Why is the depth of field greater, and *kxp t6 cz b5wka.93ldthe image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore p3a6zw9 dcxk.lk* 5tbdiffraction.

Describe how diffraction affects the statemez67, nn3j 6faulls63 3x2odaobq gc9nnt that the depth of field is greater and theadznbx6q j s3 a o9nl32cgno3f7u66l, image sharper when a camera lens is “stopped down” to a larger f-number.

Why must a camera lens be6z a wiy:g tooh*0/6bo moved farther from the film to focus on a closer objecta:h* yto0/zgwibo 66o?

Why are bifocals needed mainly by older persons and not generallynyt- q7hn gxx(y+l hs:a,vi+zom 3 i:6 by younger peopn3 -yi:,lyxm7sh n :(xt+z6aoh v iq+gle?

  Will a nearsighted person who qg fp0f/e,b3wwears corrective lenses in her glasses be able to see clearly underw qb0 epf3,gw/fater when wearing those glasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a person is3lddk/przs+h k fve 3n7) 2afr3s14an nearsighted or farsighted by looking at the width of thed) k n4pzs7ka3esl f13n v3f2drr+a/h face through their glasses. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details,u)j,tzs1rcm0gg k-h* people will sometimes squint. Why does thik u,tsj hr)0- *cggz1ms help?

Is the image formed on the retina of the .0 bzb)m0.8fpbwtmbmxm e .m754:ohqtlqh3vhuman eye upright or inverted? Discuss the implications of this for our perception of objectsf w0)0mz bm3 :.5xto8 bh e4ltm7bhmq.q.pvb m.

The human eye is much like a camera* t j57rvj6hu8rbd,q l — yet, when a camera shutter is left open and the camera is moved, tj *rd8l5j,vbuq76r h 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 ma17)lvoma /ic vo6+ : *tyxkjjjgnifier is also a converging lens. Are reading glax/okt*ci +6j: vjlv7y)joa m1sses therefore magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microscopes for childt8h+-cx d i)llren’s use usually produce images that are colored at the edges. Whytc)x - llhi+d8?

Spherical aberration in a thin lens is minimized if rays are bent equaq-5bh phhu67 we r4kxd-wqn 2-i2b9zklly by the two surfaces. If a plibb9dq w4zk2k2uhh 7 w-nxh-5p qre-6 anoconvex lens is used to form a real image of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present indwfvl9h(h( k m gb74ah3qkf.7 a simple lens are not present (or are greatly reduced) in the hul7mh7 k.a( qdfgbhv(wf3hk 49man eye?

Explain why chromatic aberration occurs for thin lenses beh0q +zg8 j.reut not for mirrors.

  By what factor can you improve resolution, other things being eqilry +h+1 b a m/h6*x 2zn2kj3mkjne2mual, if you use blue +3njr6i+x zb 2mm2j kaehmn 2/h*k 1yllight ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of lark3fj/:w)ngwuntzuo8z+ 8e :s ge reflecting mirrors in astronomical telescope:uun:+3 sz8 o8ww)ejg fznt /ks.

Which color of visible light would give the best resolution5ug7/ lras g m3*3l f43awebra in a microscope? Explaisra3l al7wfa 3 5u34/ggm*rben.

  Atoms have diameters of abo 3vvjb)7sn*h wut $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops ranginvgx 08bueotw --/ii:cx 2nyw5y o/(pnb 91lo wg 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 ac* o-mv*hatn-ia8h d*x nq92m 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports thatcf k2d;t73ve ug hjeki;6j80a4vbvu) 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 photograph 6h p5d+qj+agz ee3z y daj/7d:fczl3. 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 206.0tj*d0x;zcouh6s1 2o t6zxu /o g(r7st mm from the film. For what rang c6 o2s /6x*ooh;jztsut01u(d 7xztgre of object distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from a distance7ume1 cfes94r6fl o8m of 58 m. What focal-length lens should be used es14fmm6r c8o7 fel 9uif the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a +r ,2n 0z0/foplyq qwstiny pinhole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be formed us0fnw +q2opr qsz/,yl0 ing 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 expxunhmb(k-m- 8osure 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 aboutal9yqd;a8-qz73*r c .dkdm dl 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 usy1 a+0g4edh for the far poig4h 1a ds+yu0ent $(=\,\infty)$ 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 py:jlacc-,q4h erson 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 poi 5(oalxgf f7h1nt 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 t (fshuuh0y 8t(o read 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 bj-z f)dzib(r 0y 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 seeurzh0n( 3wnrz rn1s1x 7/wvl, objects clearly only if they are between 25 $cm$ and 75 $cm$ away.
(a) What power of contact lens is required so that objects far away are sharp? -    D
(b) What will be the near point with the lens in place?    cm

  About how much longer is the nearsighted eye in Exad yh/jxxd.af e22.k*dz*v )kemple 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has ai 4 4ek t*ot0;hxrsk)i 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 (xsso-6s4yeluur v 86 the eye–lens system when viewing an object
(a) at infinity,    cm
(b) 33 $cm$ from the eye? Assume that the lens–retina distance is 2.0 $cm$.   cm

  A nearsighted person has near and far points 5vf mt) ru:u;uof 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnification of a lens used with a relaxed eye if its focal length6 g33/y f6wq) in y7jlxw/knebavepeur7-66c i)3l6 6jq/c67g/nku 7 -3xyvbee nfyw 6rawieps 12 $cm$? =    $\times$

  What is the focal length of a magniqc3/j 2l5prtc7)ixswdkjbgd 4h.( .y c y;q ,kfying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated at 1ub56 s wqblr/$2.5\times$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 udx) xmmwirn6;)p 1d+ 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; r*lppy-fu39r cayudq 3 )q*8xmyc2p 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 plac8i80i -sf zmfkxh2o :m emcq2)ed 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 length of 68k6kld : g(0 5ts w8phzwarej8.5 $cm$ 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 rated1b(j90 cun92an kpnng 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 has +g tdsy9hufa70 +ge)vnnl) h* 9+t7g*sv )hygdel nha u+fn0) a focal 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 magnifica, pgm:q 5 ehr3 6lzi;yqtb1ire om0/z-tion of an astronomical telescope is desired to be 25$\times$. If an objective of 78$-cm$ focal length is used,
what must be the focal length of the eyepiece? $f_e$ =    cm
What is the overall length of the telescope when adjusted for use by the relaxed eye? L =    cm

  An 8.0$\times$ binocular has 2.8$-$cm$-focal-length$ eyepieces. What is the focal length of the objective lenses?    cm

  An astronomical telescope has an objective with focal lee5r5 si)sgm + vvj.)tvm,l7 icngth 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced 75.2 07 bjkvw nuue-e,drrk , l-:x/$cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relaxed eye irj) ();m ooyi .w,tujss 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 a50gcix uw, 5dngs ppl0tmt*6) reflecting mirror wht50n lwdpct*6x gp50gi u,)smose radius of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appearss:24 gien,9yl e33gfdpe :ibk6kr4 wn 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)r k1cvhf 5u qu9+yj30p has a radius of curvature of 3.0 m for its obuuc 1 hjk50q p9vry3f+jective 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 eyepiece with a focal length of0q;)ibu+/w uk.bwq 1 a5aczwk 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 1q- ;n 4tq:owj,*empxdkhbn7 ) 2.0$times$ 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 1.0ra1fh uc.+ fk8-$cm$-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 thxl4(+8e4ldlt )sgp dee final 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 tf:ir;e6(j n/)onk: ngiy jh.2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of tw . e:lks5vkup+wqk15 no very thin lenses, placed in contact, that have focal p5e+v u51nksk .:lkqwlengths 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 tt: )sd1tf : xt91phbl2. mjjzu7*bewa particular situation. A planoconvex lens of index of refraction 1.50 and rt dlp htexjf11t*wu7b9zbmj ::t .)2sadius 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 resolution9ge :c6ixlo,fj0 o7fc limit (degrees) set by diffraction for the 100-in. (25c6ig 7o0cjf:l 9xf,oe4-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to .d y:m6s;jkph .b8w hpconstruct 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 lengt9ptte1tg0; u7 akf-y xh of 50.0 $mm$. Its aperture diameter varies from a maximum of 25 $mm$ $(f/2)$ to a minimum of 3.0 mm $(f/16)$. Determine the resolution limit set by diffraction for $f/2$ and $f/16$. Specify as the number of lines per millimeter resolved on the film. Take $\lambda=550\mathrm{~nm.}$
For $\frac{f}{2}$ we have $\frac{1}{RP_2}$ =    lines/mm
For $\frac{f}{16}$ we have $\frac{1}{RP_2}$ =    lines/mm

  Two stars 15 light-years aw1-ow v;)c.xu f -2opav 5fc(up emwps;ay 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 hz2y9 8 mo+luw v+ 43(wjgftpy8i-u lhteadlights 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 p k8g vd4m*nz502tsj1lo d4zp separated 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 asztij 4e;*4m:pppumdx*0 i+planes, are spaces44du a*ppei+; j:zmpi*t 0mxd 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 nmcfu-4zfym-/v r -w(f:w3 emzt are directed at an unknown crystal. The second diffraction maximum is recorded wf-u 3t-m yfz(vw4c fw emzr-/:hen 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 diffraction is msy2y:c)a *pf 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 t2 *lu gng:qt,chat the X-ray beam consists of parallel rays. What would be the magnin gq,ug:c2 t*lfication 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 sunm:08nt bi)nvelight got more intense, a photographer n:vmb 0e8 )nntioted 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 (vid m2;za 1i-nn p-vbvery far away (assume infinity), the magnification of a camera lens is proport;-va -zb 2d1imp(vn niional to its focal length.

  For a camera equipped w s+, uwqd jg3r; gb :0-t//v8zlqpmyugith 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 henqj5zfhn .h*qln +(s vg4 n.2zr right 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 point o ojbf(/ i1/dcpf 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 + rv e-r /p)0xko t3vvan -c28hwdcpeq6q.n2vof 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 using the lenseskde xus*7skcc4q rb/5f tb9q5a0,zn 6 from his reading glasses. They havet5 asc0k b65s49r, cq*/bnqkf d 7uzxe 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 n6 xr7(n 2o ojbrq mgq1/u1u2g$+2.5-diopter$ 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 extr9 0ae9treyb6 xemely high altitudes (25 $km$) to avoid interception. Their cameras are reportedly able to discern features as small as 5 $cm$. What must be the minimum aperture of the camera lens to afford this resolution? (Use $\lambda=550\mathrm{~nm}.$)D =    cm

When shooting pictures at very short dinl)s58 ):ms cnebcq2vstances, exposure times must be increased because of the increased dis n:l)sc5e v)8qmsn 2bctance 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 eyepiece of a telescope are spaced .cbf7 ,knvin5sz7 bxl4 /m hh*6pbn-b85 $cm$ apart. If the eyepiece is $+23$ diopters, what is the total magnification of the telescope? $M$ =    $\times$

  The Hubble Space Telescope, with an objective wc4(j- a0wccg diameter of 2.4 m, is viewing the Moon. Estimate the minimum distance betc gacj-(cww04 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 witws -z9m:6k)vel.-m x yxvpr a/h $f=4.0\mathrm{~cm}$ 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 magnifii s(do2e9fffe k ,zjf+a2j)/wcation 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-h 2sj/z arj2 nv5q8hw license plate numbers. Assuming it is2hjv- an qrz/8hw2j 5s necessary 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. Bei6srp x1 3- 2.s;k 5yxpl: jbac:n (c2pxttyyplow) has one 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