Why is the depth of field greater, and the image sharperzlv)u6 z9 x+ps, when a camera lens is “stopped down vs)x6 zulz9+p” to a larger f-number? Ignore diffraction.

Describe how diffraction affects the statey6l:4 vj-bg xkment that the depth of field is greater and the image sharper when a camera lensljvxk-6y g4: b is “stopped down” to a larger f-number.

Why must a camera lens be moved farther from the film to ixr-i;+ -gfrey oh p*+focus on a closer objec;-ieph+-x*rri+ ygo ft?

Why are bifocals needed mainly by older persons and not genera.p/lv .) (9jgl izhnxln zc23nlly by younger peopn.9nngl()lzcjhp/ 3.v2 z lxile?

  Will a nearsighted person who wears correctivbts bp5 .j6xefko-0nh.;a/lh oa)rx4e lenses in her glasses be able to see clearlyjano;rk6 t0bf-/lho ebhsapx 4. x)5 . underwater 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 a7,/ kzbv8f/(due/a li bf8itkt the width of the face through their glassib8/7v e t( u k8zfafdl/ki/,bes. If the person’s face appears narrower through the glasses (Fig. Below), is the person farsighted or nearsighted?

In attempting to discern distant detaiov, kqdkrhu5n(+lkf7 ou6v w1v1s1q (ls, people will sometimes squint. Why doeso1klkwunh5r v1q vo1v(+6duq(k,s7f this help?

Is the image formed on the retina of the h pz wnc;n* +f p8xb:wd7dq yi;rf.bam47 4isx,uman eye upright or inverted? Discuss the implications of this for andn*b. 7+ pwfcbsm;x7q,r8 4ipz: f;x wi4dyour perception of objects.

The human eye is much like a camera — yet, when a cameraohasaola,5.g 0 2k-ai 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 seaa -.h0i,ook 5gl2saae clearly. Explain.

  Reading glasses use f(7ccc4qmtm9d/wy w 8l i.4wxconverging lenses. A simple magnifier is also a converging lens. Are reading glasses thiwd 7w4clmy/ (cm.qc8xf9wt 4erefore 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 usually produce images that are clygp7 . /gx2brolored at thex.gg2/l y p7rb edges. Why?

Spherical aberration in a thin lens is minimeu-ekuwzbs0ar di46in gvt37)gcuf.- u f2 83ized if rays are bent equally by the two surfaces. If a planoconvex lens is used to form a real image of an og-f -7ib dawei nz2 ce.v8uug6)usrk4uft0 33 bject at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations present i-*xmv r8e93v dht 5bcrn a simple lens are not present (or are greatly reduced) *-cv53b8mtr xrdvh9e in the human eye?

Explain why chromatic aberration occurs for thin lenses but not for mirror6r6-xw6rjig wx f9fro:o6s:ls.

  By what factor can you improve resolution, other thi +ykv+w:i sj+lngs being equal, if you use blue light (slyvj+ +:w+ik $\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two ad em5i kibhyk4ji8eby4,:i 8n;vantages for the use of large reflecting mirrors in astronomical telescopesik8yi 4e :i5;bmh nyk,84ibe j.

Which color of visible light would g (v9sy5f; e/-zn, embj bvy)ygive the best resolution in a microscope? Expy5b9e),y -b/ysf ve;mngvjz(lain.

  Atoms have diameters o 4u0, ybea9:zu*dhpssrpl79 bf 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-stopsk3+ k;nog( 3 uau23dsl)voiqv 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 14nv ,c5hmd4z-my)znn(;e t*mrz m, ie.-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports+-cmh m*h*hwxfn7y h 9 that 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 phy2zz*kf1 3h8 2qhgyp ne fa(6kotograph is taken at $f/16$ and $\frac{1}{60}\,s$ What lens opening would be required if the shutter speed were $\frac{1}{1000}\,s$? $f$/  

  If an $f$ = 135-mm telephoto lens is designed to cover object distances from 1.2 m to $\infty $, over what distance must the lens move relative to the plane of the film?    mm

  A 200-mm-focal-length lens can be adjusted so that it is 200.0 mm to 206.0 0 0zo*xrgkqlav.ru+il 3c :y1mm from the film. For what range of object distances can it be adjus+cxi l1v*ul q. az0og3r0:kyr ted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall tree from tj:/w b0kje/ qw0up,u wt 1.nz8y+wf ta distance of 58 m. What focal-length lens should be used if the image is to fill the 24wjq0+uwpk ey0ft/ n: tj w8,tuzb1.w/-mm height of the film?    mm

A “pinhole” camera uses a tiny pin ;(j5 q58kr+u543. ufnf( lz ala-ubohc zpxfohole instead of a lens. Show, using ray diagrams, how reasonably sharp images can be 5r43(5ujp;uz- x5l.a oqnzffoh(u+fkbc8 a lformed 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 hr7 yf(2u)sj t0tgkf7exposure 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 2.0 (pamqujh ..s ,$cm$ 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 worek niycr5xj1 58 contact lenses corrected for the 5x8ky5j n1r cifar point $(=\,\infty)$ show that the near point would be 41 $cm$. (Would glasses be better in this case?) glasses would be  ----待选择----betterworse 

  Reading glasses of what power are needed for a person whose near)a2wq.bwe* )iqtdy 8f 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 o0qvit) dw,,0 o*cxv vrf 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 nuz4 y l,lt1z/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 ckfu; jlu zx acf.mqt(*8u.gmd7ex(-8 orrected 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 objec;f9nansp ( 8zdts 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 nearsighh,l,+b lx gj lre.w7w;ted eye in Example 25–6 than the 2.0 $cm$ of a normal eye?    cm

  One lens of a nearsighted person’s eyeglasses has a focal length ofl3l4an qhvo 2 9w.8,sn fxjzkpe36)qsb*dtq8 $-22.0 \, cm$ 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 lenl/j-1c 6 83l jcfirhqpgth of 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 of 10.0:7xom8m xu u3mk;jx xr(j, 8f ;aybu4q 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 used3pad s c)ffbj8i;5+o ga7e chks s8y1) with a relaxed eye if its focal length i)c 5s1biky+ j7pcasg3 afes 8h;)dfo8 s 12 $cm$? =    $\times$

  What is the focal length of a mtv e 0g(jb y3-glnaj8(agnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated atuvnq ( 20j,csyi 2io+k $2.5\times$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 9.00w4fwyn w r +umhz+xbtp*t,1 -;-$cm$-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*7+0jshg7u h lvncdh0 is viewed with a 9.50-$cm$-focal-length lens. A normal eye views the image at its near point. Calculate
(a) the angular magnification, =    $\times$
(b) the width of the image,    mm
(c) the object distance from the lens.    cm from the lens

  A small insect is placed 5.55+, xcb2jejz(j $cm$ 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 a9;ayh h9qrnt,0lr) vn focal 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 ra7nh h0(xvj h*ry/ep1m ted 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 aayzlu1(no 8l (stronomical telescope whose objective lens has a focal length of (n lz l81oay(u76 $cm$ 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 teleg:d89exl 6(:egi jpu pscope 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 leixm nlowo h*678snnw( p;xxi2xim v:c /, r2r2ngth 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescopekb,1 t3 4bp;sa x5tcxs has its two lenses spaced 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 adju0euha0+83i 09bjus w. xrzu/r/dp ntdsted for 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 powekkiw,god.zd z u2,*w 3r of an astronomical telescope using a reflecting mirror whose radius of cu, z3kd izg2,*o kuw.wdrvature is 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears to be magnified 1-pjri k (*,k3icha ba*20$\times$ by a reflecting astronomical telescope with an eyepiece having a focal length of 3.2 $cm$. What are the focal length and radius of curvature of the main (objective) mirror? M =    m r =    m

  A 170$\times$ astronomical telescope is adjusted for a relaxed eye when the two lenses are 1.25 m apart. What is the focal length of each lens?
$f_e$ =    mm
$f_o$ =    m

  A reflecting telescope (Fig. Below) has a radius of mxfa 2dr237j1w0 dnnj2if1nycurvature of 3.0 m for its objective mirx 0fm37 2fji1 d r2ynnw1a2njdror 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 w8wlc,muew1sb+j, o) zi1sin 3ith 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 1ymt5**j wbb 6s 0cywxkir++v. 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 1.8h lodyib0eul loxy3) / 8-t8y4-$cm$-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 assuminx.r(q k9;rb), m4i7zva zpiws g 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 mig71pg j6sl, j)g (ocnplk,vo;croscope has a focal length of 2.70 $cm$, and the objective lens has $f=0.740\mathrm{~cm}$. If an object is placed 0.790 $cm$ from the objective lens, calculate
(a) the distance between the lenses when the microscope is adjusted for a relaxed eye, $l$ =    cm
(b) the total magnification.    $\times$

  An achromatic lens is made of two very thin lenses, placed in coe;mb,3(qy eus+:.3 de cxb xjbntact, that have foc3x e :d bbq c;m(xb.+eej,u3ysal lengths of $f_1=-28\mathrm{~cm}$ and $f_2=+23\mathrm{~$cm$}.$
(a) Is the combination converging or diverging?  ----待选择----convergingdiverging 
(b) What is the net focal length?    m

  Let’s examine spherical aberration in a part gu : 3byph59xe(aqk;vicular situation. A planoconvex lens of index of refraction 1.50 and radius of curv5gb ;quevpyxh9ak : (3ature $R=12.0\mathrm{~$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 fmgc y1w yht6y5*eh8h,or the 100-in. (254tcy* yhw1 hy ,e6g5mh8-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wish x(3, u2mnu+8rwtvf td 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 p u;w2y+tq:spa 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 areeng wh3 t2vnu )jr8lqn.o.+4p 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 headlights bpbh 0jm q3lx8b7bpc( knm; 2.2.0 $m$ 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 s7l ts, 2f l:ikzum0*maeparated 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 planes,ut5 k1 rp a)p7r*df7gu are spaced 0.280r7prpg1u* )ktfu75 ad $nm$ 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. p 6;wteo-mtlgn go+9cq (:hc0The second diffraction0; +woegq tg96h -to(cmncpl: maximum is recorded 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 diffraction is observedydqb 59 /s9a9 zoy ,lgl9ysut, 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 t,qpe je* agtbv 8z:/hz/qw,;d5kem (yhat the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificzdz,py h:,e(v8/ te5j;wbeqqk/mg *aation 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 thq a-n2m id9a -jvr/wa.e sunlight got more intense, a photographer noted that, if she kept her shutter speed constani2d wqa a.-vrjn9/am-t, 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 magnificatii wf3,ehshk -q2:0pgk on of a camera lens is proportiones2h :k,fh0- w ki3gqpal to its focal length.

  For a camera equipped with a 59(n 7-ma8d, jeap5 fhv lf5xcu0-$mm$-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 rigeidg+ j.;i fusic4g. 7ht 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 v cd4v1a(7.suihs dyq: ;enp ;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 power ofngbaxb a+;: q7 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 usin60mvd7q3.6 xqb vg)l1qvn pd7s wys 8rg the lenses fromlqd 7v wd0 8.b3qg)7mp1rsyvvn6qxs6 his reading glasses. They have powers of $+2.0-D$ and $+4.0-D$, respectively.
(a) What maximum magnification telescope is possible? $M$ =    $\times$
(b) Which lens should be used as the eyepiece?    D

  A 50-year-old man us/;vyv0ka 2l a stfhl ;12xr:ckes $+2.5-diopter$ lenses to read a newspaper 25 $cm$ away. Ten years later, he must hold the paper 35 $cm$ away to see clearly with the same lenses. What power lenses does he need now in order to hold the paper 25 $cm$ away? (Distances are measured from the lens.) $P_2$ = +    D

  Spy planes fly at extremely high altitudes s x2(aadns(k pn vb(2el6hbm- h1h rz1mw5 *:k(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 time *grex dz;k6/us must be increased because of the increas / 6gkrx*u;zeded 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 a telescope arewj48l(qfym k*qqs.r7jq:yov1m6 ,v w 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 viewiqhq/c3rhc- yhz67;mbu i*gl2ir r8h( ng the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Consider diffraction of light of wavelengthi;2rc(qm*gh3-zcqhy8/i 7 urh hrlb6 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, w5ud;gu4) qy -zz*5fbli 8ykaone 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 are 7.30foope :n lydni jgi( *.gq28 $cm$ 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 photogr4.;nq+3.g; srf -jswnccpzd p aph license plate numbers. Assuming it is necessary t+ s;w d.njf.q c;4cgrppnsz3-o 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 (Fi+ cupf*ol,1ta 6yn mk1g. Below) 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