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2 86 Copright c 005 Kumanekosha 4.1 ( ) ( t ) t, t t Step! (Step 1) (, 0) (Step ) ±V t (, t) I Check! P P V t π 54 t = 0 + V (, t) π θ : = θ : π ) θ = π ± sin ± cos t = 0 (, 0) = sin π V + t +V t ( ) (, t) = sin π ( V t) = sin π V t «

3 = V T (, t) = sin π t «T t t Step! (Step 1) (0, t) (Step ) ± V (, t) 55 = 0 + V t T t T θ π J t ( = 0 ) ± sin t : T = θ : π ) θ = π T t ± cos (0, t) = sin π T t = 0 P ( ) V Check! = 0 V P V P t t V ω = π T T t V t (, t) = sin π t T V t = sin π T «V T = V T t (, t) = sin π T «

4 88 Copright c 005 Kumanekosha I 56 t = 0 + (1) 0 F () F (t = 0 ) V C D E F (1) 0, C, E

5 () = 0,, D, F v > 0( ), F Check!

6 90 Copright c 005 Kumanekosha 4 Step! (Step 1) (0) (Step ) (Step 3) + + (Step 4) I (t = 0 ) V 57 P T (1) P Q R S T U () (1) Q, U () ( )...Q, U

7 NTES

8 9 Copright c 005 Kumanekosha, 4. C t 0 t, t = 0 C, D D D C C t = D t = t = Q 0

9 4. 93 m = m = 1 m = 0 m = 1 m = P Q P P P P = PQ Q Q () Q Q = P P P P = m (m = 1,, 3,...)... 1 P P = m 1 «(m = 1,, 3,...)... 1 m = 0 P = P P, m = 1, 3 0

10 94 Copright c 005 Kumanekosha (1) 58 () or or 3 Step! (Step 1) (Step ) or 8 < : 8 < : (Step 3)

11 ,, = 3.5 = I Check! 3 3 = 6 60 J, =, = = = 3 10

12 96 Copright c 005 Kumanekosha Step! (Step 1) (Step )

13 = 0 = 0 = 0 0 π 3 Step! (Step 1) (Step ) π (Step 3) π π π

14 98 Copright c 005 Kumanekosha Check! ω = π T k = π T (, t) = sin π π ( vt) = sin π «T t (, t) = sin π π ( + vt) = sin + π «T t ««α + β β α sin α + sin β = sin cos (, t) + (, t) = sin π {z } cos π T t {z } sin π t sin π = 0 Check! Check! = 0,,,... Check! = 4, 3 4,... π = 0, π, π,... 0 sin π = ±1 π = π, 3π,...

15 θ v C, C t C= v t v t 3 Step! C D θ θ (Step 1) C (Step ) (Step 3) C = D \C = \D = 90 C D ( ) = ( )

16 100 Copright c 005 Kumanekosha n n v = v n = v f = n θ 1 C θ D Check! n 1 sin θ 1 = n sin θ I II n = 1 v v 1 = v n 1 ( I), v = v n ( II)... 1 θ 1 I II C C t C =v 1 t II t v t v t D D D 3 Step! (Step 1) v t (Step ) (Step 3) C = v 1 t = sin θ 1 D = v t = sin θ n 1 sin θ 1 = n sin θ = n 3 sin θ 3 v 1 t v t = sin θ 1... sin θ 1 v 1 = sin θ 1 = n v sin θ n 1 n 1 sin θ 1 = n sin θ I θ θ n n 1 n 1 n 61 n 1, n (n 1 < n) θ θ n sin θ = n 1 sin θ 1 =... = n sin θ ) θ = θ n i sin θ i θ

17 n 1 n n 1 sin θ = n sin r... 1 n 1 > n 1 r > θ θ θ = theta c r = 90 () 0 θ > θ c θ c θ r n 1 n n 1 sin θ c = n sin 90 ) sin c = n n 1 θ c 6 n 1 n n θ (1) θ θ 1 n () (1) (1), P P θ 1 θ, θ c n sin θ 1 = 1 sin θ c θ P θ 1 1 n 1 n sin θ = 1 sin θ c ) 1 = n sin θ 1... = n sin(90 θ ) = n cos θ q = n n sin θ p = n sin θ c p ) sin θ c = n 1 Check! P 1 θ 1 Check! θ 1 θ c sin θ < p n () θ (0 < θ < 90 ) 3 p n 1 > 1 ) n >

18 10 Copright c 005 Kumanekosha L n = 4.5 L L n = n n = L L 1 L L L = m (m = 1,,...) n L m L L = n L = m (m = 1,,...) I L L P 63, P n P L( ) = nl nl n L L = m (m = 0, 1,,...) n(l L ) = m (m = 0, ±1, ±,...)

19 n 1 L n l L( ) = n 1 L {(L l) + n l} J L n 1 n l (n 1 1)L (n 1)l = m + 1 «(m = 0, 1,,...) (n 1 1)L (n 1)l = m + 1 «(m = 0, ±1, ±,...)

20 104 Copright c 005 Kumanekosha n 1 n n 1 < n 0 n n 1 n 1 n π π L = m + 1 «L = m I a π d b 1 n 65 d n(> 1) a b 1 L = nd 0 a 1 n(1 < n) π b n 1(n > 1) a π 8 >< nd = m + 1 «(m = 0, 1,,...) >: nd = m (m = 0, 1,,...)

21 n 0 n d θ a b n 0 > n (1) r r J b a d θ r 1 n () θ n 0 (1) a b C d b a θ r 1 n L = n(c + C) 0 C n 0 = n(c + CD) = n(d cos r) D = n d cos r 1 n(1 < n) n n 0 (n < n 0 ) nd cos r = m (m = 1,, 3...) () 1 sin θ = n sin r L = nd cos r p = nd 1 sin r p = d n n sin r p = d n sin θ p d n sin θ = m (m = 1,, 3...) Check! r θ r θ

22 106 Copright c 005 Kumanekosha 4.6 ( ) ( ) 3 Point! F 3 1 F I F F 67 F 1 a b f a, b, f 1 a + 1 b = 1 f or

23 Step! (Step 1) 1 3 (Step ) (Step 3) b 68 (a)(b)(c) a b f (a), MF F J (a) (b) m = b a = b f f M ) 1 a + 1 b = 1 f f b (c) a F (b), m = b a = b + f f b a M ) 1 a 1 b = 1 f f MF F F (a), (b), (c) M F (c), m = b a = f b f ) 1 a 1 b = 1 f MF F b M F a f

24 108 Copright c 005 Kumanekosha V m 4.7 m V m V f V m m f V m/s f = V f = V V m/s m f V mf V 1 V f f V V, 1 f u m/s m (1) () = V V f u V + u f 1 V T f 1 = V + u = V + u f V... V T V T V T = V T = V f

25 () V T v C, V T vt vt = V T vt = (V v)t = V v f... D C 69 f = V = V V v f... 3 f v f = V f 1 = V f V + v Check! D 3 = V + v f J f v f 1 = V + v = V + v f V f V f = V = = V v f 1 V V v f 1 = V + v V v f f V = V u f 1 f f 1 v V 1 = V + u

26 110 Copright c 005 Kumanekosha 4.7. f 1, f f 0 f 0 = f 1 f... 1 t 0 f 1, f (f 1 < f ) t 1 t f 1 t f t t t 0 f t 0 ft 0 t 1 f 1 t π t 0 = t t 1 f 1 t 0 f t 0 1 f t 0 f 1 t 0 = 1 t 0 1 t 0 = f f 1 f 0 f 0 = 1 t 0 = f f 1 f 0 = f 1 f

27 () 1 = sin (ω 1 t k 1 )... = sin (ω t + k )... 3 Check! k = π ω 1. =. ω, k 1. =. k ω1 ω 1 + = cos «t k 1 + k {z } () ω1 + ω sin «t k 1 k {z } ()... 4 ω L = ω 1 ω ω L =.. 0 ω S = ω 1 + ω ω S =.. ω1 =.. ω 1, 4 T S = 1 f S t T L = 1 f L ω 1 = πf 1, ω = πf f L ω L = ω 1 ω = π f 1 f f L = ω L π = f 1 f f 0 f 0 = f L = f 1 f

28 11 Copright c 005 Kumanekosha = V T f = 1 T v = v n = n ( )=( ) (, t) = sin π t «T (, t) = cos π sin π T t f 1 = V 1 = V + v 8 >< = V v f >: f = V = V V v f n 1 sin θ 1 = n sin θ 1 a + 1 b = 1 f Φ = π L = πm L = n(l L 1 ) = m π f = f 3 f 4

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ

1 (1) ( i ) 60 (ii) 75 (iii) 315 (2) π ( i ) (ii) π (iii) 7 12 π ( (3) r, AOB = θ 0 < θ < π ) OAB A 2 OB P ( AB ) < ( AP ) (4) 0 < θ < π 2 sin θ 1 (1) ( i ) 60 (ii) 75 (iii) 15 () ( i ) (ii) 4 (iii) 7 1 ( () r, AOB = θ 0 < θ < ) OAB A OB P ( AB ) < ( AP ) (4) 0 < θ < sin θ < θ < tan θ 0 x, 0 y (1) sin x = sin y (x, y) () cos x cos y (x, y) 1 c