Why is the depth of field greater, and the imaq-t) fr2- ouu iiel-q/ge sharper, when a camera lens is “stopped down” to a larger f-number? efri-2 i--q/t uq)lou Ignore diffraction.

Describe how diffraction affects the statement t w/rnguw1 ,-ahtqhh jd 8de:),hat the depth of field is greater and the image sawjh-dhw dhgu/8e 1t,qn, :)rharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be moz vfujr7gl h6ppa: j3omd91 .:ved farther from the film to focus on a closer object?ov9d36fr.:ajlzp p7mgh u1j :

Why are bifocals needed mainly by older persons and not genagh(a. hl e z0fd43u8nerally by younger people?8 e dzhagu(4a.lhf0 3n

  Will a nearsighted person who wears correc84efst ) 7wvzeaiqtp z;7nkjiq;)r -0tive lenses in her glasses be able to see clpz e r8f;kzvts) q7)j ;7n qi-4w0taeiearly underwater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a persog rs0ntb;o+ g9n is nearsighted or farsighted by looking at the width of the facgb ;o+r gs0t9ne 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 detai9llp/pd)aqa6o ,,o dyls, people will sometimes squint. Why does y )pado/la9,p,6q dolthis help?

Is the image formed on the retina of the human eye upright or invert*v/pbzlb7to 9ed? Discuss the implications of thi/ob b9z7*pv tls for our perception of objects.

The human eye is much like a camera — yet, when a camera shutter is lefjacwqgs5wf1, v2 zv10 t open and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.0av2v1cz 5w fjwg1 q,s

  Reading glasses use converging lensepdhj/r+k ;m;v 5iy/ r8iwmt8q5sg pd 0s. A simple magnifier is also a converging lens. Are reading glasses therefp/r0mdhr8 yk5pqg+stw;8jv i 5m/ id;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 usually p1gok ru:h5gple( 1 aqf)/,xokroduce images that are colored at x(kah1)1,lug/or op :fkq ge5the edges. Why?

Spherical aberration in a thin lenkip9/5gfx6qjomjp.y( :rtgcy8( b6ay n 0gn- s is minimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an objecygnmpoyjn-(0 fgaq65 :9rjk6t8 (p.y/ xigbct at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present in a simple l himj ,kll3,*z0 imoo34i )txwens are not present (or are greatly reduced) in thj*i,iw tix o)o,3l m340lhkzm e human eye?

Explain why chromatic aberration occurs for thin lense( ww,ks0e oz *x8t6xuls but not for mirrors.

  By what factor can you improvd r dg37bc(5nd9yvg*hjbwq1 +)i ,zxl e resolution, other things being equal, if you use bluwx57(+* bhi cnz)j19gb dr,v3 dyqglde light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting mirrors ing+ s(df ad0mg3 astronomidgf gs(ad3+m 0cal telescopes.

Which color of visible light would give the bestvpfe5 hoxi-7s2 f+s+mnq g6w ; resolution in a microscope? Exp mvgqf s-2o n7fesp5++xh6; wilain.

  Atoms have diameters of 75w)vu z,ddtt6 opaw8 about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens ha;kyr+ns i(g -t(yf4xos 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 ab6uo.hnwe0 ,ha/r -nr 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a ca) 1zfl1 , lyhud65ygusmera 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 i*2 :r0+;-adf dddfbxicx/weo/ zpy+ks 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+9b 9dvn:z6cp.l*c eoo3mzm y so that it is 200.0 mm to 206.0 mm from the film. For what range zcmm p+v9c 3*ey :.oob6z n9ldof object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograp7)n +: w rgcdvdt*m dsi:0vpe/h a 28-mtall tree from a distance of 58 m. What cd:m srdg/vp*di +07t) ewnv:focal-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 ofel, sh3d1u5. -tfnozw a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pf3.1z ndlhu -5oetws,inhole 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 e3ucb+w/p8uz h xposure 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 abouvmm k.a 2 kyw3ebgyqn5y); 5c)t 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 corrected for the +o.u. z(5w vyan5ffk4uv 5ykh5vyh.u 5 o4+5nv.wkzaf ( fkuyfar point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person whose near point isq-nvg m t4ol(z) cn38q 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 ofprlz/zu /)p, z o:ukd1: heb)p 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 b3+ rk6.e9u.tsidbl bwy holding 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 b5sl*g9o )pl6f t 6m( dk,hnhauy 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 a u1zp ffq6)q2vre 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 eyeh(6vg/cwe 4p 5h sbe za.:e 4zp/4 ojsz7*xzjg in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted per:*zm/ddng 2 gdson’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 f h4ku+o9/ai kimw:x+z . +q/v-a eecjwhen 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 points of 10.0 a7x )uqy 8zq+yvnd 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 length*boc:69q exg d,wdki3 us;t./jpauf, is 12 ;3uddo,/c ep.j ,6 :k9xfsqwgbi*tau $cm$? =    $\times$

  What is the focal length of a magnifying glass of zz e vaajmxz2:196q8lcz3 40pmhmzm8qv d4 6e$3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedpjnqzv a:y or6 gn:0 jwm,-:w9 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 usinctg;m3bsy2rd itn n ;q4e6b*wzpas ) *d;x *s-g a 9.00-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle is vi)wt ,tp7nd c7pewed 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 5.kjgb vwyz 39q04e/c0n55 $cm$ 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 nk :n url6nz.7$cm$ 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 ish /-m/:yqnja4hk8j by 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 magnificatic-e 2 igy 0gwtkr.;re0on of an astronomical telescope whose objective lens has a fty rrw g 0.0ke;i-g2ecocal 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 i+pq *eh )psvi9,h k/frs 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 f mkx 5sx6hb.d+k bho:4ocal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75.2 5e9 jfr5+ueaq4we yv .d19vso$cm$ 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 for5-ib6.,,d c ipb)qxw ra k3nbr a relaxed 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 using afnr eqa1t* p,x,kbw+ 9 reflecting mirror whose radius of curvature is 6.0 e fp1b* 9q+,txw,nark$m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appqepw2 ; owez60/ hvi3nears to be magnified 120$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

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

  A reflecting telescope (Fi0:xtu30q z ;iro/zmaug. Below) has a radius of curvature of 3.0 m for its oq03tz0z;ia xor:/m uu bjective 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 eyepied e88 yx1-uz.yej+wll, ag5 avx -bqw-ce with a focal length of 1.40 $cm$. Using a normal eye with a final image at infinity, the tube length is 17.5 $cm$ and the focal length of the objective lens is 0.65 $cm$. What is the magnification of the microscope? =    $\times$

  A 620 $\times$ microscope uses a 0.40-$cm$-focal-length objective lens. If the tube length is 17.5 $cm$, what is the focal length of the eyepiece? Assume a normal eye and that the final image is at infinity. $f_e$ =    cm

  A 17-$cm$-long microscope has an eyepiece with a focal length of 2.5 $cm$ and an objective with a focal length of 0.28 $cm$. What is the approximate magnification?    $times$

  A microscope has a 12tdcm + * z0ici-og8.uwce:ui5p1s3 fl3wjr(g.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 1.8y8wgm fh.f2jd y8j8.mg,bg+z -$cm$-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 jp+r8gcw0/1 x hv3alnlocated 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focaljj p gy5 q1);cbcoxlwr, 0ua7: 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 co*itw/ y:g( ss d.zkm)hntact, that have focal lengths of )wk( tszsih.* :mgdy /$f_1=-28\mathrm{~cm}$ 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 spheri (amdj6g wb1ghvi(ful 1 .7v0xcal aberration in a particular situation. A planoconvex lens of index of refraction 1(mhig 1j. a1bv6 lx(wdgv7uf0 .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 diffracxa 1/gdb9i qx6tion for the 100-in. b gx1qx6 9/dai(254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to c3 dhai:2y)t o*u)9 d:aeqcety onstruct a 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 5y q z:x. d xoll()27pbvia1l(t0.0 $mm$. 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 55-hw hex,z y/,q9xn*z3i $cm$ (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 headlights ee(yg/vpwrvu.pn b qwy14z- t 7o94c*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 s 8iqdy 0(35obf xgevv m4ndt2;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 crys3kl c1;zh48i u z6fqn.qzl.latal whose atoms, lying in planes, are spaceqc n6llh3.kzq l;8i af.zu14zd 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 crysta)u5yxc*1h odj +oefb) l. The second diffraction maximum is recorded when the X-rays are directed at an ang* dxyoceou)j1hb+) 5fle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffrac vu1axsx:0/l ltion 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 beam consist/o, 7pl3wxjg9yawjc mt.u - 2ls of parallel rays. What would be the magnificatiox2,j o 9ma.twy7-w/u jclpl 3gn 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, 1:pxb4g(2iskcygykg hb;8: q a photographer noted that, if she kept her shutter speed constant,b1;p c4 (s 8yi2bhk::qyg xgkg 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 e 4kjxuql6u5tu21 gau (28iv d xxi9k5away (assume infinity), the magnification of a camerki 9ug ux dxv tu(aji65el245k1x28qua lens is proportional to its focal length.

  For a camera equipped6 4byw5q - osh0+ jubz)p(ntol 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 when ob;hj:/3bv xt+ qg7)*)irtr tb/ vddior, (gfgpjects 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 poinutyd*el w39*a1h b 3un by4n5at 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 magnifyid+g d :usbt 2ke(wls24ng 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 (fl h.lhipm9w 6cn:m(to make a telescope using the lenses from his readin(c w 9(nmlp6:lmhi.h fg 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 usesbdrvml5ru ( 24 $+2.5-diopter$ 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 au)trag6)zhgdcg 6z 3;ltitudes (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, exposu-,ayfib1n g 4hre times must be increased because of the increased distance of the lens from the film for a focused imbng 1h,iyf a-4age.
(a) Show that when the object is so close to the camera that the image height equals the object height, the exposure time must be four times longer (or 2 f-stops) than when the object is a long distance away (say, $$\infty), given the same illumination and f-stop.
(b) Show that if $d_o$ is at least four or five times the focal length f of the lens, the exposure time is increased by less than half an f-stop relative to the same object being a great distance away.

  The objective lens and the eyepiece of a telescope are spacen;/ yzq2ae9x +g+yim+//fx i0 lh mmrcd 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 viewin -.f2pxb.,t8a onuaeug the Moon. Estimate the minimum distance betu p .e,2o8-xaunt fba.ween two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, one :r;jn,g-le / 4za3o sjtjx,vi 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 ofaru zsq+ohu,o ,*8o 2+wo/tkl 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 n/ p*ywcmigpn w 5m/y.d,/wq /eumbers. Assuming it is necessary to resolve points syn/mq* w/ me/gwc / p5d.ypwi,eparated 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 subp41 p):fbvwy rface 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