Why is the depth of field greater, and the imab usl,-f76 pdijq,) kqge sharper, when a camera lens is “stopped down” to a larger f-number? Igno7slufq,b,i)pk 6j -qdre diffraction.

Describe how diffraction affects tnpvyh its)k/+y9 h5 +4kap*opg xtv-3 ocb30zhe statement that the depth of field is greater and the image sharper when a camera lens is “stopped down” tsaz i0vhgy4k hkx+p3-cnv*tt3o )9+ppb y /5oo a larger f-number.

Why must a camera lens be movw( xcx ld,:ve6ed farther from the film to focus on a closer objecxd:(c ,vlex6wt?

Why are bifocals needed mainly by older persozc0bie+j( e+pu ml;e/,lbdg p 9s(+azklyn(-ns and not generally by younger people?s(up0 /;zi ynbbll g+, ld(em- k9+ aee+p(jcz

  Will a nearsighted person who wears corrective (k.4shiqqd6r lenses in her glasses be able to see clearly.s(qi4hdq6k r 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 farsighted by l0ad q;km2(n0hctz) )qgk im0tw syoe g7405rbooking at the width of the face through their glasses. If the person’s face appears narrower through the glas))5qsqik4(dbo hkcz2ygm0a0 0 mnewr;0 tgt 7 ses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will sometimes sy :e ojhl-.-2idhf,dvquint. Why does this helpedl-y dh.2io-f ,:hv j?

Is the image formed on the retina of the humm * m28xzxze)ian eye upright or inverted? Discuss the implications*82miz xmze) x of this for our perception of objects.

The human eye is much like a camera — hdz-ej,i78 jqi)z f8m yet, when a camera shutter is left open and the camera is moved, the image will be blurred; but when you move your head q fd,jm8z)z8e hi-7ij with your eyes open, you still see clearly. Explain.

  Reading glasses use convergineduxxncet/ 4i:o3+a 9g lenses. A simple magnifier is also a converging lens. Are reading glasses therefore magnifxdx9tea 3ie :/no 4u+ciers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for childreq 8np8xin+z,cw quq1(5z 0 aucn’s use usually produce images that are colored at the edges.5qxwzq, i u(08q capz18nc+nu Why?

Spherical aberration in a thin lens is rs6 :ad kbgnud 7 h,6gj,+w4nrminimized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a dw +r ksuh7g6:6djn,,nr4a gbreal image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations prhf ob3z2/nnd,yzqgp6zs4. 2 jesent in a simple lens are not present (or are greatly reduced) in the4of 3 zpq6z2j/z bd 2nhgs.,yn human eye?

Explain why chromatic aberration occurs for thin lenses but nb 1pr+nh9eve (ot for mirrors.

  By what factor can you improve resolut tv-cro(t 0/;9 63i*q qqbv m 5rcdrdri0qt8raion, other things being equal, if you use blueqb09m r8*-6vt aqt5 ; vr0o3rtir( cqcqr/ddi light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages foriy/2f)pbsu-k;3bn *dp 3ub zd the use of large reflecting mirrors in astronomical teb ; pn /uizs3bp)3fu*2-kdd yblescopes.

Which color of visible light would give the best resolution in d03u9+ *giw nkam1iin a microscope? Explainn+k niimgidw9u a 1*30.

  Atoms have diameters of abounl7p v )rxgmh7mp.), xt $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has .ykcck:e/bx 1 x; 9zmcf-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 ha 1.clko c a* tbd+3jhsisp+9*n)du2vw s 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 setzmupe9 mns .ov v-.(z8ting 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 atz8,pmx n;k k4u/ o)uuf $f/16$ 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 )) 8nrso* juxois 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjust)sujo*ox8r ) ned?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance of 5y f1o,z9p8qa n8 m. What focal-length lens should be used if the image iszf81p anyoq9, to fill the 24-mm height of the film?    mm

A “pinhole” camera use.(fsk tc ,8fwls a tiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2lf8.kwts(cf , .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 exposkx+5oozx e/s1; 1 iulpsc:mu)3jw vz)j0dow 9ure 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 abvw+1/g.v i; alb7zojoout 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 cor anv:2u4a na/t/t 0fjcok ;;sgrected for the far point 0uvt4csn;ofn jka /a t2/a :;g$(=\,\infty)$ 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 powe/0 9vh ps+kqe4p tso63ymfnb4r are needed for a person whose near point is 115 $cm$, so that he can read a computer screen at 55 $cm$? Assume a lens–eye distance of 1.8 $cm$.+    D

  A person has a far point o t1i jk6+ hux9(u g.,ighy;saof 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 7mz-uypkl 3 9cholding 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 cs gt:s;9) 2i fwhqmi1korrected 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 y08 9*4ixg jmhfomww54 y1v lb nnps.-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 nearsighta:m3n38qld8 na pj8:cy eleu)ed eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted gsdlzk,,:gdv ;1g ylsv8+n+ rperson’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 whe 5 )kt;tw9gkfs)h/( qjod 4u0iez5gbe n 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 n.lhr8c 44fpnx*pxs7g9 5v kml u,sjz0i2 xc4near 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 used withbn:vq, z a2-av l6-bs,1nbrcn a relaxed eye if its focal length is 12 ,rbs c,6n 2:vvzanl-- n1qbba $cm$? =    $\times$

  What is the focal len5aw++e 5pyi8 h.f m6u yyr.*jfo 1neefgth of a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated av*z+eko9 ) 7gvsvku07gem.f ot $2.5\times$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 9. cty)r.78-4u- nhlbr zic zv:f00-$cm$-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 withh7* 4qqot fbqt2kvqwh()( jx1 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 5.5533t bx w.2mqbma:xb0o $cm$ 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 lengt: zm y/4/dd.emn sej*qh 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 ifff607coztg 24a -6nikkbb - vs 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 astronomi4we put dfp+mzoc2 (ih-/ 32tfcal telescope whose objective lens has a focal lengtt e-z(t2fpdwfp+2ho43/mc u ih 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 aq,cfi((4i;lnf ht(ni wcnb,pk4a4v 2n 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 ha 1p gcp uhro*0h.jbp ().s*o(xjltq2ps 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 spaceda wtd xz :vsm3he7/+qy4.n3g v 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 fkpv1pb***ruu 0,f uo d4 0-ti/f zpfjlor 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 ak5fx8j q ,y8k z7pf3cm reflecting mirror whose radius of curv,f y3kk78cxmz85qjp f ature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified 12+t6a /5w;:zldqs xxzx0$\times$ 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 foq+r1g/nt0;el, t j bhcr its objective mirror,tg b;/qne hjt0 +1lrc 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 length ofv.yg.( ct9qxrga:i 3 of3 ffq9 1.40 $cm$. Using a normal eye with a final image at infinity, the tube length is 17.5 $cm$ and the focal length of the objective lens is 0.65 $cm$. What is the magnification of the microscope? =    $\times$

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

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

  A microscope has a 12.0bpk+jv+52 dafh*mq. e$times$ 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 1oe4zpc9n re. 1.8-$cm$-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 fi1u-3htzy0ek2; kc ctbnxu/mn-*2rh t nal image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compound microscope has a focal length of 2.70t1ydh:3. ;g 3*gydl avh klj/t $cm$, 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 owv4bybpl q rwh 0;)v, rwkgt/nz67x4cpv8*0ff two very thin lenses, placed in contact, that have focal lep*q 0vpl4xr f)zywb7 vcv4 b 0,kg/t;w8hwn r6ngths 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 do v p/it 8*hyh9,sdn7kdt 7(eaberration in a particular situation. A planoconvex lens of index of refraction 1.50 and *,tps( 8id 7 h7k9v onyteh/ddradius 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 fohbwox vny-l qo)bj* -i,sn,7ha7).nvr the 100-in. (254i )ovqhxn7o- ysb*-w ,n. ,)vljab hn7-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to ogq8el5yhj+ xpq.7x( construct 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/zlsfsr6al .sf;c1 1qt ydl9j2zy (w4 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;y 5kddj(cgtd)3n re5 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 huot)le*(-4ace s jl/ 9a ya2dihman 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 separat5e54 dt*bngz+r- gq8gisf 7sved 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, lyinrm*gv:ls1 t*o s gfjze 8zy ,.sgpnhr6bd+1 75g in planes, are spaced oysh7+d.v6*:z1r* jg tlp8er, gzs g s5fn b1m0.280 $nm$ 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. 8kp 9ub3h/xpf fsjk360973 nm are directed at an unknown crystal. The second diffraction maximuu36kp bf/sx3hfkjp89m 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 diffractio64n,5 otfmcx.zw6c8n3v u wvo n 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 bec0d kg9gb9e; eam consists of parallel rays. What would be the magnification of the image? a the magnification c gg;99dbeek0is   
(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 mo8s; ggg 65d5f3bi0 k vydlg9htre intense, a photographer noted that, if she kept her shu5il 9gfd sdt3ybgg560h g;vk8 tter 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 (asa cv)xlw/ 9jk:sume infinity), the magnification of a camera lens aklj/cw x)9v:is proportional to its focal length.

  For a camera equipped with0pe opdv, 5fjdr :xx(39uof6i 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 objects are beb/.zp7tvc h3ctween 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 la toi9xm k):*l47rb;yg:yo6pl g)ba 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 :(ytbd7fn fw. pe1c vgi jx,(7$+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mp nl72a wdn88znu 9arxmr ,/rcn4:5qlountains tries to make a telescope using the lenses from his reading glasse94 8/5,lnp7n8ual dr nz2cn:rmax wqrs. 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 bv:7fc 7*4hmcuduln* $+2.5-diopter$ 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 extremdu1dae f 87 ig-3swj/i/ uzgk7ely 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 ver9 -u 2n./xomb4a oa-0ttljymry short distances, exposure times must be increased because of 0ymtm 2ubalnr4to/.-9- xjoa 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 ao101ji8ahr71pbjj/ :g p qpzpnd the eyepiece 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 diametf)ifdpib: (8.hen9x l er of 2.4 m, is viewing the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffractio8 feliif(d9x :p.b)nhn of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses,u qg lxh3f (w9i-6nlix, q)ta9 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 magnification 8sat0vk8x pz/ur 9gcp )*ij4ncsbp: 8 of 8.0. If the two lenses are 28 $cm$ apart, determine the focal length of each lens.
The focal length of the eyepiece lens is    cm
The focal length of the objective lens is    cm

  You want to design a spy satellite to photograph license plate numbers. Assuminc- /6xw3u49c hddx qatg it is nec -a34d cxqdu96/xctwhessary 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 surface l3 z:e*f - cruic69a/h 4lttsuand 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