Why is the depth of field greater, and the image sharper, when agz s*ouba /q,, camera lens is “stopped down” to a lar/qb a,so*g,zuger f-number? Ignore diffraction.

Describe how diffraction affects thj4 5xnu:/;u ei0s/ ej3b3np9oqiqe fc e statement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a larger f5p:qi fsji4 /neu;3jne3 /9x0ecqbou-number.

Why must a camera lens be moved farther from the film to focus on a closer obje) w(s9o6 kpxycctyock )6wp(sx9 ?

Why are bifocals needed mainly by oldrm5w-4p4)o nf wrrjqsf*n/o + er persons and not generally by younger peop-jrqon+)opws wnm5r/r44 f* f le?

  Will a nearsighted person who weab2 jsau-:; gt,i liix5 )/d omd5pc*pars corrective lenses in her glasses be able to see clearly underwater when wearix5ji; dba glum ,idiopp*-: a/ sc25)tng 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 l iad8r(i5xp24ym cae4ooking at the width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsigh2 4x ypde8i5ai(acr m4ted?

In attempting to disce2 nx)k wr+t)a7frn:kb o9f(yern distant details, people will sometimes squint. Why does this h ynf2kn9r+ oar)fbktx):w7e(elp?

Is the image formed on tvcb1nmde.n; b kl9 6l3he retina of the human eye upright or inverted? Discuss the implications of this for our perceptib1md3 .;clln6bv n9e kon of objects.

The human eye is much like a camera — yet, when a camera yv spu ,41 1ajxd(hkx kg*fm2(shutter is left open and the camera (1xh*2x sumpj(,1 k ady4kgfvis moved, the image will be blurred; but when you move your head with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a convergingmdm 1eh4t-7 p*vbfrz( lens. -z1pe( bmvthm4 7drf*Are reading glasses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for chi:k5qwsqy. a6 dldren’s use usually produce images that are colorq y.s d:56wakqed at the edges. Why?

Spherical aberration in ar8n f3,*lfdqcpwq1 0v 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 an object at infinity, which surface should face the object? d *n8lc rw, q01pfvfq3Use ray diagrams to show why.

Which aberrations present i atkbhk;5)zop2:p9d5l aqdgs x 4f70zn a simple lens are not present (or are greatly reduced) in the human xd50kqgd; kpsza t5:74zlp h29 f)abo eye?

Explain why chromatic aberration occurs for thin lenses bmdgj)xq0d)0wst335 zdf v9 d7nsop4kut not for mirrors.

  By what factor can you improve resolution, oo 1gf jq0no1 0qx9+l:7irnvdw ther things being equal, if you use blue lgvod01n91+oqf lxnjqwi : 0r 7ight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages flh 5mra/j( qojo)y z)8or the use of large reflecting mirrors in astronomical t) jjo( omyr 5qah)l/z8elescopes.

Which color of visible light would give the best resolutionfc8 xmq)-9m0pa2u jjo xg6c pq)br 2d/ in a microscope? Expmp ucx )qjpd) 82gf6-cqmobr/a2 0jx9 lain.

  Atoms have diametersh-m0z +vtanse5-+pf ds sg48g of about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lensoez+ r,nf-l):v 8gqzito2 ah 7 has f-stops ranging from $f/1.4$ to $f/22$. What is the corresponding range of lens diaphragm diameters?    $\mathrm{mm}\leq D\leq$    $\mathrm{mm}$

  A television camera lens has a ydga ap(1g;c)h0bhx y,6i x9e 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 setoawp/th ) u;pk+gv- 03vl(w knting 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 pho*wqmzd8 -ij u+h0yc 4btograph is 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 200.0 mm to 206.0 mmben9k3l;skn i(3)dsv9oh b w.z/um*g fromks(mwgz; 93l3bni)esbv .h9 nkuo/*d the film. For what range of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wi( ul bchlodu(;/n(b qt/r )v6caw81jmshes to photograph a 28-mtall tree from a distance of 58 m. What focal-length lens should be used if the image is to fill the 24-mm heig o c(l/(ncwajbq/uml;rd 618h(uvt)b ht of the film?    mm

A “pinhole” camera uses a tiny pinhole insmu tl5o;hcy4 m.di09btead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed using such a pinholum5ib90dot.l4cm hy;e 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 e7)wvpr8pxyqlm; yh 5: 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 ab,d ic 0/jq3ophout 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 Exampledu/r8:vj-dv :r*d ovo 25–6 wore contact lenses corrected for the far*8:ddjo:vorr -duv /v 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 nz /-.d;xsx -yk/osewiear 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 of 1wu*j 75lfr+h n4 $cm$. 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 re-4+injinm v (y4f 2 3tijxg(inad by 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 by atga+yd l; )bl7 $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly only if they are betr5*pf(:z ; eq ;c) 4rqpxqjgufz8(arcween 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 Exaxpa2r.m s hoa1xta1wzs/q(21 mple 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted pers+m riuu 3x6 wbqcw p;:)ce42 u0tu;yslon’s eyeglasses has a focal length of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when v(vsy qrz2ja.n s68k a8iewing 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 tr2 r4i+tmd +qand 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 wzx7f2ee+ipqx .tdw0.sk88 p8i e;x k qith a relaxed eye if its focal length is 12 et;qx70. ekqi8ks+wpi2. ed x8z x8fp $cm$? =    $\times$

  What is the focal length of ac +rq +o rmr)gtgjv9eax (/h78w*q.ex magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedsco2mml a+,dd/xx0 2y 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 using q/2icwd6 q+uxa 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 k 3 )etk(3q) lt0-djokqc*zgb is viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is pla-owhfa g45s k:ced 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 focal len- e-,qcac(zyh2pn g+ mgth 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 rateda18d;3en i4 vem7ie*rf0ml jxx 6 z+bs 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 astronomi54w u,sf x3yo7j8gjk3 bhtd/m cal telescope whose objective lens has a fos5 3 3b7w4,h/dmuo8jjt yxkgf 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 desi+cvfmv .hq8heoq1n:s h(n.6ured 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 object (drqzzk-zwx/:upt a -:2bg/iive with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaw.e48l4cxod 00 amlamced 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a r/i1ubu3nqf(a9:a u gi elaxed 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 oo*ely:9r2vh9ge6 af bhr 5t/cf an astronomical telescope using a reflecting mirror whose radiurvyeho9 9 ac r*glh/65ebtf: 2s of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified . jqv6g) )dpel120$\times$ 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 qoln a7s0j f8(qni)h43.0 m for its objective mirror and a radiu70ho)qnal sif84 qjn( s 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 fde3, od* zgy1length 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 12.0:fy+ut6mg)e8 al8s es$times$ 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 1.8:2i/ :j/hf dn xtt8col-$cm$-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 th3ovvm *(cycxkc1fcd3l5ustar.mbs m p;079 ,e final image is located 25 $cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compowb. 1l ug+1wj98l )n0 ttdsxemund microscope 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 d rqdp( q6; pf:ejp3vwi3 lo*)contact, that have f3:;pevpl q*pf3dj w)d io(q6rocal 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 aberration in a par( tbjr 9uv95dyticular situation. A planoconvex lens of index of refract9 dytv 9r5(jbuion 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 resolutio q(i7k:eqt5oqi nta.1 n limit (degrees) set by diffraction for the 100-in. (25 5oq 7 kiq:.qnet(iat14-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that jg,8- j5a t uwc x2w 8yr,ckjimnytkf*i13e*8can 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 o2f3t (vi0 axc-*ag yvh2 xci(uf 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 4y3turv g+xem:4 a:eoaway are barely resolved by a 55-$cm$ (mirror diameter) telescope. How far apart are the stars? Assume $\lambda=550\mathrm{~nm.}$ and that the resolution is limited by diffraction.   $ \times10^{11 }\;m$

  (a) How far away can a human eye distinguish two car hen/6m/jst ior0aim 8;,r/ttsm adlights 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 ses cn 7 c*9f32rr3uiljn,ivfn2kz; h; gparated 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 plmi es5gp*)xr2 anes, are spac* xgei p)msr52ed 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 di hsh43 hm; rsv8:vied0rected at an unknown crystal. The second diffraction maximum is recorded when the X-rays ar83e 4shs:h0ri;vm vhde 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 dirk/e8 h*:u rruffraction 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 bea:apvg9, n uq9mcxk5g)fgkh8/m consists of parallel rayschufak p gg/5k9n:mg)v,8q9 x . 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 midday, and the sun38vyh9yf e7by light got more intense, a photographer noted tha93 fbhyevyy87 t, if she kept her shutter speed constant, she had to change the $f$-number from $f/5.6$ to $f/22$. By what factor had the sunlight intensity increased during that time? $I_2$ =    $I_1$

Show that for objects very far away (assume infinity), the muy 0p(1cx galkzb+1/q9cp1 giagnification of a camera lens is proportional to its focal lengt /lqc 11 gc(u1g0xb9kpi+z pyah.

  For a camera equipped wit fp8 bst1,gu(th 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 eiucw ,8tvx:+bye 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 of5/f;mx fq)n zd 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 po2)wi0w4g*jgliyi jq, kq7 we, wer of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mweainn+n8vkt - y3:d7 g-zg*9 voofo:ountains tries to make a telescope using the lenses from his * o:wvoe-dnkn azg:f3 7t - o8iv9nyg+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 use,4wx;vu.rya v*kegd9s $+2.5-diopter$ 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 altitudes (inv n3 l9-w uez9b7oi .sw5o(s25 $km$) 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 distamo/ nghf 3qmi5 jn zsom,(z9/:(pz5n gnces, exposure times must be increased because of the incr z n95oq/53(o,hmg:mz jpfm(i znsg/neased 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 tho830qh 7eeek- zx.pfje 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 aq kbkd+nz8ht 6jxw* );n 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. Ass)*k6;zdbj kwhxt q +n8ume the Hubble is near the Earth.    m

  Two converging lenses, one )ogw ;b9: az g,yjr :gds,dz2pwith $f=4.0\mathrm{~cm}$ 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 art8hrl g9b* 2ele 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 number s+d1bp7q sih-s. Assuming it is necessary to resolve points separap1q -7+ss ihbdted 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 surg-y7y hr;wyx) 1-xe mmface 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