Why is the depth of field greater, and the image sharper,,ln2cc.wffj 1 when a camera lens is “stopped down” to f jc1fc.ln2w ,a larger f-number? Ignore diffraction.

Describe how diffraction affects the statement that t9mio1 ; aq3lau-x 3vilhe depth of field is greater and the image sharper when a camera lens isl1uav - l33 ;mixo9aqi “stopped down” to a larger f-number.

Why must a camera lens be m9d6f *fz+, ewdc:+qftii0kz xoved farther from the film to focus on a closer objecq tc i d+f*fe+6k09dxi:w,fzzt?

Why are bifocals needed mainly by older persons and not generally by younger peor +7qikb0-2cke wkf 1hple+efi-h1 0rkk7w bcq k2?

  Will a nearsighted person mf a 1wkzm+g4;who wears corrective lenses in her glasses be able to see clearly unzm+;mfw4 k1 gaderwater 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 looking at thtku 7)*ub y+ cy,y 79zanoa5jge width of the face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or noyb nky* +5agz,uj7 ya)c9u7 tearsighted?

In attempting to discern distant details, peo7t41tvo9 uxhwple will sometimes squint. Why does x4 tv1t o7uwh9this help?

Is the image formed on the retina of the human eye upright or inverted?h b *k4q)jhs1lhqc52o Discuss thbc qhqh2hljks541 )o*e implications of this for our perception of objects.

The human eye is much like a camera — yet, when a camd:q kunm3 scwy57:ir b*r r6:zera shutter is left 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. Expqdkm::c*ys7u:z ir3 65rr b wnlain.

  Reading glasses use converging lenses7jir;jnt:: kkhyx6azxk8(df3i c (4 i . A simple magnifier is also a converging lens. Are reading glasses therefore d6jy(z iit:krfx4nix kh j;ac:37 (k8magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for children’s use usually produce images+.iw6p)dtf vl that are colored at the edges. Why?lw+vtfdp.i6 )

Spherical aberration in a thin lens is minimized if rays are bent equallsns-cas.93x (yt pn4r gh-t g:y 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? Usesn :-(ca.t-9nxyts34srg gph ray diagrams to show why.

Which aberrations presh0wmnp:xrfb w );azxl;.q;0p ply 1p; ent in a simple lens are not present (or are greatly reduced) in the hnx0 z mf0:p;la;pwhx w;p;ybqr 1p).l uman eye?

Explain why chromatic aberration occurs for thi rme(pt 6; t:2 hhhj8h as)m(jmdxnt81n lenses but not for mirrors.

  By what factor can you improve resolution, other 9tfy4ws id: q68p7e pjthings being equal, if you use blue light p7 6jspdiw4:qf9 8t ey($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages fo1q6k5)-r8ty 6 ttdgpu5fgb m mr the use of large reflecting mirrors in astronomical telescope 5 u-ytp)bt kgqd6m8tmr5 gf61s.

Which color of visible ligh8ttf 1z l)vp.m.yxaw, t would give the best resolution in a microscope? Exp8t pz.v m,1axf ywl)t.lain.

  Atoms have diameters )q12qqyr an 6cof about $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops rangifj3if1:-ccpcr 0le)3o sn ix(ng 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 s248ly tajgiknkf 9. qev;8*ia 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports n. m,uqah tu35lh *)ss4krb i2that a camera 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 photograznn kfc)ddq . :j71d)dph2oo1ph 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-lengt8m0;l f8ezgsgs;f-uu h lens can be adjusted so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adjustfsu-0u eflm8gz; g8 s;ed?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograp-q; na9u /n5yesomiwv yg 9(4xh a 28-mtall tree from a distance of 58 m. o9 m-aw/ ny4yu(ign9x;ves5q What 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 of a lens. (ct*dm2xsnl crr/gb30b mu ee-x 1c;0Show, using ray diagrams, how reasonably shar/c m3r1lx 2es ;gntb0*0-xubmcdr (ecp images can be formed using 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 exposu8w,j8t.bkjl of nf40 gre 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 abouv/2ih h,ebed /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 Ex5h7u t3n(lv deotf)e5 ample 25–6 wore contact lenses corrected for the farle) ovdnfu (3t5t57he 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 personz4h kqd+r.- sjf:y. h: 9c0ijkc)y fnp 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 poih ym j8 tytb fuowq.22a/,c4x3nt 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 a book at arm’l(yj4 +bxr lsn159 xyus 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 cortt50- pu ydw r,u+mob+8i5jbnrected 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 they are between 35umgg yr n-h76 joci0m5iyq(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 than the 2.0 o+bt0k 3k7mi.xkur 2c $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has akyfz6c:3x sgul8gbx / ey0f*8 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 wheni 0 mmj1 ckc(z2,q+yqy 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 8u)shbvake7e99 73yn vb v9ipfar 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 itsjv4;3 m ;0i:r .rryq*f egchjs focal length isq:rr03h*esr.yfv m;icj g;j4 12 $cm$? =    $\times$

  What is the focal length of a magnif;( 4tez o9mbn4 5fhp83m au9+yenxzmfying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated a+k9 ib 14 cipwx )da+emh(-xbki b25kpt $2.5\times$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 9.0:2ciz 94tazk x0-$cm$-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 vie86 , 0gb hpojz(;yvkubwed 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 5.55wd 6w5d b .:1l gaxuso/;pbgsa02km16c nivx+ $cm$ 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 5 h+tr uhh35ifof 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 isb /t ogg,g5s3 z2efuy, 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 whose objective lens hqhki6 b t,n88mzv 9+j4djc95r uud:rias a focal length of 76q: ib+iku4 5,drr c 9tj9zd8 um8j6hnv $cm$ 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 astronqoz* r sx o/r(li4zz*6omical 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 length 8- v6bgpved 5*i1sqrpn-6js e.w7nsy95 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spsp(p:v gr4d; yaced 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 relaxeyx/wr7o o)m ef2 s-ux8d 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 au n/ xpi,bx*ccr -1ma2stronomical telescope using a reflecting mirror whose radius of curvaturem*rxci1nx2/u-ac,b p is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appe6( kedw-h- )6y 2 hraibo;pyzf usd*;bars 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 (Fig. Below qjzn*d. 2 ivzvp8yl2e:( :gng) has a radius of curvature of 3.0 m for its objective mirror and a radius of curvature ovz8*eg ydz:(2:j2 n ngl.qvipf $-1.50m$ 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 (sjes v*/bykc fg x5j.kr,x+(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 12a 6mj n/zrmfmnl:ki- rq;k807pov* 0z.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 1.8-rkxvr8ri(m n5t80h 30yb) pso$cm$-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 h(dwehp-0 ckf3(j 7tj :k2eza 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 le m3e;x+xzc uo6ngth 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 ve vo z8 co-+ejz9c*8rkbry thin lenses, placed in contact, that have focal len-zoco*j9v8k+b cz8 regths 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;7 jg px1u8 ba:ztvurxke 5q6s80c9/c e;hmiz particular situation. A planoconvex lens of index of refraction 1.50 and radius of curva:8vetc cr8u;1x/zjxge i aq7 u90z hm 5bs;6kpture $R=12.0\mathrm{~$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 diffra kq .bepglm) g9q1qy3-y -ukh4mid6-e ction for the 100-in. (254e-gyq9 pbym6k gkhm d q--.u3)ql1 i4e-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish. hqkymx/*nf7 to 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 ofs9 siclsm 9p2dzed24:2. kafz 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 aoy6; fwp7 :pu;/ avkkpre 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 ah8d v )nyhfn-:e0r+7vv,f g x (tuz6vv 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 separated by abojkk3q2; afk. e*zh8z(j ahi:g ut $400\times10^6\mathrm{~m.}$ 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 whom dta5ub)xqzd.x 7q4 1se atoms, lying in planes, are spaced 0. mqbx4dt zxa)51d .u7q280 $nm$ 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 nujq*: ; k90uyo djgem)m are directed at an unknown crystal. The second diffraction maximum is recorded when the X-rays are directed at an anyje u k u:gqd*9)ojm0;gle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg diffraction is obs/y9*y6vn*3d wei irut 3qaj8 jerved 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 conventruft;ig2d va o2 /;n8eional X-ray image that the X-ray beam consists of parallel rays. What would be the magf28end;it/orav2 ; ugnification 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 photf40r c8,y7 o4*o bkbt /cmp-,yusexooographer noprc o-74sy8, fyobct/*ooumx , k40e bted that, 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 magnifmgzlaus *t .s+ g(uycqc-/r-it de /89ication of a camera lens is proportional to its focal ledcrt y*uu9 l-g/t(m/s zc-sig.e8a +qngth.

  For a camera equipped wl i t+7evobpg )v./7loith 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 ri-o+rnr;kxiv 3yo .4:im x8 qwight eye only when objects are between 45 $cm$ and 155 $cm$ away. Prescription bifocals should have what powers so that she can see distant objects clearly (upper part) and be able to read a book 25 $cm$ away (lower part) with her right eye? Assume that the glasses will be 2.0 $cm$ from the eye.
$P_1$ =    D(upper part)
$P_2$ =    D(lower part)

  A child has a near pointdsrw j s5)h (jj1.8z-:tcpjbd 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 magnifying a ca.ywk5u(b m4ijy( 0power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the mountains tries to make a telescope usin5lm6y4q whymfqug-z+n 1p p): xl-ps4g the lenses from his reading glasses. They -u ):h1l 5mqz-qlnw m g fspy4p6xyp4+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 usesb p qik4602e*1* 3dx lemfspmj $+2.5-diopter$ 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 altitudcv .18*guje tlnc6 wq,es (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, exposure times must2/2yg 8*v5a kd4wb 6gnj8wqiju;hv mi be increased because g2wdba / yi 25mq vwun8;g6vjj8i* 4khof 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 eyepye92:dp, js(f e qh-woiece 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 objectivefz,*6cl wm fz, 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 m6c,z*fz, lwf light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, 3cbhd/ycb+ w44 lm8yn 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 of 8.0. If the two lenses b2qgdc7k ey-7i9q3i u 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. Astgi+qfqp( 9 y7suming it is necessary to resolve points separated by+yq p 9it7q(fg 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 ku7arrq:;)dx a+w,yv4 lvtb0 flat surface 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