Hß╗īC247 xin giß╗øi thiß╗ću ─æß║┐n c├Īc em t├Āi liß╗ću L├Į thuyß║┐t v├Ā b├Āi tß║Łp X├Īc ─æß╗ŗnh c├Īc vß╗ŗ tr├Ł tr├╣ng nhau cß╗¦a hai hß╗ć v├ón trong Giao thoa ├Īnh s├Īng m├┤n Vß║Łt l├Į 12. T├Āi liß╗ću ─æŲ░ß╗Żc bi├¬n soß║Īn nhß║▒m giß╗øi thiß╗ću vß╗øi c├Īc em hß╗Źc sinh phŲ░ŲĪng ph├Īp giß║Żi c├╣ng vß╗øi mß╗Öt sß╗æ c├óu hß╗Åi v├Ā b├Āi tß║Łp tß╗▒ luyß╗ćn c├│ hŲ░ß╗øng dß║½n cß╗ź thß╗ā. Hi vß╗Źng ─æ├óy sß║Į l├Ā 1 t├Āi liß╗ću tham khß║Żo hß╗»u ├Łch trong qu├Ī tr├¼nh hß╗Źc tß║Łp cß╗¦a c├Īc em.
X├üC ─Éß╗ŖNH C├üC Vß╗Ŗ TR├Ź TR├ÖNG NHAU Cß╗”A HAI Hß╗å V├éN
1. V├ón s├Īng tr├╣ng nhau
C├Īch 1:
\(x = {k_1}{i_1} = {k_2}{i_2} = {k_1}\frac{{{\lambda _1}D}}{a} = {k_2}\frac{{{\lambda _2}D}}{a} \Rightarrow \frac{{{k_1}}}{{{k_2}}} = \frac{{{i_2}}}{{{i_1}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}} = \) ph├ón sß╗æ tß╗æi giß║Żn \( = \frac{b}{c}\)
\(\begin{array}{l} \Rightarrow \left\{ \begin{array}{l} {k_1} = bn\\ {k_2} = cn \end{array} \right. \Rightarrow \left( {n \in Z} \right)\\ \Rightarrow x = bn{i_1} = cn{i_2}\\ \Rightarrow \left\{ \begin{array}{l} {x_{\min }} = b{i_1} = c{i_2}\,khi\,n = 1\\ \Delta x = {x_{n + 2}} – {x_n} = b{i_1} = c{i_2} \end{array} \right. \end{array}\)
Trong ─æ├│, xmin l├Ā khoß║Żng c├Īch tß╗½ O ─æß║┐n vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt v├Ā ╬öx l├Ā khoß║Żng c├Īch giß╗»a hai vß╗ŗ tr├Ł tr├╣ng li├¬n tiß║┐p ( \({i_ \equiv }\)). TrŲ░ß╗Øng hß╗Żp n├Āy \(\Delta x = {x_{\min }} = \left( {{i_ \equiv }} \right)\)
C├Īch 2: \(\frac{{{i_2}}}{{{i_1}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}} = \) ph├ón sß╗æ tß╗æi giß║Żn = \(\frac{b}{c} \Rightarrow {i_ \equiv } = b{i_1} = c{i_2}\)
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö l├Ā mß╗Öt vß╗ŗ tr├Ł v├ón s├Īng tr├╣ng vß╗øi v├ón s├Īng n├¬n:
\(\Delta x = {x_{\min }} – {i_ \equiv }.\)
C├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc: \(x = n{i_ \equiv }\) (vß╗øi n l├Ā sß╗æ nguy├¬n),
2. Vân tối trùng nhau
C├Īch 1:
\(x = \left( {2{m_1} – 1} \right)\frac{{{i_1}}}{2} = \left( {2{m_2} – 1} \right)\frac{{{i_2}}}{2} \Rightarrow \frac{{2{m_1} – 1}}{{2{m_2} – 1}} = \frac{{{i_2}}}{{{i_1}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}} = \) ph├ón sß╗æ tß╗æi giß║Żn \( = \frac{b}{c}.\)
(D─® nhi├¬n, b v├Ā c l├Ā c├Īc sß╗æ nguy├¬n dŲ░ŲĪng lß║╗ th├¼ mß╗øi c├│ thß╗ā c├│ v├ón tß╗æi tr├╣ng vß╗øi v├ón tß╗æi)
\(\begin{array}{l} \Rightarrow \left\{ \begin{array}{l} 2{m_1} – 1 = b\left( {2n – 1} \right)\\ 2{m_2} – 1 = c\left( {2n – 1} \right) \end{array} \right.\left( {n \in Z} \right)\\ \Rightarrow x = b\left( {2n – 1} \right)\frac{{{i_1}}}{2} = c\left( {2n – 1} \right)\frac{{{i_2}}}{2}\\ \Rightarrow \left\{ \begin{array}{l} {x_{\min }} = \frac{{b{i_1}}}{2} = \frac{{c{i_2}}}{2}\,\,khi\,\,n = 1\\ \Delta x = {x_{n + 2}} – {x_n} = b{i_1} = c{i_2} \end{array} \right. \end{array}\)
Trong ─æ├│, xmin l├Ā khoß║Żng c├Īch tß╗½ O ─æß║┐n vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt v├Ā ╬öx l├Ā khoß║Żng c├Īch giß╗»a hai vß╗ŗ tr├Ł tr├╣ng h├¬n tiß║┐p (\({i_ \equiv }\) ). TrŲ░ß╗Øng hß╗Żp n├Āy \(\Delta x = 2{x_{\min }}\,\,hay\,\,{x_{\min }} = \Delta x/2\)
C├Īch 2:
\(\frac{{{i_2}}}{{{i_1}}} = \frac{{{\lambda _2}}}{{{\lambda _1}}} = \) ph├ón sß╗æ tß╗æi giß║Żn \(= \frac{b}{c} \Rightarrow {i_ \equiv } = b{i_1} = c{i_2}\)
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö kh├┤ng phß║Żi l├Ā vß╗ŗ tr├Ł v├ón tß╗æi tr├╣ng v├Ā n├│ c├Īch vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt l├Ā \({x_{\min }} = 0,5{i_ \equiv }\) n├¬n c├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc: x = (n ŌłÆ 0,5) \({i_ \equiv }\) (vß╗øi n l├Ā sß╗æ nguy├¬n),
3. V├ón tß╗æi cß╗¦a ╬╗2 tr├╣ng vß╗øi v├ón s├Īng cß╗¦a ╬╗1
C├Īch 1:
\(x = {k_1}{i_1} = \left( {2{m_2} – 1} \right)\frac{{{i_2}}}{2} \Rightarrow \frac{{{k_1}}}{{2{m_2} – 1}} = \frac{{0,5{i_2}}}{{{i_1}}} = \frac{{0,5{\lambda _2}}}{{{\lambda _1}}} = \) ph├ón sß╗æ tß╗æi giß║Żn \( = \frac{b}{c}.\)
(D─® nhi├¬n, c l├Ā sß╗æ nguy├¬n dŲ░ŲĪng lß║╗ th├¼ mß╗øi c├│ thß╗ā c├│ v├ón s├Īng cß╗¦a ╬╗1 tr├╣ng vß╗øi v├ón tß╗æi cß╗¦a ╬╗2).
\(\begin{array}{l} \Rightarrow \left\{ \begin{array}{l} {k_1} = b\left( {2n – 1} \right)\\ 2{m_2} – 1 = c\left( {2n – 1} \right) \end{array} \right.\left( {n \in Z} \right)\\ \Rightarrow b\left( {2n – 1} \right){i_1} = c\left( {2n – 1} \right)\frac{{{i_2}}}{2}\\ \Rightarrow \left\{ \begin{array}{l} {x_{\min }} = b{i_1} = \frac{{c{i_2}}}{2}\,\,khi\,\,n = 1\\ \Delta x = {x_{n + 1}} – {x_n} = 2b{i_1} = c{i_2} \end{array} \right. \end{array}\)
Trong ─æ├│, xmin l├Ā khoß║Żng c├Īch tß╗½ O ─æß║┐n vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt v├Ā ╬öx l├Ā khoß║Żng c├Īch giß╗»a hai vß╗ŗ tr├Ł tr├╣ng li├¬n tiß║┐p (\({i_ \equiv }\) ). TrŲ░ß╗Øng hß╗Żp n├Āy \(\Delta x = 2{x_{\min }}\,\,\,hay\,\,{x_{\min }} = \Delta x/2.\)
C├Īch 2:
* V├ón tß╗æi cß╗¦a ╬╗2 tr├╣ng vß╗øi v├ón s├Īng ╬╗1
\(x = \left( {n – 0,5} \right){i_ \equiv }\)= (n ŌłÆ 0,5)i= (vß╗øi n l├Ā sß╗æ nguy├¬n).
* V├ón tß╗æi cß╗¦a ╬╗1 tr├╣ng vß╗øi v├ón s├Īng ╬╗2
\(\frac{{{i_1}}}{{2{i_2}}} = \frac{{{\lambda _1}}}{{2{\lambda _2}}}\) = ph├ón sß╗æ tß╗æi giß║Żn \( = \frac{b}{c} \Rightarrow {i_ \equiv } = 2b{i_2} = c{i_1}\)
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö c├Īch vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt l├Ā: \({x_{\min }} = 0,5{i_ \equiv }\) n├¬n c├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc:
\(x = \left( {n – 0,5} \right){i_ \equiv }\) (vß╗øi n l├Ā sß╗æ nguy├¬n).
4. B├Āi tß║Łp minh hß╗Źa
V├Ł dß╗ź 1: Trong th├Ł nghiß╗ćm giao thoa l├óng thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi hai bß╗®c xß║Ī ─æŲĪn sß║»c vß╗øi khoß║Żng v├ón tr├¬n m├Ān ß║Żnh thu ─æŲ░ß╗Żc lß║¦n lŲ░ß╗Żt l├Ā i1 = 0,8 mm v├Ā i2 = 1,2 mm. X├Īc ─æß╗ŗnh toß║Ī ─æß╗Ö c├Īc vß╗ŗ tr├Ł tr├╣ng nhau cß╗¦a c├Īc v├ón s├Īng cß╗¦a hai hß╗ć v├ón tr├¬n m├Ān giao thoa (trong ─æ├│ n l├Ā sß╗æ nguy├¬n).
A. x = l,2.n (mm) B. x= l,8.n (mm)
C. x = 2,4.n (mm) D. x = 3,2.n (mm)
HŲ░ß╗øng dß║½n
C├Īch 1:
\(\begin{array}{l} x = {k_1}{i_1} = {k_2}{i_2}\\ \Rightarrow \frac{{{k_1}}}{{{k_2}}} = \frac{{{i_2}}}{{{i_1}}} = \frac{{1,2}}{{0,8}} = \frac{3}{2}\\ \Rightarrow \left\{ \begin{array}{l} {k_1} = 3n\\ {k_2} = 2n \end{array} \right.\\ \Rightarrow x = 3n{i_1} = 2n{i_2} = 2,4.n\left( {mm} \right) \end{array}\)
C├Īch 2:
\(\begin{array}{l} \frac{{{i_2}}}{{{i_1}}} = \frac{{1,2}}{{0,8}} = \frac{3}{2}\\ \Rightarrow {i_ \equiv } = 3{i_1} = 2{i_2} = 2,4\left( {mm} \right) \end{array}\)
Chß╗Źn C.
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö l├Ā mß╗Öt vß╗ŗ tr├Ł v├ón s├Īng tr├╣ng vß╗øi v├ón s├Īng n├¬n c├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc:
\(x = n{i_ \equiv } = 2,4n\) (mm) (vß╗øi n l├Ā sß╗æ nguy├¬n).
(─Éß╗ā t├¼m ta nh├ón ch├®o hai ph├ón thß╗®c \(\frac{{{i_2}}}{{{i_1}}} = \frac{b}{c} \Rightarrow {i_ \equiv } = b{i_1} = c{i_2}\) ).
V├Ł dß╗ź 2: Trong th├Ł nghiß╗ćm giao thoa l├óng thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi hai bß╗®c xß║Ī ─æŲĪn sß║»c vß╗øi khoß║Żng v├ón tr├¬n m├Ān ß║Żnh thu ─æŲ░ß╗Żc lß║¦n lŲ░ß╗Żt l├Ā i1 = 2,4 mm v├Ā i2 = 1,6 mm. Khoß║Żng c├Īch ngß║»n nhß║źt giß╗»a c├Īc vß╗ŗ tr├Ł tr├¬n m├Ān c├│ 2 v├ón s├Īng tr├╣ng nhau l├Ā
A. 9,6 mm. B. 3,2 mm.
C. 1,6 mm. D. 4,8 mm.
HŲ░ß╗øng dß║½n
\(\begin{array}{l} \frac{{{i_2}}}{{{i_1}}} = \frac{{1,6}}{{2,4}} = \frac{2}{3}\\ \Rightarrow {i_ \equiv } = 2{i_1} = 3{i_2} = 2.2,4 = 4,8\left( {mm} \right) = \Delta x \end{array}\)
Chß╗Źn D.
V├Ł dß╗ź 3: Trong th├Ł nghiß╗ćm giao thoa I├óng, thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi vß╗øi hai ├Īnh s├Īng ─æŲĪn sß║»c khoß║Żng v├ón giao thoa lß║¦n lŲ░ß╗Żt l├Ā 0,21 mm v├Ā 0,27 mm. Lß║Łp c├┤ng thß╗®c x├Īc ─æß╗ŗnh vß╗ŗ tr├Ł tr├╣ng nhau cß╗¦a c├Īc v├ón tß╗æi cß╗¦a hai bß╗®c xß║Ī tr├¬n m├Ān (n l├Ā sß╗æ nguy├¬n).
A. x = l,2.n + 3,375 (mm). B. x = l,89.n + 0,945 (mm).
C. x = l,05n + 0,525 (mm). D. x = 3,2.n (mm).
HŲ░ß╗øng dß║½n
C├Īch 1:
\(\begin{array}{l} x = \left( {2{m_1} + 1} \right).\frac{{0,21}}{2} = \left( {2{m_2} + 1} \right).\frac{{0,27}}{2}\left( {mm} \right)\\ \Rightarrow \frac{{2{m_1} + 1}}{{2{m_2} + 1}} = \frac{9}{7}\\ \Rightarrow \left\{ \begin{array}{l} 2{n_1} + 1 = 9\left( {2n + 1} \right)\\ 2{m_2} + 1 = 7\left( {2n + 1} \right) \end{array} \right.\\ x = 9\left( {n + 1} \right).\frac{{0,21}}{2} = 1,89n + 0,945\left( {mm} \right) \end{array}\)
Chß╗Źn B.
C├Īch 2:
\(\begin{array}{l} \frac{{{i_2}}}{{{i_1}}} = \frac{{0,27}}{{0,21}} = \frac{9}{7}\\ \Rightarrow {i_ \equiv } = 9{i_1} = 7{i_2} = 9.0,21 = 1,89\left( {mm} \right) \end{array}\)
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö O kh├┤ng phß║Żi l├Ā vß╗ŗ tr├Ł v├ón tß╗æi tr├╣ng v├Ā O c├Īch vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt l├Ā \({x_{\min }} = 0,5{i_ \equiv } = 0,945\) mm n├¬n c├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc:
\(x = \left( {n + 0,5} \right){i_ \equiv } = 1,890n + 0,945\,mm\) (vß╗øi n l├Ā sß╗æ nguy├¬n).
V├Ł dß╗ź 4: Trong th├Ł nghiß╗ćm giao thoa l├óng thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi hai bß╗®c xß║Ī ─æŲĪn sß║»c vß╗øi khoß║Żng v├ón n├¬n m├Ān ß║Żnh thu ─æŲ░ß╗Żc lß║¦n lŲ░ß╗Żt l├Ā i1 = 0,5 mm v├Ā i2 = 0,3 mm. Khoß║Żng c├Īch gß║¦n nhß║źt tß╗½ vß╗ŗ tr├Ł tr├¬n m├Ān c├│ 2 v├ón tß╗æi tr├╣ng nhau ─æß║┐n v├ón trung t├óm l├Ā
A. 0,75 mm B. 3,2 mm
C. 1,6 mm D. 1,5 mm
HŲ░ß╗øng dß║½n
\(\begin{array}{l} \frac{{{i_2}}}{{{i_1}}} = \frac{{0,3}}{{0,5}} = \frac{3}{5}\\ \Rightarrow {i_ \equiv } = 3{i_1} = 5{i_2} = 3.0,5 = 1,5\left( {mm} \right) \end{array}\)
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö O kh├┤ng phß║Żi l├Ā vß╗ŗ tr├Ł v├ón tß╗æi tr├╣ng v├Ā O c├Īch vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt l├Ā :
\({x_{\min }} = 0,5{i_ \equiv } = 0,75mm \)
Chß╗Źn A.
V├Ł dß╗ź 5: Trong th├Ł nghiß╗ćm giao thoa I├óng thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi hai bß╗®c xß║Ī ─æŲĪn sß║»c vß╗øi khoß║Żng v├ón tr├¬n m├Ān ß║Żnh thu ─æŲ░ß╗Żc lß║¦n lŲ░ß╗Żt l├Ā 1,35 mm v├Ā 2,25 mm. Tß║Īi hai ─æiß╗ām gß║¦n nhau nhß║źt tr├¬n m├Ān l├Ā M v├Ā N th├¼ c├Īc v├ón tß╗æi cß╗¦a hai bß╗®c xß║Ī tr├╣ng nhau. T├Łnh MN.
A. 3,375 (mm) B. 4,375 (mm)
C. 6,75 (mm) D. 3,2 (mm)
HŲ░ß╗øng dß║½n
\(\begin{array}{l} \frac{{{i_2}}}{{{i_1}}} = \frac{{2,25}}{{1,35}} = \frac{5}{3}\\ \Rightarrow {i_ \equiv } = 5{i_1} = 3{i_2} = 5.1,35 = 6,75\left( {mm} \right) = \Delta x = MN \end{array}\)
Chß╗Źn C.
V├Ł dß╗ź 6: Trong th├Ł nghiß╗ćm giao thoa I├óng, thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi vß╗øi hai bß╗®c xß║Ī ─æŲĪn sß║»c khoß║Żng v├ón lß║¦n lŲ░ß╗Żt: 1,35 mm v├Ā 2,25 mm. Tß║Īi ─æiß╗ām M tr├¬n m├Ān c├Īch v├ón trung t├óm mß╗Öt ─æoß║Īn b cß║Ż hai bß╗®c xß║Ī ─æß╗üu cho v├ón tß╗æi tß║Īi ─æ├│. Hß╗Åi b chß╗ē c├│ thß╗ā nhß║Łn gi├Ī trß╗ŗ n├Āo trong c├Īc gi├Ī trß╗ŗ sau?
A. 3,75 mm. B. 5,75 mm.
C. 6,75 mm. D. 10,125 mm.
HŲ░ß╗øng dß║½n
C├Īch 1:
\(\begin{array}{l} x = \left( {{m_1} + 0,5} \right).1,35 = \left( {{m_2} + 0,5} \right).2,25\left( {mm} \right)\\ \Rightarrow \frac{{2{m_1} + 1}}{{2{m_2} + 1}} = \frac{5}{3}\\ \Rightarrow \left\{ \begin{array}{l} 2{m_1} = 5\left( {2n + 1} \right) \Rightarrow {m_1} = 5n + 2\\ 2{m_2} + 1 = 3\left( {2n + 1} \right) \end{array} \right.\\ x = \left( {5n + 2 + 0,5} \right).1,35\left( {mm} \right)\\ \Leftrightarrow x = 6,75n + 3,375\left( {mm} \right)\\ \Rightarrow \left\{ \begin{array}{l} n = 1 \Rightarrow x = 3,375\left( {mm} \right)\\ n = 2 \Rightarrow x = 10,125\left( {mm} \right) \end{array} \right. \end{array}\)
Chß╗Źn D.
C├Īch 2:
V├¼ tß║Īi gß╗æc tß╗Źa ─æß╗Ö O kh├┤ng phß║Żi l├Ā vß╗ŗ tr├Ł v├ón tß╗æi tr├╣ng v├Ā O c├Īch vß╗ŗ tr├Ł tr├╣ng gß║¦n nhß║źt l├Ā \({x_{\min }} = 0,5{i_ \equiv } = 0,375mm\) n├¬n c├Īc vß╗ŗ tr├Ł tr├╣ng kh├Īc:
\(x = \left( {n + 0,5} \right){i_ \equiv } = 6,75n + 3,375mm\) (vß╗øi n l├Ā sß╗æ nguy├¬n)
Chß╗Źn D.
V├Ł dß╗ź 7: Trong th├Ł nghiß╗ćm giao thoa I├óng thß╗▒c hiß╗ćn ─æß╗ōng thß╗Øi hai bß╗®c xß║Ī ─æŲĪn sß║»c vß╗øi khoß║Żng v├ón tr├¬n m├Ān ├Ānh thu ─æŲ░ß╗Żc lß║¦n lŲ░ß╗Żt l├Ā i1 = 0,5 mm v├Ā i2 = 0,4 mm. Hai ─æiß╗ām M v├Ā N tr├¬n m├Ān m├Ā tß║Īi c├Īc ─æiß╗ām ─æ├│ hß╗ć 1 cho v├ón s├Īng v├Ā hß╗ć 2 cho v├ón tß╗æi. Khoß║Żng c├Īch MN nhß╗Å nhß║źt l├Ā
A. 2 mm. B. 1,2 mm.
C. 0,8 mm. D. 0,6 mm.
HŲ░ß╗øng dß║½n
C├Īch 1:
\(\begin{array}{l} x = {k_1}{i_1} = \left( {2{m_2} + 1} \right).0,5{i_2}\\ \Rightarrow \frac{{{k_1}}}{{2{m_2} + 1}} = \frac{{0,5{i_2}}}{{{i_1}}} = \frac{{0,5.0,4}}{{0,5}} = \frac{2}{5}\\ \Rightarrow \left\{ \begin{array}{l} {k_1} = 2\left( {2n + 1} \right)\\ 2{m_2} + 1 = 5\left( {2n + 1} \right) \end{array} \right.\\ x = 2\left( {2n + 1} \right)0,5\left( {mm} \right)\\ \Rightarrow {x_{n + 1}} – {x_n} = 2\left( {mm} \right) \end{array}\)
Chß╗Źn A.
C├Īch 2:
* V├ón tß╗æi cß╗¦a ╬╗2 tr├╣ng vß╗øi v├ón s├Īng ╬╗1:
\(\begin{array}{l} \frac{{{i_2}}}{{2{i_1}}} = \frac{{0,4}}{{2.0,5}} = \frac{2}{5}\\ \Rightarrow {i_ \equiv } = 2.2{i_1} = 5{i_2} = 2.2.0,5 = 2\left( {mm} \right) = \Delta x = MN \end{array}\)
Chß╗Źn A.
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