Why is the depth of field greater, and the image sharper, when a camerau.)cri);k(3u yt ri4c p96q o(cbw v-z,ljc jg lens is “stopped down” to a larger f-number? Ignore diffr3ku 4yob().rclr);j ic ci-wg, cv9p ujzq6(taction.

Describe how diffractionatjop6d, q.x 9if )a ys 1tg6,.6ibtpv affects the statement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a large a,tip,.) v.gb6atsxof9dt6yi j 1pq6r f-number.

Why must a camera lens be mo bd1wlm3wfm6/2oc 6m.so(p ndved farther from the film to focus on a closer objec63m2.om( wmsob p6cld1dfw/nt?

Why are bifocals neededx5 xfr x z/xoijp1+zh+y7)ml * mainly by older persons and not generally by younger peo 5zx++7jx)z 1yhf x r/i*pxmlople?

  Will a nearsighted person/j4(qtoz yo117xgo2jio 1,jdtm ibi0 who wears corrective lenses in her glasses be able to see clear0x1j ,(1zobjo/g7jtty1i idi2q4o omly underwater 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 or,a, ne*lgd,ga farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person fganl ,ed*, ga,arsighted or nearsighted?

In attempting to discern distannfz) ca62 gsnl +r;n/et details, people will sometimes squint. Why does gen lc6+ rfnnas/2; )zthis help?

Is the image formed on the retina5lef*:l5ahzuv u0a *:o2 xrnj of the human eye upright or inverted? Discuss the implications of this for o :**u2arflo5l0 jah 5evnuxz: ur perception of objects.

The human eye is much like a camera — yet, whevjrr+buxci(;v+d-be,5fr *g j tf(y+n a camera shutter is left open and the camera is moved, the image will be blurrev5rtu(xbg+; -ed* vc (+,i fy+jrbjfrd; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A8cz ec+5oz : . .,aiuxnt/kwly2hu; ae simple magnifier is also a converging lens. Are reading glae5.a2ocw+nk 8te /,ia:luy zz.c;xhusses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s use usually produce images that are col i zsf:3(eq8fhored at the edges. f3i(qf zhe 8:sWhy?

Spherical aberration in a thin lens is minimized if rays j6 kf:in em 2.+prfre6k+60tzx rbzh +are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an object at infinityr0zkf jkrzx6e+r6 ep2h+f.nt+ 6mib: , which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a d)n *bxx+w r*rrfo;m-simple lens are not present (or are greatly reduced) in the human e+dr*wxm-r )on* f xb;rye?

Explain why chromatic aberration oaj b2i/n+7 nc nom4t:occurs for thin lenses but not for mirrors.

  By what factor can you improve resolution, other things bei*0fuae i+t lw4aa;0zmh*s5uohib: 73l- v johng equal, if you use blue lig a+m;e5 o vh:li0*04 af3*7-sjtibwlahzhuouht ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirroh7 *h9t yk tfq8ybkj s-u7is:+rs in astronom7 hst kbfiu+jh-k8 9*ts7q:yyical telescopes.

Which color of visible light would give the best res889 2foai lryuolution in a microscope? Expla yol8 ai8u92rfin.

  Atoms have diameters :z s ho0:x2yfp/-afiz of about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops t da0t4md,1;sljwv69uj ss0 tij a:*u 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 )rti9yaiuj uy0qtl5n5o (5: dhas 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 camera settij4:hep x* 9sqmng 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 q,prf0,p9 tjataken 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 200.0 megr h lasn2:ik2 ;,yf(m to 206.0 mm frnyg22e(h isa r ;lk:,fom the film. 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-mtall tree r gc(8 c+s6o7 8.w5 5g0znbkxwaz azwsfrom a distance of 58 m. What fz8nco wg.r6ckxaaw 7wzs5s(8zb 5g +0 ocal-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 inst p/2mo+ iws63rkcj 6icm8 v3rgead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular,+mmcc vr63i/wj 6i3s82rkgo p 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 exposure is d x le;jkzy+t;c6lj+x5(5a zm)flly 4$\frac{1}{250}\,s$ 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 279npaq(v5acb9tck( st3atxl0( x3 dz.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 contacl+do):m6za lgt lenses corrected for the far point)lzg:6+ ldmoa $(=\,\infty)$ 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 po9v/ x/bnyu xt2int 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 1iy0f mbtxsjf51hx5im;+z 2m* 4 $cm$. 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 ku:jzz- a8*fr 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 corrected x2e ,zj2xtsltw x 15jw 7,(vtoby 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 the4f7peevk q51ck x0 6kl m3 m8rv,xunp/y 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 in Example 25–66p ce+izvyn 2e,p d()m than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal length of 18zav:p, r0us bt m0cn$-22.0 \, cm$ 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 objec(i akn2j/ 5drge tfv u5st+v/-t
(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 ay)zf/q-e aidr gr1;-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 relaxetxx9uxec1vz br.2 7t tbkt6-/d eye if its focal length is 12 t7tbx.vzx2uktx c/ - 96tre1b $cm$? =    $\times$

  What is the focal length ox hv 01kxcd40nf a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated*mm6iu yy ,;qcs/mvohepz dp8r8g-*b6p + + fs at $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is u5ljtqd/ yl5o/d ksik.jf k x-65zs2+rsing 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 9. 52wsi.0ieuto*jz:qqpd + x 9y50-$cm$-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 placejvvtb30v8nvma* j-x 8d 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 fo-kz*cmo72fpt afy b 4oqe+)ncse:rt5br1i + :cal 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 ratejpztk kgp/no, q4vn 71bt8*s7d 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 astro mswe +/n9ob rf6n3p3zrcl;ng6832s o+vblc jnomical telescope whose objective lens has a fo z bl3 snr cjm+9l2n 8 ;pvren66bo/owfs3c3g+cal 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 telescope is de11,:jkyfed g hsired 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 obp,0k1se4cjen+d3niy d8 2 jx9y2/ytdays 3xr jective with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75a3:rs iaad 42 jt5dpofu k0.3h.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 rel*l26xeqwq-u q 1m2jp laxed eye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical telescope usingfuj** r rok1bmud95 9e a reflecting mirror whose ra9mfr 5k *db*e1j o9uurdius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be maghg,5yq1e8 h)d)y gvbsnified 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 f vx5kc 3mb2.wkor its objecti5m2.cwx3k bvkve mirror and 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 with a focal lenq9vjo l 9qd3z,ok 49jcgth 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 12b mq )wu1*dd*w.0$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1.4 d sqzqg)(a*wqn.j +n /fiqxp ,apu7(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 imago2eaj m9i /a:2ki yf m.*x)vcje is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound m iiiga7w v5ga+.26y(nfw1tpixo 9ks39o 3ndi icroscope 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 contact, vvugzon9.a(q/ew: 0rthat have focal lengths v a0q(e u9o g:wrvz/.nof $f_1=-28\mathrm{~cm}$ 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 sphericauc(+clya e7qh)6oo3 m6d4w kgl aberration in a particular situation. A planoconvex lens of index of refraction 1.50 and 6u7+3qkl c6w( mo4eocgy h)adradius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction forz3pc xfetrgn 4:.s*y- the 100-inp -fy: xrt*ng4e3z .cs. (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct -6ynd isj1l: ;v6xlpha telescope that can resolve features 7.0 $km$ across on the Moon, 384,000 $km$ away. You have a 2.0-$m$-focal-length objective lens whose diameter is 11.0 $cm$.
What focal-length eyepiece is needed if your eye can resolve objects 0.10 $mm$ apart at a distance of 25 $cm$? $f_e$ =    cm
What is the resolution limit (radians) set by the size of the objective lens (that is, by diffraction)?
Use $\lambda=550\mathrm{~nm.}$ $\theta$   $ \times10^{ -6}\;rad$

  The normal lens on a 35-mm camera has a focal length of 50:tsuvgc q ,izgqwo : 7z-*:hv+.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 resolv50xpnx /wn p*led 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 ca z;vzlmq (bi*aix:u 35r 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 ajt5 puf24wmkyugp3 5njnh5 91re 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 fall on a crystal whose atoms, lying in pla sk-qgaf3 cs-b.c(ny+xyx (r* nes, are spaced cqy+y.(g-b(sna-x k c *xfsr3 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength h(r8myx,r6l:dmk r 5q 0.0973 nm are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an angle68ly(xr ,h5rmmrdkq : of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffrackegv)6n2obk xn*o4mm) -k q)6x kifl: tion 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 91ala6gkk 3aqs5 io)p-ray beam consists of parallep3ka)6 a19i 5 glqasokl rays. What would be the magnification of the image? a the magnification is   
(b) Suppose, instead, the X-rays come from a point source (as in Fig. Below) that is 15 $cm$ in front of a human body 25 $cm$ thick, and the film is pressed against the person’s back. Determine and discuss the range of magnifications that results. $m_1$ =    the magnification is  

  Sam purchases $+3.50-diopter$ eyeglasses which correct his faulty vision to put his near point at 25 $cm$. (Assume he wears the lenses 2.0 $cm$ from his eyes.)
(a) Calculate the focal length of Sam’s glasses.    cm
(b) Calculate Sam’s near point without glasses. his near point is    cm
(c) Pam, who has normal eyes with near point at 25 $cm$, puts on Sam’s glasses. Calculate Pam’s near point with Sam’s glasses on.    cm from her eyes

  As early morning passed toward middayda9g x m9jx(9o.b /*v8po qnpv, and the sunlight got more intense, a photographer noted that, if she kept jp.n(8m9p9d/g oq*x obxv9a vher 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 magnificap,ap2t4d e- rqtion of a camera len d,2-tq4ear pps is proportional to its focal length.

  For a camera equipped with a a*esew6jhs x p m6a42+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 heeqo n/vc:9u-; v gxpgd*m3pz9r right eye 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 point ofd ,yxct)ol kv3ux6+ 9x 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 magnifyin 6+ rc).ekpnckg power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a telescom5 + *n)epambkp s r:hn;e-1anpe using the lenses fro5 mphe*n ) sb+:prmkaa -nne;1m his 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 uses /n-lz-: zr z:7 v7ziiiafxce8$+2.5-diopter$ 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 ext :jb rt+6g+vkrremely 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 s yelcd+)l*nod)l 0 u4q d5hv0rhort distances, exposure times must be increased because of the increased distan y0dvr ell+dd5c0u lqh* o4)n)ce 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 eyepiece of a telescope a2,)vvr-qctz 7 gnmwzf 8(5o6dulb 5v- ebpsn8 re 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 a4pbxwzvp/*t9 cvf20an objective diameter 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 nm. Assume the tawp0vv/*4fz9b2c xpHubble is near the Earth.    m

  Two converging lenses;tkkj4* 80g rtlc+tdi p*:3 tazianj 6, 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 magnificatyg a+xcw(rmsa g, 8299nlede,ion 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 :rx9p r* yzd4ephotograph license plate numbers. Assuming it xz*4r :y drpe9is necessary 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 szf0,4yclxj5w5 wzx g3urface 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