Why is the depth of field greater, and the image sharper, when a camera lens iw7yaf6m0vau, fgs3 h-s “stopped down” to a largerf3yugfahv,07 wam6-s f-number? Ignore diffraction.

Describe how diffract 65vsv y 4qiq6u.a t7cyu7cfb:ion affects the statement that the depth of field is greater and the image sharper when a camera lens is “stopped down” to a l u:u 6v 7ify5q7vacy4scb.6tqarger f-number.

Why must a camera lens be o0c lxbj8tv o a(tt1 )t:l8/nnk.wh0kmoved farther from the film to focus on a closer object0 t(kl18bvlnt 8a /ktow:no0j).thcx ?

Why are bifocals needocg pp-srt *a8ejh)-,ed mainly by older persons and not generally by younger people gc o-hpr8a-,e pj*t)s?

  Will a nearsighted person who wears corrective lenses in her glasses be able t i4o6+(uvzpmu*rm k ju74ai 5go see clearly underwater when wearing those gl+4p( 5 zm avguur67*4iimujk oasses?  ----待选择----yesno Use a diagram to show why or why not.

You can tell whether a persofb t+bxj r;4c1n is nearsighted or farsighted by looking at the width of the face through their glasses. If the person’s face appears narrower thb b;j +xcfr41trough the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant details, people will ikx8 x/1wstr lu)w o.(sometimes squint. Why doesowx1/x l kw)(tu ir8s. this help?

Is the image formed on the retina of the human eye upright or inverted? Discu8)du6g+ kj jip hcv.z7ss the implications of this for our perception of obj6k78j+cu )ivd .zhjgpects.

The human eye is much like a camera — yet, whenak p4 uk7(kriq9dd6-f a camera shutter is left open and the camera is moved, the image will be blurred; but when you move your hea kipk-af 7ur4 (6kq9ddd with your eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple mamatk) l, 6c uy: c1p8i3bf rq8r.kuyl:gnifier is also a converging lens. Arek3, l :yqlrutrcy 8 ).1kcbaipm:fu68 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 children’s use usualll3 .xvazs l6f1y produce images that are colored at3lsa6zxv1fl . the edges. Why?

Spherical aberration in a thin lens 4fsh 3g ny( o3,hll9;n*okoigis 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? Use ray diagrams to show whyifl;o 9ng, soo 33ly( kh4*ngh.

Which aberrations present in a simple lens are not presentsr70vo2w: w rnl ij6h0 (or are greatly reduced) in the humarnhowrw0 jl:i672 s 0vn eye?

Explain why chromatic aberration occurs f0t -p k)pedt--dhyz2uor thin lenses but not for mirrors.

  By what factor can you improve resolutiona cl0dgog ayo n-1)0c,, other things being equal, if you use blyalc c0o0go1g dna)-, ue light ($\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of large reflecting0 , 0cbn2cj;; 8ounqzo.xxekh mirrors in astronomical telesco;hcxx nqeb.;j8zco,2 no k0 0upes.

Which color of visible liyufm*t t v+0wo7tg:i87 bx/ ibght would give the best resolution in a microscope? Explf7x 0o8my:g*itbvi u /7bttw+ ain.

  Atoms have diameters of afx9al( v;9br zbout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stops ranginloh7 p22, 6a(zn/ eosxqxm5jjg 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 dcwg82 c gu2pnd15z3 ohas a 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports tztex ma-;ro 91hat 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 is taken 8v9t;eicka8kofn 6vw) k9 a;t 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 adjustxtth;s-.bfimhlp3 ,3 ed so that it is 200.0 mm to 206.0 mm from the film. For what range of object distances can it be adph m-ibl fx3t.th3 s,;justed?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph j/cv6vg pja1lijl+ -l1 )+soqa 28-mtall tree from a distance of 58 m. What focal-length lens v+l)1+gl / l saivo6j-1jcj qpshould 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. Show, using ray dip08 1 ew*pbm t+zu+whaagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, consider two point objects 2.0 8pwmtze1ub h*p0a++ w$cm$ 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 corre5 p sl6xlopz2g)rk-c8+q x/qkct 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 1 ;04j s3u dyolt1atgh2.0 $cm$ 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 :bce; /k8byy8ikd3kz contact lenses corrected for the far point kkby zy88 i:;/k becd3$(=\,\infty)$ 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 near poin,f;;b5 bb gdhtt 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 146*os(cpzi up-0q e. ugb5iy7x $cm$. 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 lv: 87jozq* zqgength, 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 correcteda: gpn0/m+ a6zwxbguqe2j.rl6 fb7 z1 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 o3k)stlmx4)qsc7fwi fw6 (2:zcv s+zo;uhun /bjects 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/dlz5pnkv 2-fz n ,x)cfx (5qa Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal leb w1;(jpship7h3lg. u ngth 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 olrep11f lv2 x0f 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 ha/toi;hvr1qe 5w8 yb+bs near and far points of 10.0 and 20.0 $cm$, respectively. If she puts on contact lenses with power $P\,=\,-4.00D$, what are her new near and far points?
near point    cm
far point    cm

  What is the magnificg.: n6bz qh7 )vk2lejzation of a lens used with a relaxed eye if its focal length is b7z)n:kv 6lgq e2. hjz12 $cm$? =    $\times$

  What is the focal length of a magnifying glass of (y) 4csdqt,l.krwbui4h h7 3w$3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated zdm8l, zmv4m shmf;2o 2+fvs )*oswo5o (yw+dat $2.5\times$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 using2hctwh6q (q pj k+*7pw 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 viewed with y j l6m8ic*)f rvyg3p+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 place5u6vp j:s q4fod 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 foc)d++lcflmqwy 3+ pytkbv 27o0 )nv5lr8o pv(g al length 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 rateiv0 hl 0ycwmp7 k.e,:bd 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 ter fw,-r )rtn)surh,o *lescope whose objective lens has an,r)tw r ho-rufs ,r*) 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 magnification of an aste 15uk+zv1h916qiino sr-gv b ronomical 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 focs0m8u u e .fu17/5mfae3ut99 z*ljmdk-egnn aal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spacrgotfp l( .6bf;rx9z 1ed 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 fouf34 c 0ik9m* feo5z )whev/oyr a relaxed eye is 32.8 $cm$ long. If the objective lens has a focal length of 36.0 $cm$, what is the magnification? =    $\times$

  What is the magnifying power of an astronomical-o8fy x6zqx(o() zhzw telescope using a reflecting mirror whose radiuz (zxw)hfx(6ooqz 8- ys of curvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appe4 ( / vzpu74ws3xdagrcars 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) hase/rpcsk f j2vyi :/rw-v+- m(93wruhl a radius of curvature of 3.0 m for its objeem hw-r/l9wy-2sr u(jpk f rv/:+3icv ctive 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 e/ vg 6vzzhj):iox8pe( pr).g(dkrv6q yepiece with 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 12.agh1 j zocf39;djlh y.kyj890 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 1vgikhd ,by syc,fd-cd))hfe 87*5 gt.tte3z /.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 assumiw ru*i:jm golg0 fvr7v 0jgs0h61:0eing that the 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 zab;r2zn( 3fvl* zgw4of 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 vzshcx:z15( n8s,enr eery thin lenses, placed in contact, that have focal lengths 5hsrn, ce(1e nzsx: 8zof $f_1=-28\mathrm{~cm}$ 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 situati,vk h/lgf.:q von. A planoconvex lens of index of refracqv: lkh gf.v,/tion 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 (degkt*f hyvyl)e vr*4y09rees) set by diffraction for the 100-in. (25)rk* 94t*yvlfyy v he04-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish to condtiv 9-e;f ij9struct 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 camer)n/fv w1 f,lr:a y-mbva has a focal 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 bare7m :5o . zhsgu) inrddwx+6pdkve57z /ly 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 headlightua(q)p t(yt+mf0d/0lb c o2gps 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 sepc6 hrm, q(b3dgarated 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 cxo 3571liadkurystal whose atoms, lying in planes, are su7lok5 1iad 3xpaced 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 crystal. The second div m* 5dbmgf*ew)tu.d) ffraction maximum is recordbtm* mg5 fwuv)*. )edded when the X-rays are directed at an angle of $\mathrm{23.4°}$ relative to the crystal surface. What is the spacing between crystal planes? d =    nm

  First-order Bragg difkmy .8xux)b-cfraction 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 ima hp4ptj,k my vmxm:.7jc3r9+pge that the X-ray beam consists of parallel rays. What would be the magnif7m:tj. yh,j3m4xp mpvc9+r kpication 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 qb mj(,j-wvf 0j44ld csunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had to -jqcf0(jj4m l vdbw4,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 magnification of a +w hcj0qri9 4wx ef:a3camera lens is proportional to its focal length.qrwiwafe 0x+: 493j hc

  For a camera equipped w3 q 3ci5 gi 8nis::fi2gfztxa(ith a 50-$mm$-focal-length lens, what is the object distance if the image height equals the object height? How far is the object from the film?
$d_o$ =    mm
d =    mm

  A woman can see clearly with her right eye only when obje(*n5e/tr f 2fc2kbtef cts 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 poin)pia3j lj4 2blf9 a4dgt 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 ;9pph o n+gsp36lbtq2power of a $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in the moune*vr8*+cgppyp eq+/o .0s ukptains tries to make a telescope using the lenses from his reading glasses. Thg0e8 *s.ppp+eyqo c+u*kr/p vey have powers of $+2.0-D$ and $+4.0-D$, respectively.
(a) What maximum magnification telescope is possible? $M$ =    $\times$
(b) Which lens should be used as the eyepiece?    D

  A 50-year-old man uses -mw)le2aeo))1t bj,ds*ku yf $+2.5-diopter$ 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 hisupnz1l 7x:ds/o1 3vigh 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 distances, exposure times must be increase::a*8wtjfvq 7qy md v6d m:aqqv w8yv*:j7 f d6tbecause of 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 eyepiece of as +k,je uj .jic0fc;s, 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 viewin jx5aim1l2;vo/n-7j:vohy z ryo ok* .g 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. Assume the Hubble is n-y1jx or7kmyov/a5oo;j2 n liz hv.:*ear the Earth.    m

  Two converging lenses,duim8pr3t0 h1 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 h6y8c p6.iqeckm;cr *aas 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 h )wlvq2ai 9;lo s9u ,qnbe88jsatellite to photograph license plate numbers. Assuming ib ;8 29lq9 )senvljoi h,8aquwt is 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. Below) has one flaf9jsib6q (h /5xi mg0lt 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