Why is the depth of field greater, and the image sharper, when a t i 3lkb26 kn.1f3mwfb pnsc)3camera lens is “stopped down” to a larger f-number? Ignore diffractio 32nwbski3c)kbtm3p l. 6nff1n.

Describe how diffraction affects the statement that thikhr1nv+4. c2od. wfm e depth of field is greater and the image sharp4 o.fkcvi.ndhrw2+ m 1er when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be mov6kors6p *y8:g,e e jvi /bs(fmed farther from the film to focus on a closer objece8mv gobi jsy : (psr/f6e,*k6t?

Why are bifocals needed mainly by older persons au*hsy:q oq0eyd0k.p,okb 9ao c0yy8 ( nd not generally by younger people e098 oboyoa.y: kk,ys0q qyd0cu(*p h?

  Will a nearsighted person who wears corrective lenses in her glasses be ablc9fel4 *vsh8hpqam);e to s 4lvapqch)f mh e98*;see clearly underwater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person iu5u r1+q*vfk7hx6ob(i eglcb9-w : p us nearsighted or farsighted by looking at the width of the face u1hok 6buc5 v-e wi:r+bf9x7lpqg (u *through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes squ; gn-*yf;g lcsint. Why does -gsc glf*;yn;this help?

Is the image formed 1 z bw.vya5 ey)x4*qpjkw9q* qon the retina of the human eye upright or inverted? Discuss the implications of this for our perception of obj xvyyz 91qq w ej*qp.)w*5b4kaects.

The human eye is much like a camera — yet, when a camera shutter is left ope./65jd 1fehkgs6u dban and the camera is moved, the image will be blurred; ba.ef5g1bj ddsu/6 6khut when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use convergin.iv m bh3tbm05g lenses. A simple magnifier is also a converging lens. Are reading glasses therefor5h0.t mmbbv3ie 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 ima)j 2 ca1v s ar90:a*(vyocntns 3p/bqvges that are colored atqnvbscojv( *2/0psc a1na:r3 )tv a9y the edges. Why?

Spherical aberration1yc.bc47 ck mfqm.ns/ in a thin lens is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of ancy q m..bc4kcfs7/nm1 object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple lens are not present (or er oj(b*6gsk6 are greatly reduced) in tg6osjekb(* 6 rhe human eye?

Explain why chromatic aberration occurs for thin lenses but not for mirrors.ozns0(-li2g pw )x2a k

  By what factor can you improve resolution, other things 9k/i5i p7jepc * ugb*q.l5sdibeing equal, if you use blupiql u5i* b*9d/s jcp7eig5k.e light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantageb:r.)ytwp z pn m3kc+w-r;o0 rs for the use of large reflecting mirrors in astronomical te+:cwt nrbk-)p3.pr; r owmzy 0lescopes.

Which color of visible light wouo/n.ehq*h9bnh1 rbcz vc81(r ld give the best resolution in a microscope? Explainn .z/bn91 o8h 1hc(*v ercrqhb.

  Atoms have diameters o.fd81u1ob, vsck b4qg f 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-stoty8/7opbob:yf9pw, ve2zz.y ps 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,hyh ;st/pd7 ga-:umu 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 sef *rf9hyb;tdn03 a m/ntting 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 iswz9mo,koj 1b wxf-ju k//2t0b 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 adjusted so that it is 200.ic)7 : ji/xgfy0 mm to 206.0 mm from the film. For what range of object distances can it be adj jy:gfci xi/7)usted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtaller,vivy1: 8rw f; )7uevdd4ab tree from a distance of 58 m. What focal-length lens should be used if the image is to f:br)78vue,rwfdv d i4eya1v ;ill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lense 0k75pr2gmhp u .;djn. Show, using ray diagrams, how reasonably sharp images can be formed u j;h5 r nmpgd7u0e2p.ksing such a pinhole camera. In particular, consider two point objects 2.0 $cm$ apart that are 1.0 m from a 1.0-mm-diameter pinhole. Show that on a piece of film 7.0 $cm$ behind the pinhole the two objects produce two separate circles that do not overlap.

  Suppose that a correct e0wg7b ./dud3( fyop xbt.z coo-/n(pfxposure 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 2.zgdl,s/4(s - 4fvuv is0 $cm$ 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 Exampl s t:kpy*. e:;itf5*vohyxg ,ve 25–6 wore contact lenses corrected for the far poin oy,hgsk*yfv* .5t t; :v:ipext $(=\,\infty)$ 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 point is 1zu3p, /e*p-tu7b-aek+ i z thh1a ler/ama)o 715 $cm$, 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 poizu-:t11jw euu nt 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 wf kov)an8;3u dw g cgee/r mdt:23i+,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 z fjtosl) )obz2u)ih: u0/0ekby 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 onu6 jidw5 ttcui e;(0mya80k0f ly if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Example 25–6 t3/eb5.wpf ijl gvx;5 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted p xi/1nbam-xhx5(s1 gc erson’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 e *wh.p-uu yyi/ye–lens system when 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 a8q v* 9z1(hukhs xfxu-nd 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 focal lengtyioqcr3c/wfjs np2/ ,;1jcr60dm 5o t h ic30 t1j dcpio2,r 6ny;5/qjcomfrw s/ s 12 $cm$? =    $\times$

  What is the focal length of a magnifyij uugjmfy 1ng;),5n .vng glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at -g8: y:ba1bnq vwbzx8 $2.5\times$for a normal eye focusing on an image at the near point.
(a) What is its focal length?    cm
(b) What is its focal length if the $2.5\times$ refers to a relaxed eye?    cm

  Sherlock Holmes is using a s5/ktpx a miynar/ xky*e,38 +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 w/ kzjm3/3 ques t1z4lqith 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 wjqnv8,0kz+pr h /ph ,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 8 6iqv7vaq(b ic m2ml)igmks ev7 8k35focal 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 7sreq1;r xv;gd( yk*w rated at $3.0\times$ for a normal eye that is relaxed. What would be the magnification of this lens for a relaxed eye whose near point is
(a) 55 $cm$, =    $\times$
(b) 16 $cm$? Explain the differences. =    $\times$

  What is the magnification of an astronomical telescope who)b:e+ur:vrd uf/, mm cse objective lens has a focal leng cer+, drmu::fm)v /buth 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 magnificnj7vez k+1 zax4cy-*nation of an astronomical 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 lengtm y mpln5g;fo*m h+j9+h 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75.2 fk;);-orbk3w s d7vhm 5kemc+ $cm$ 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 9 c3*.i0js hghd; qt*y4gnnzc 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 tel sy sh6fj.(f:tescope using a reflecting mirror whose radius of cu 6s.ftj (ysfh:rvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to bep c8fr:fwvs4rb68ji f(4 b e5l 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 cuyt,.2kvboc 8 drvature of 3.0 m for its objective mirror and a radius of curvaturevc8o. ,t dykb2 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 foc061bu. gewf vcal 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 123k/dpge19)vk yy /ze5ey, liz.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.ljks dj;m6zyhs)3m w +a0,xy5 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 located 25 dd d t2e9zr5;f$cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length ;r 7)bgmvo h5.-ysaua 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 tw;q ixgcs ldi:3*jzv6 5o very thin lenses, placed in contact, that have foqil5 s *zx;j:3dgicv6cal lengths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberratizvp ;pxq h85hy/ bl9j e4-f6 :wtm0wjeon in a particular situation. A planoconvex lens of indetlj 8e/9v 04p;xhwm fy6- j: zqbwhp5ex of refraction 1.50 and radius of curvature $R=12.0\mathrm{~$cm$}$ is shown in (Fig. Below). Consider an incoming ray parallel to the principal axis and a height h above it as shown. Determine the distance d, from the flat face of the lens, to where this ray crosses the principal axis if
(a) $h=1.0\mathrm{~$cm$},$ $d_1$ =    cm
(b) $h=6.0\mathrm{~$cm$},$ $d_2$ =    cm
(c) How far apart are these “focal points”? $\Delta d$ =    cm
(d) What is the radius of the “circle of least confusion” produced by the $h=6.0-\mathrm{~$cm$},$ ray at the “focal point” for $h=1.0\mathrm{~$cm$},$? r =    cm

  What is the angular resolution limit (degrees) set by diffraction for thez7 m7it k9 g1o)lc2pca 100-inic2pak l7gc9)71mtzo. (254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that cwfq/xmw /yod q/3i 7(wan 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 camer1f a 3zf0isf:fa 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 by a 5op 3g6um hq:o *b-z6td5-$cm$ (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 v8y6vy hl ej .6cll7)pa human 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 92mrc0y i :a-gcmh/o rseparated 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 0m*r aw7rty mm. 7)(mgdwcp qhqj62w:/.133 nm fall on a crystal whose atoms, lying in planes, are spacrdhawm pq)jcmw*7: mg t(6.r2m/7qwyed 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 0.0973 nm are directed at an unknown crystal. The seq m34d7.3zo2)ug4izm o ccqmmcond diffraction maximum is recorded when the X-rayszu .mdq3m gmzoq o)44cic237m 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 is observed azu1 nv vb-17h6q lh/ldt $\mathrm{25.2°}$ 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 beam consists 9q:fi8 7bb(6o rzf; 2hc0 x lt6xairxeof parallel rays. What would be the magnificatic6207hb z o96txix;bl 8ia(rfqrx e :fon 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 the sunlight got more intense, a 5yym/j5mbs0ka6snge6 eop k +jl,0-iphotographer noted that, if she kept her shutter speed constant, she had to change a+nlm05 6kg,o6ye sj/impe bjyk0-5sthe $f$-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* 8nixzxug7l n1g 8/fv far away (assume infinity), the magnification of a camera lens is proportional to its foc7 nvxz/1nuflx*gi8 g 8al length.

  For a camera equippeb8tct5 3sy r2zd with 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 h(di joc )o1d fp l(.k-hww4q3when 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 15 ;7xuw d:ik,c0(vxmajb(.rra $cm$. 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 magnifyinvxgcbe/i .u;71c 9q tq3lfp) ng power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains wzt nl qr hsldja3by78o1s7+ 1p+1ft.tries to make a telescope using the lenses from his reading glasses. They hav1 +ato1r7 j.dnqp3 lfhy+7 lwtzssb81e 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 fpj hbo mh/d53g1,,zaho7f6r $+2.5-diopter$ 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 extremelyb x;j.7,q fr7vtkrncp) 1d7 rc 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 shp lld ;efaz0ske3-3 3xort distances, exposure times must be increased because dl33aek xs p-zf0le3;of the 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 eyepieceu5) pz0ej2jlu5. vuxwlp0y k ao g++w6 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 of 2.4 m, is viewh 1+:xkbv6j oding the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelengthohd x+:1jvkb6 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, onewh 7idkwx 8e/53we2cw** mrtz with $f=4.0\mathrm{~cm}$ and the other with $f=44\mathrm{~cm}$ are made into a telescope.
(a) What are the length and magnification? Which lens should be the eyepiece?
The distance between the two lenses is   cm
M =    $\times $
f =    cm
(b) Assume these lenses are now combined to make a microscope; if the magnification needs to be $25\times,$ how long would the microscope be?    cm

  An astronomical telescope has a magnification of 8.0. If the two lenses yi a 4s1+rdo, ;u6zfcvi;oo0lp e8j:jare 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 numbersq r+l(kl:(y ua. Assuming it is necessary to resolve points separaq kyrau(( l:+lted 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 t/y;m /o3tzjz lq2vtw,n qq32z he 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