Why is the depth of field greater, and the image sharper, when a ca836 *xw coa rra)9lefbmera lens is “stopped down” to a larger f-numcfeoax ba *98w6r 3r)lber? Ignore diffraction.

Describe how diffraction affects the statemn;v ev 2kqrz7b(yx ou+0w)3w qent that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a larger f-number.3qzy0; woxrknwv 7e2uqb +)v(

Why must a camera lens be moved farther from the film to focus on a clo*z4;5 v c 3mj-hf up8ytlfvur2ser object?5f 2ml p8 zh 4*yvcr-j;fu3tvu

Why are bifocals needed mainly by older a mjyzny*;a8s hp76k- persons and not generally by younger peoplehm6* -; jy8zpyaks 7an?

  Will a nearsighted person who wears corrective 3kv/h3, : dyoq xyrqh0lenses in her glasses be able to see clearly underwater when wearin v hqr:3, 30okyx/hydqg 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 an;j n:ow31y:r-ug czmf y fwr5) yz/w*t the width of the face through their glasses. If the person’s face appears narrower through the glasses (F)gn 1w-jnfzzy 3cywfow:/ ymr;* u5 :rig. Below), is the person farsighted or nearsighted?

In attempting to discevlfo; x uv:7v.rn distant details, people will sometimes squint. Why does this hel;. lvf7xv:v uop?

Is the image formed on the retina of the human eye1j 43i2jaai jh 1/a4ukf khrg) upright or inverted? Discuss the implications of this for our perception o14/)gf hajkju 2a4ra k31jiihf objects.

The human eye is much like a camera — yet, when a camera shutter is left open hmu3an2;1 z-xp kd xc3and the camera is moved, the image will be blurred; but when you move your head with your eyes open, you still see c - cz;m3a2px3uxdn1hklearly. Explain.

  Reading glasses use converging lenses. A simple ma0ls eycuc72lqj tpw.k k/+84cgnifier is also a converging lens. Are reading glasses thereforek c uc +ty4cspq0 2.ljwkle/78 magnifiers? ----待选择----yesno  Discuss the similarities and differences between converging lenses as used for these two different purposes.

Inexpensive microsco*x-jvjlv 0kc ;pes for children’s use usually produce images that are colored at the edges;jjk *lc-0vvx. Why?

Spherical aberration in a thin lens is minrh 5enm;o vbb0gst/ +/imized if rays are bent equally by the two surfaces. If a planoconv+/o5bh m nvt;s0 grb/eex 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 in a simplenwi4c49x 9+je/ up4 mhel0iu4fxl9jf lens are not present (or are greatly reduced) in9jxn9ue40 miwh 44x9clfi u4elfp/+j the human eye?

Explain why chromatic aberration occurs for thb le. 9bibv:-min lenses but not for mirrors.

  By what factor can you improve resolution, odwvjc8wkzu ws.5 932xther things being equal, if you use bluz2wv dwc5.x39ks8 jw ue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantagn/(kjzb ;x d7ues for the use of large reflecting mirrors in astronom7(ukd;jb nxz/ical telescopes.

Which color of visible la j:1)ktllrx7/-vgve l*pf r+ight would give the best resolution in a microscope? Explkr+ ):evv7rtp x/ 1*-llalgfjain.

  Atoms have diameters of mu8 7(7jlw ;s*vdgt-h43;ckckmhx3(aj om htabout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens : ev)s vd8kr;x3mr32vgmy-ghhas 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 14-+m btcqu ipgirc;t*k qkk.1(l eu,:( )$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports that a camera settik4n 5tc;(qncs ng 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 photographm sursqm4 m.+0ks8 p4m 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 20umxho)86-vg ) sphwr3 0.0 mm to 206.0 mm from the film. For what range of object distances )w h3 uop8)6mxg-s rvhcan it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes tovbez,8dg k4x* photograph a 28-mtall tree from a distance of 58 m. What focal-b zd48gk,v *xelength lens should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhol wo1.4m.rm0d*w irehxm90apcnpp6 *b e instead of a lens. Show, using ray diagrams, how reasonably sharp images can 0bia1rw p0dm4 xwep mon .m**69phr.cbe 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 correc+ch t8 d3pnqim /w,oq8hlt: /vt exposure 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 about 2tnkzxi7*dvxxze f)(z qy.;0t( )(x4nj l7gxe .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 co0z)tlctt2f uu2 x4f-7 glec- zntact lenses corrected for the far poin fc-t4cle tu )z0 7f2lgxz-2utt $(=\,\infty)$ 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 p sk4qdl .m8+58xvxnm serson 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 of cs++t, mtaw,c glwi7 614 $cm$. 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’s length, a ddh+9ymxw4 oi ;zvc 8w,istance 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 tv bau5fye*k- 2(qdb) 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*;st (a itk*je 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 iuk r 3iz,3 mfa:ajxcqq4 n5l*6n Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eye /k0yey g ajy:)go,x7/s4i mauglasses 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 syst.1wif 6d5q 5xeoihx/ xem 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 of 10.0 and 20.wiygek/: x:zt70me in6 r-ao /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 magnificatip7nwegx3l-f/r m5v w)on of a lens used with a relaxed eye if its focal length is nx l/w5vfg -wm 3)er7p12 $cm$? =    $\times$

  What is the focal length of a magnifyino u vi*e:1sw0dg glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is ratedh/npid g2u/9ag j6wk wrg/ t*- 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 usiyz1k0546oa7 yzcykqz ng a 9.00-$cm$-focal-length lens as his magnifying glass. To obtain maximum magnification, where must the object be placed (assume a normal eye), and what will be the magnification?
$d_o$ =    cm from the lens
M =    $\times$

  A 3.30-mm-wide beetle is viewedwgl5vanse,5n s (97n h 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 plac uttxgyy1n4w4o 9+7oyg5k1ds,kh 2mned 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 8.5 o cx w )a2ih00k7jqcgq:cw *y*+bc2vy $cm$ 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 rac9;5my+yejwd xuo * h v2tb,rn,k*-u xted 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 astro;ur wyll *xqp- ;ud*-6dqjlh8nomical telescope whose objective lens has a focal lengd-hqjwulpl y;rx * ;8l du-q*6th 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 tel bpmcw *+ y2ubo(sd6r8escope 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 hw l4)fl:l :iccas 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 spaced 75.)i rn7.bp8t fen4zzyljbp j, ))/oj1 w2 $cm$ 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 rel adp78* v2 v7j-ljksy4shlg, 5tmu :uwaxed 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 telescopei7dmm hp;q u 0) ac6orxe.ffxr30hc 4( using a reflecting mirror whose radimx0) a(dcmu734 oirfe x.rq0h f6; hcpus of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to ov6fa :c,v-q qbe 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) has a radiods9:q1 +x immus of curvature of 3.0 m for its objective mirror and a radius of curvature of+9 :m sdqx1imo $-1.50m$ 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 kq y1.v:o8hj0o*gny elength 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 12.9tqcir0(wb/89bfbrl, m e+op0$times$ 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.+j req2ohvy:2 ;ehlv.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 mr-9lgvh- ywz9 0vil4 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 fooow,/ xm1:xj8d0llqs+5yqwp cal 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 two4-hcx8 l9ys9-i-x ci zre0lpc very thin lenses, placed in contact, that have focal length 8-ex-9 9lc 4r plxc0cihsyiz-s 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 particular situation. A plano9 z8m8 p/c(ix2xikmzjconvex lensp(8mk/i9jm8xzzi2x c of index of refraction 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 resolution limit (degrees) set by diffraction for tgv8fsyn: i,oohos,0+ pyl 0j;he 100-in. n :+v sio lf,,y 0ohyp0j8os;g(254-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to construct a telescope that can resolve fe.dc7w nz*h(qm, z2ll2vvf/ z datures 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 foc90mbwic m zmi2i-h 1o5al length 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 away are barely res :k/yr n)f/71wnzor lcolved 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 ey9g xv7)v66 mcnjabbc/e 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 sepu5w0 ot 5h e-(ecwa-bzzj+fr /arated 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 crystapf(ay 1euj4:m6g/g s il whose atoms, lying in planes, are spaya 1/p4ugi(:es6fgjm ced 0.280 $nm$ apart. At what angle \phi (relative to the surface, Fig. Below) must the X-rays be directed if the first diffraction maximum is to be observed? $\phi $ =    $^{\circ}\,$

  X-rays of wavelength 0.0973 nm are directed at an unknown d3c kkoie; q4 42l*vpicrystal. The second diffraction maximum is recorded when the X-rays are directedv l id44pk2*ckoe3q ;i 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 observed atr ;d3kl7q , rejn djwt+)cmq;3 $\mathrm{25.2°}$ related to the crystal surface, with spacing between atoms of 0.24 $nm$.
(a) At what angle will second order be observed? $\phi_2 $=    $^{\circ}\,$
(b) What is the wavelength of the X-rays? $\lambda $ =    nm

  (a) Suppose for a conventional X-ray image that the X-ray beam consisvwjor 6 lxu-d33n43f pts of parallel rays. What would be ldwnvu-x o3j 43 36frpthe 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 passevq1vw-jyvti m fqpig5 2.:1v5 d toward midday, and the sunlight got more intense, a photographer noted that, if she kept her shu5y:1 2igqmpwqj1tf 5i.vvvv-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 (assumdi qnxx.51bt5-qnw :xe infinity), the magnification of a cawx.nn5 : qdqxbi- t15xmera lens is proportional to its focal length.

  For a camera equipped with a 50 pffpk 62jacfhwm(:6 4-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when ob bv.b9ek u bs,i;t*,; *rpsfoujects 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 of 15 ; bbp p:ornu mr-1a(duh k).*b$cm$. 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 .)9zquqfhgy4 power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in tx2 p80fz /ih:rv5u3ntcr8m fohe mountains tries to make a telescope using the lenses from his rea 2ro/ir:3zpn hutmxfv8f 8c50ding 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 szt 7+x;eh/gqs $+2.5-diopter$ 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 extremel0;u 5zcge +w mhksk/c7y 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 d le.2 :t;8qmdmsd3gx zistances, exposure times must be increased because of the increased distance of the lens from the film f:x;dlm. 8 se23dqgtmzor 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 o twvu2wu(v *k0f 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 diameter of 2.4 m, is viewing th 2x.ng v* 7qc*aouw1fpe Moon. Estimate the minimum distance between twavupx1qo2 7.g n*c *wfo 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, on..nndtf64xmm e 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 ha 80ynods fk(9 dnpc-) 3zvo/wqs a magnification 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 ;fyy6k les yj00:ith 3to photograph license plate numbers. Assuming it is0yh l; 6esit j:yky3f0 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. Belo36o fo i-r t+udoi sh6cw:2jc1w) 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