Why is the depth of fie1qy t4i/mtk, bprb,a) n.p:v fld greater, and the image sharper, when a camera lens is “stopped down” to a larger f-number? Ignore dit / mk )tb:n,v ia4p.1yprf,qbffraction.

Describe how diffraction affects the statem1q+c4ww ij-o/us n lhf4 ila-5ent that the depth of field is greater and the image sharper when a camera lens is owf/+4si45 -q uh-jwlci ln a1“stopped down” to a larger f-number.

Why must a camera lens be moved farther from the fimqg8u+u 3i( gjlm to focus on a closer object?gqi38 uju+(mg

Why are bifocals needed mainly by older persons and not generally by y hhc5-gt.2niqwzex 2: r.;vno ounger peoplec. hove 5x :22iz qt-hg;.nrnw?

  Will a nearsighted person who b-dec9g.wuo1 qj uwi-9/uf*s mi*5mowears corrective lenses in her glasses be able to see clemgiq-.eo 9*u du9f mcswj*b1u5/-i woarly 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 b8c g0zgvzi6hbczr,mvyd h+75e 6y/9f y looking at the width of the face through zz+7bzcg cr h6im 8eg6v59fvyy/0hd, 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, bzn4eptr5is j,2c 3l zx9kw9. people will sometimes squint. Why does this helpep3 kjrzit45cs9wxn z,9.b l2?

Is the image formed on the retina of the human eye upright or inverted? Discus/5x 70c nvaeeqwa8+yc s the implications of this for our perceptionnyw+x vcec8q/aae07 5 of objects.

The human eye is much like a camera — yet, when a camerat z1ij (hf+q( s)mx(qf shutter is left open and the camera is moved, the image will be blurred; but when you move your head with your h1q+x)z((t (im ffjsq eyes open, you still see clearly. Explain.

  Reading glasses use converging lenses. A simple magnifier is also a conve+irru4(9kjy z0nm tu z+f+m6arging lens. Are reading glasses th u9tk+m+r4uirz0njf (a6mzy +erefore 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 imaya7vm9 ijklaq0*)d 8 uges that are colored at thyu 8*dm 0avaq7)ik jl9e edges. Why?

Spherical aberration in a thin lens is minimized if rays are ben0/xc,s8pi5gr +m/4o ipon cwrt equally by the two surfaces. If a planoconvex lens is used to form a real iw/rpo gn5/ xsorm8,ic40i+pcmage of an object at infinity, which surface should face the object? Use ray diagrams to show why.

Which aberrations prqql wphu1 :i2*pk n,h5esent in a simple lens are not present (or are greatly reduced) in the hu:ph* q,hpiw 5qunk 21lman eye?

Explain why chromatic aberration occuktwl kx5 (qwb7qgu 26xt(n, x7rs for thin lenses but not for mirrors.

  By what factor can you improve reso qe9i/ivv3rha v*pn6 08- bxuolution, other things being equal, if you use blue light ( nuvipr3aveiv/h 0 9box*6q-8$\lambda=450mm$) rather than red (700 $nm$)?  

Give at least two advantages for the use of larv m;qdl tut-qyg-a, 0*ge reflecting mirrors in astronomical qu *aq,yml;t v-tg-0 dtelescopes.

Which color of visible light wo*g r:b /g)zsutuld give the best resolution in a microscope? Explsz*/trgub: g)ain.

  Atoms have diameters of **knu pv+j*xeabout $10^{-8}\,$cm$. Can visible light be used to “see” an atom? ----待选择----yesno  Explain.

  A 55-mm-focal-length lens has f-stv d6b d *wzmy+z/)8vltops 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 2fjo5wsgq;-f 14-$cm$ focal length and a lens diameter of 6.0 $cm$. What is its $f$-number? $f$/  

  A light meter reports lefx2walco .kyb / .)8that 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 ph: : tztvde0o-vkgiw/5otograph 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 t 4/,; e9yk3dsat qakuehat it is 200.0 mm to 206.0 mm from the film. For what range of object qkdyka9a43 ues/, e;t distances can it be adjusted?    $\mathrm{m}\leq d_{\circ}\leq\infty$

  A nature photographer wishes to photograph a 28-mtall t;e0r 1b/qdyai.x 6c fjree from a distance of 58 m. What focal-length lens1afc. ;djby qxi re06/ should be used if the image is to fill the 24-mm height of the film?    mm

A “pinhole” camera uses a tiny pinhole instead of a lens. Show, usin-/be4 lll 9zoxg ray diagrams, how reasonably sharp images can be formed using such a pinhole camera. In particular, cexlolz b4-9/lonsider 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 exposurh9.wdqz jo zwvqf3owk -3;0.52e2yns ia9s uje 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 kyix 4z,kod*/4/vp uh 8tm7r2n h(u0uadbn 5p $cm$ 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 pei 0 x rl7b;+a.cqk9fofrson in Example 25–6 wore contact lenses corrected for the far poikf;0 i ql7x.aocbr9+ fnt $(=\,\infty)$ 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 poinyfbrv;+3t4r t- jl6+7f o bjqct 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 p(*b dbtdq9uog lb3r g2s03v;0q pq uw;oint of 14 $cm$. What power glasses would correct this vision if the glasses were placed 2.0 $cm$ from the eye?    What power contact lenses, placed on the eye, would the person need?   

  A person struggles to read by holdino mj1q701bk o 4fmm3bmg 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 by af4y7*sqyak p3v b kln2q x4,c. $-3.50-diopter$ lens, 2.0 $cm$ from the eye.
(a) Is this person’s left eye near- or farsighted?  ----待选择----nearsightedfarsighted 
(b) What is this eye’s far point without glasses?    cm

  A person’s right eye can see objects clearly opt)*+ qybk4icnly 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 n 821 fbv-kbsqtearsighted 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 lenqruly 40, ew.qgth of $-22.0 \, cm$ and the lens is 1.8 $cm$ from the eye. If the person switches to contact lenses that are placed directly on the eye, what should be the focal length of the corresponding contact lens?    cm

  What is the focal length of the eye–lens system when v*9 zv9smxt he+ *4bn;6dkgppa iewing 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 io2 y 5vtin/er2bc. mua/49 a9 paf8pafar 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 magnificah+ h eh*c/tfnbl/,ho4 7u 1ybition of a lens used with a relaxed eye if its focal length yl 17hb fce,o/+un4bih ht*h/is 12 $cm$? =    $\times$

  What is the focal length of7 okf.h v2h6xs a magnifying glass of $3.5\times$ magnification for a relaxed normal eye?    cm

  A magnifier is rated atzxf8ez542a yg $2.5\times$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 u5q n.wtgto// tsing 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 view54kqxnlx.uj4n ;:xw g-knv 4ned 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* xmgc y:e6y-ous tm/r k /,u6)t+pzng $cm$ 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 omx. xf 8/7,3 dhk 3ex4rdh7r/cotbthdf 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 r3pn/sel/0y6pb 1mbd23 w/9f vhwhcqe ated 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 astronomin1d0g2rb 6+ gfwcf y9vcal telescope whose objective lens has a focal length of 7 1 y+g6frdn92w0fvgbc6 $cm$ 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 telescope is de4fgzwn 7rf 67ssired 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 object,ibri:wch16du3ye q9 ive with focal length 85 $cm$ and a $+35-D$ eyepiece. What is the total magnification? =    $\times$

  An astronomical telescope has its two lenses spaced+cji9ol m f:caoby +;4 75.2 $cm$ apart. If the objective lens has a focal length of 74.5 $cm$, what is the magnification of this telescope? Assume a relaxed eye. =    $\times$

  A Galilean telescope adjusted for a relaxed eye is 32.8 jir-up) l82vi;e pwz k4:l 1cmptqglz/ pu1 ,,$cm$ 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 a r);9yl -9km ).veqxk0 xkth jireflecting mirror whose radius of curvature ik9jhk x9 mi;)rx.tl)vy0qk- es 6.0 $m$ and an eyepiece whose focal length is 3.2 $cm$? =    $\times$

  The Moon’s image appears t6( ckoio+n .cs pt*u-mo 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. Belo b3gclbu. eu1s 2g++cow) has a radius of curvature of 3.0 m for its objective 2c+ ces+ lb ggo1uub.3mirror 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 len-ej .-vmv *s0y8s/5mdud r vtngth 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 12.0usdf6a* as lfss- x):-ou*3x v$times$ eyepiece and a 59.0$times$ objective lens 20.0 $cm$ apart. Calculate
(a) the total magnification,    $times$
(b) the focal length of each lens, $f_e$ =    cm $f_o$ =    cm
(c) where the object must be for a normal relaxed eye to see it in focus. $d_o$ =    cm

  A microscope has a 1.8-6sb/d.msa( ) 4xd6h qxty,rpj$cm$-focal-length eyepiece and a 0.80-$cm$ objective lens. Assuming a relaxed normal eye, calculate
(a) the position of the object if the distance between the lenses is 16.0 $cm$, $d_{oo}$ =    cm
(b) the total magnification.    $times$

  Repeat Problem 61 assuming that the final image is located 25 0nuzk e/s6dcvq za6)*$cm$ from the eyepiece (near point of a normal eye). $d_{oo}$ =    cm   $times$

  The eyepiece of a compo6yy2gh 1 yj/byund microscope 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 lensb4fmjc tf+ x yx1q*k+9es, placed in contact, that have focal bfkt9*+ c1xm4+fq xjylengths 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 situatio4xhxxnm u,,o 42p2 emln. A planoconvex lens of index of refraction 1.50 ande xl22uhxp4xm ,no m,4 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 th*1q +rj *o76qh aejgsjhupx/wgv*6 ;we 100-in. (25jgw h*rv/uj;6aqj6 g*p o 7*qwes+ hx14-$cm$ mirror diameter) Mt. Wilson telescope ($\lambda=550\mathrm{~nm}$)?   $ \times10^{ -5}\;^{\circ}$

  Suppose that you wisfh8*8tj0 /xgmr1mfuo h 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 cab p2ugw(q*yvd .tf:*59 x. jhd-ilb tpmera 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 barely resolved by a 4 qe(k;xnaka,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 humaqkjz 9n:k8a+qw96* 0qmctflon eye distinguish two car headlights 2.0 $m$ apart? Consider only diffraction effects and assume an eye pupil diameter of 5.0 $mm$ and a wavelength of 550 $nm$.
L =    km
(b) What is the minimum angular separation an eye could resolve when viewing two stars, considering only diffraction effects? In reality, it is about of arc. Why is it not equal to your answer in (b)? $\theta$ =    $\times 10^{-3}$ $^{\circ}$

  The Earth and Moon are separated by about rc dq8-z3efa*; p1y khpe1:l6lny 9gg$400\times10^6\mathrm{~m.}$ 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 abgea ;q4pbo+ zm *a/p1.v p5evtoms, lying in planes, are spaced 0.e*o.p b4 ap +gambv1vp;qze /5280 $nm$ 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 directe4s vhy::byd eq t6kjtk wtz;o8g195c8 d at an unknown crystal. The second diffr j5t8qc :z: dk8thgsy tv9ko6b;14wyeaction 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 :n(v b k/m+-l;hee2r xqlx8rzobserved 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 bda- uh6,rbk-i0:1 dka/d gcv image that the X-ray beam consists of parallel rays. What would be the magnification of the image? a the magnificati1/ guc,b bav6dk 0a-ikd-:rhdon 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, avs:;s7touzsa 3. dwznb8 3xn9nd the sunlight got more intense, a photographer noted that, if she kept her shutter speed constant, she had tszsaw t 7u9zdsv;b3: n.8xno3o 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 d1)v/2hijh/o i7 ypq sa camera leqdj1 po )h h2iy7/vsi/ns is proportional to its focal length.

  For a camera equipped 7 (i)aldp8rejc s58ttwith 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 g dumiuy0( bm4+3pu7aeye 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 pointaoz*y2n )c y0)ohc-y d 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 of ocdb0:;0 m+9u/arej1w o:v mergmxpss * *v;ya $+4.0-D$ lens used as a magnifier? Assume a relaxed normal eye. $M$ =    $\times$

  A physicist lost in th5va njt-f q 2+si.nv:fvem(8 re mountains tries to make a telescope using the lenses fromnvf2ntvs5(. -qia m e: 8+rfvj 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 usescdb+yi (4nzt+5.xbwm+x zz) m $+2.5-diopter$ 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 altitu su7vls., gcb:des (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 )slohqot9fx1 eu1u6 8increased because of the increased distance of the lens from the film f 9 oesx)tfo6h1u qlu18or 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 arozibpi u1g54 ht5 ymtls47x3) e 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 viewfq / ,u*gbq(nming the Moon. Estimate the minimum distance between two objects on the Moon that the Hubble can distinguish. Con*mg ,u(f/q bnqsider diffraction of light of wavelength 550 nm. Assume the Hubble is near the Earth.    m

  Two converging lenses, o vbc3gtzba9.f7 tz1 5ene 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 thee*vpzag cgn-/7 s*n h5 ixm(c4 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 ngm-+fmj n95x ,j8 xmsb (ews5spy satellite to photograph license plate numbers. Assuming it is necessary to res 8 gfnwx 5mb(mejnxj9m-5s,s+olve 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 flat surfax,qn 3k.gf m+ice 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