Why is the depth of field greater, and the ima*,ucom 0x ecn/ge sharper, when a camera lens is “stopped down” to a lu/ xe,nomcc *0arger f-number? Ignore diffraction.

Describe how diffraction affects the statement that the depth o7 * w1; mqahssu b9bk e1qum3chl)b-h)f field is greater and the image sharper when a camera )ekuscbqmb;a91*)s7 lqhmhb-w3 1 uh lens is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to focus on a closer)u 7aehsq-bfc.xme:t4 orfs1 6nc.i / objectq/f-sa:x7noe1 be c.hf r6m sct.iu)4 ?

Why are bifocals needed mr1clsq* v 68bmainly by older persons and not generally by younger peo1m8r s6*cl qvbple?

  Will a nearsighted person who wears corrective lenses in her glcw.qz,pc .i q7 cu;mj005yhpcasses be able to see clearly underwater when wearing th ;.czqiq .phcc0 ,y57wpcjm0 uose glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is ejh 8(f s di4/*v*cs6o. pjztfnearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses/chsj4f*sv o p8(zf*6.j i det (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern d.t+-g9upvgz distant details, people will sometimes squint. Why does thid9z+pgv.t -ug s help?

Is the image formed on the retsv-9 *ixq nxozs 8j0m8ina of the human eye upright or inverted? Discuss the implications of this for our perception of objectsqx0-v zjno sx8 i8ms9*.

The human eye is much like a camera — yet, when a camera shutter is left mcw553ofbqhc h)* e2m open and the camera is moved, the image wil *)foec hbcw3m525hmql 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 converging :v qn5de3c+1 xy/hynclenn n x d+5y:1yqc/3ecvhs. 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 f-k frbs al2rp3 6 03bjgj3ib:aor children’s use usually produce images that are colored at the edges. Whyb 2ar60a3 3jsrbjk f:bg3-ipl?

Spherical aberration in a thin 1m9o4wo zyv:z+0 ogms lens 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 surm1o g +ozsv09ymow :z4face should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not prese 6a :yoq0m02pscix6c tgvz8h; nt (or are greatly reduced) in the human eh0go0qayi zp 28:tx;v6 ccms6ye?

Explain why chromatic aberration occurs for thin lenses but not for mirr9 qyf+q:zeo8rwdrzxw) c 3w8+ 6pyjn9ors.

  By what factor can you improve resolution, other things being equal, if you u s:*fkn jo(m+ose bl:o os+nk*m(f jue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two adva jv0oq0p.o 2cdntages for the use of large reflecting mirrors in astronomical telp 0c2.d jvoq0oescopes.

Which color of visible light would give the best resf q su*o.;iy hu)p,dx;olution in a microscope? Explah ,;sy.iu *qpofux);d in.

  Atoms have diameters of aboutjaf)jodv *s:v 6,;jnp $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has7,zn(k aw awwylp x5mb2,:g7kl e2, ow f-stops ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a 1j sfc 9h bk c2 .6mi(r;zx)5tmsdw7befmmc. 9)4-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camer.5m2vdq li:5zb yu ))fjj(xl*qa rin8a 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 taken rg-47f*: oo e qa0iq/3h 0rqxfmvu+c d3xu n3kat $f/16$ 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 adjustedjr2xf1;r s ako9zd mzt*;l r9j7:ya5b so that it is 200.0 mm to 206.0 mm from the film. For what r*adm9;a29jl: zrk;yx fjb5 tor 7 1zsrange of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograpx;u45 wjv7ah ikugs37b) ra5zrss6g) xrt,2n h a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the imas4j sz gxtv27r6 ixwhnarg),7)53 usu5ar k;bge is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, usingj:zw+fev js qa,,8t 9i ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In p+qezj:tj,9i ,f8v asw articular, 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 exposur6z7tu2xl 2pzwe 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 abozftyjf, vkk fg7b-68v e v8cq)wp0/h/ut 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 Example 25–6 wore contact lenses najdywos.c(2pk2dym6wysj v/* - y );corrected for the f2vw)-cpy6.ymao j;y k2 d* ds sywn/j(ar 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 50nnz9duqlw,kvo ;: e 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 oq z 18qs0zv5 s1epud(jf 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 lhpa 10van0/o a 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 correct1 h* )jwq:uy*ve8mzqo ed 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 between 25 3t da* owe4oax;(;edt $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Examp v)rbx ,pq6e;yle 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted personfkvu uad a86j8f6v*+ q’s eyeglasses 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 when viewing ku yq(wv+ : qbcc1p pu6.3py1han 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 nearkfye46-u qy25ph,zt )-sc+gs4pdbt l 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 use w1z.( pfwcs*djp sf4-do8ve4d with a relaxed eye if its focal length is 12wp. dw(fe 4czfd*- 8s4pj1s ov $cm$? =    $\times$

  What is the focal length of a mai tjgx3 z6,1m e5q/em)ov orkx*d* jt7gnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated ac 1+oit; rtxe +z+eu,pt $2.5\times$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 u, qihtx ac, z ,b.vgt6,n.)y*cyrmr c-sing 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 beetle1xmq6,zpz . cdz q(lr;f 85sgy)0rbkr is 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 placed 57:kbtrty10 pgn (b znax y+,-r.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 focalcj) k-ng udlp 9iq0. ck)wv*w; 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 rate0cfo 22f jhr,yd 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 magnificatirkk;rhe:0vyybkg+/,j y 2huxb n*12vlft..con of an astronomical telescope whose objective lens has a focal length of rt:,ych l;/fn r e+kby1b2gvvhy.k j .x0ku2 *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 is desired to be u ;r4s 9v ohz04z+spti25$\times$. 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*mq1pvrya s39 p e :5,v.b1vvo0ucqt g an objective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced+ow0ia7dcom j9 p*oo9t- pc n) 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 3;yzto a wg9-wm75p pu(2.8 $cm$ 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 reflec3zzwo v 2xb7;qting mirror whose radius of c bo2vw3zxq7 ;zurvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magn - xkr651 rysdo98xgzx4l 7ygdified 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 fo 2q2tpk 00s0k8wtjkuv r its objective mirror and a radius of curvature k0pw kjvuqkts 2t0802 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 of 1.40 v3-bt-w-,x vvubq0tk03+uzbv dbe t.wen8*d $cm$. 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. :wiwgqzr j.wx6k-s ;+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 1c6 cu*q s/a8s;de:dh r.8-$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the final image is lgu3tpdncy6)k3o i m1 a-:1us pocated 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal lengt u)qkt,u) d50yhz*gsnh 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, pll7c ecv cz(j,opsj*n w,;occ b8b-+ 1caced in contact, that have focal lengths of p8c l,oes j,ccn7( cw1 o+j;zvbc-c*b$f_1=-28\mathrm{~cm}$ 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 particularf1dod/ zna4iwqr m7/8 1z, mgx situation. A planoconvex lens of index of refraction 1.50 and r8xa r4qf7 1zm1/i ,gdwodmzn/ adius 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 resolud8 yhe6fp,tf (tion limit (degrees) set by diffraction for the 100-in. dy f,h8t6 epf((254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope thak-c f;w1p q c2d0vwhr:t 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 camer4ud fj 41.8/)uljwrvz( 2d tiwme qtp2a 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 resolved -shk zrb dr6 (9;e3c7jkeqsl -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 two car headligh-s 1 y mkd3uo42zruocbj*qgvg+67hm *ts 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 sia)n3u 6 rabn i8dom1wn,7sb:eparated 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 fall on a crystal whoseh6k* j7qvnd /dx9j t4e atoms, lying in planes, are spaced 0.2/hxkn96j v t*7dj4deq80 $nm$ 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 a18 b *b o/ms74hveoywmn 06w+cnza9ssre directed at an unknown crystal. The second diffracto1*a4o0+7vsn/s8w z ne cw6msmh b yb9ion maximum 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 diffrac)0w vhxbulu+ o.z *.cztion is observed at $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that the X-ray bebn.oj4 i8k6 6y,c lvx-g0snmjam consists of parallel rays. What would be the magnificj c6vi0x8k.mslg6o ybn 4,-jnation 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 thrf.8 2:3u)y lm gqnegqfl v5l)e sunlight got more intense, a photographer noted l neyrgq) f5)mf:ugl2.q8lv3that, if she kept her shutter speed constant, she had to change the $f$-number from $f/5.6$ to $f/22$. By what factor had the sunlight intensity increased during that time? $I_2$ =    $I_1$

Show that for objects v4q8f v (pn xz2;g,fdpcery far away (assume infinity), the magnification of a camera lens is; 42xcfdg(,qfp8p znv proportional to its focal length.

  For a camera equipped with10h*vld3ph vw 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 eye0 upy1fq -l1ec only 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 po5 seeq h 5nc 74j:qs/jf4nn)kyint 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 power of a k b5bqhl/cgh awe1/2d(wj,.o$+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains ylnz6(*bhv z :/sp0kotries to make a telescope using the lenses from his reading glasses. They 6z:oh(vyb /pzl 0*ks nhave 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 usesj,bp 4+vgjlrj1 +k0ay $+2.5-diopter$ 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 exob7fy/i,+5o 3 zhje jztremely 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,;6tx) .xe9x2d qf b2* fnd1hywuqc)wi exposure times must be increased because of the increased distance of the lens from the film f2 1)2* qbdi hxwn9y.t wefcux x;q6df)or 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 eyep:hnqs;a8x v7c:s vv /kiece 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 diatn l e 9w ru:0df5w9iikxg+j57meter of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 +5rt05wfjwg lkii9 de: nx97unm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one with3g t(qu qc)-sy $f=4.0\mathrm{~cm}$ 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 8.0d0hy 1jp rkq -;/.-v m/qztzou. 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 photograph9j ut ld9cl3to.-34ftpt/ i )dthst /m license plate numbers. Assuming it is necessary to resolve upd/-4 fltt tjdiolh3t3sc) 9t m. 9/tpoints 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. Be;lt5nvisn / k5low) has one flat 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