)$ 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 ps 5j7v5p3unq4ljm+h 1ewb r k)erson 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 poin)o-z-nt6hm ddt of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holding a book at rxq/ g lg*0 xbpf-9 3a;fl)qlzarm’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 isp+tm/w:m dtzzz4c k)0e 1rsp 6rij9 :b corrected by a $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly only if they are bety,8hron d. )qyyy s;-zqaf:1yween 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 nearsighqwuyyeb*95b7 t(cz.mted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses ha5pjti lkx2k16s 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 w04;w yg uxzo/yhen 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 pointstqac/ b3vb-/n;ydy /s 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 usf ay5 wmd7/kc+ugs 1p(ed with a relaxed eye if its focal length is uafgm 1w c+ks7ydp (5/12 $cm$? =    $\times$

  What is the focal length of a magnifying glass of5r2ei13hfyn m b9twt - $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated a6h seh :z(o6vhtyxd 5ae 5eg( e89owta8k-a *dt $2.5\times$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 ai3ilx vc2u o*6 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 isp; o:ityu7o 3s viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is plqjlp8v0 f(. uhaced 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 focal length of 8.5 s 2qbbz0yx.;a $cm$ 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 s e0 xf k +qro;47;bm0o)lnxyurated 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 telescope whose ob1.or(-tagf . oqf 6qwfjective lens has a focal (wfagq1.o6f tf oq.r-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 axf9+ dkqk ; bdu;yganmqw dr8*db87 6)stronomical 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 length l xzhfeo496j/85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lensernz9e 4 9q:does 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 iejub zmg*d(v/9r. 83uzsy3 . u kkomlsau. 1s;s 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 astronomical telescope using a reflei3- zx aqub kr;hkl c7--y;v(dcting mirror whose radius of curvatz-dkih-ykqbvuar c3-;x( ;7l ure is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to benco,d+4k9:2q pwp 7 ciwz4 kvy 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 a radius of curvature of 3.0 m fosgz(--m t u749szduxu r its objective mirror and a radius of curvatu- xzd9 4us-gms(tu7uz re 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 length wkfa,f0 la3y3 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 12.0dk,z.mbnej(q0ar a/9j8l t q*( qv3xq $times$ 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.zvkew8+vt +3:0hcp7 dia bq7a 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 finw: /blh)k1ty ral image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscok rg;q ,667 johijojvl5vpj 6v3f7 4pbpe 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 is made of two very thin lenses, placed in contat ccmcv-pf qm v 1*ekbc/t( .dxt)36k,ct, that have focal lengvc,fxp*. tbtq6c1k3ck( e)/mmv t -cdths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a particular situation. A 7tug/ fpj07tg/ 5yskiplanoconvex lens of index of refraction 1.50 and radius of pgkg5 tutyj //f70 i7scurvature $R=12.0\mathrm{~$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 v,i8dm zzi 4zu2ez7y/d2bbroo3) g :n (degrees) set by diffraction for the 100-in. (zod y zieg 72inzv,bb m /du82z)o43:r254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolv7i5k/bm,t*ubzd nir 29ysn 9a e 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 length of 500fer x* ogrz8,rul/r 4.0 $mm$. 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 5 3ic3iesba6byj);;: tb /mtenkbcqub- x-79v5-$cm$ (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 huma+uih ysngoao1 + a-8s9n 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 are7n9pko+pg )d fxqig m i 3z+gf */oj**33mxove separated by about $400\times10^6\mathrm{~m.}$ When Mars is $8\times10^{10}\mathrm{~m}$ from Earth, could a person standing on Mars resolve the Earth and its Moon as two separate objects without a telescope? Assume a pupil diameter of 5 $mm$ and $\lambda=550\mathrm{~nm}.$  ----待选择----yesno 

  X-rays of wavelength 0.133 nm fa;uqc92t h,pi :m v:wvkm7;lgull on a crystal whose atoms, lying in planes, are spaced 0.280p:m2vg:i c ; h lqu9mt,7kw;vu $nm$ 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. 2i,o)+ q 3vwrv13 / xtebzdddwThe second diffraction maximum is recorded when the X-rays are directed at an w2etxzid)3qwdv+ r3o, b/1d vangle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is observed at pgzr/aojvr5j5 kc4/9$\mathrm{25.2°}$ 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 conventiona4u26:ywzj2d7 +s5t fzosk mkcl X-ray image that the X-ray beam consists of parallel rays. What would beu5zwy +sc: 4 mdok7f2tz jk2s6 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 towa*r2,) lhlnun wrd midday, and the sunlight got more intense, a photographer noted that, if she kept her shutter speed const *u2h rlwn,l)nant, 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 verytnn0;w -culc, far away (assume infinity), the magnification of a camera lenn nuc;l wc,-0ts is proportional to its focal length.

  For a camera equipped wi*,db;epyi p 1zth 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 on +p.tuo,b8nm tly when objects are between 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 1wyotx7 -ox,r+ ccp(k65 $cm$. 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 a 5jfqp9sfx5;tb ps/:g)xpn3 j$+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountw nm65t,t zs6gains tries to make a telescope using the lenses from his reading glass6 w6ms,g5 tztnes. 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 a/4lmv;corh l3bl(3r 8/btjsu cx6:ws $+2.5-diopter$ 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 altitudec, 3: tm)nv5 ssdqcdtf4wxn.-s (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 time7g nt-1k xt0bb 8mh3qr(nyi ,ns must be increased because of ir n nby q,h( 1-tbntx0g378mkthe 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 the gc lt 4g4/bgqgi) *md3eyepiece 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 to))yx:d,*z4tw/fwliuw t n .22fsi7fvct.k of 2.4 m, is viewing the Moon.4w w:f/s,.f7.ztioi)2 ct l2ufyk t x*dv)ntw 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 the Earth.    m

  Two converging lensesc8u4v5 zqt e*i, one 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 magnifioysn 4u,8xfr8 k / 87ael*dfbncation 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 plate numbersmrtvo.:) vgevq7 e*hpc4qz5 -. Assuming it is necessary to resolve p :4v e7g vht-zm)qvoqpcr.e5* oints 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 and1u 1o ea*3zigo1u1f9ev n9wqz 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