5.96.(a) kmax = 2d/? = 1.0.10 5 , (b) AX, = X/k = X 2 /2d = 5 pm.
00
5.97.(^) $ I(r)r dr.
o
5.98. b = ar 2 /(k?.a — r 2 ). 2.0 m.
5.99. X, = (r: — rD (a + b)I2ab = 0.60 gm.
5.100. (a) I (^) 44, I 2/ 0 ; (b) I 7 n (^7) % IO•
5.101. (a) I 0; (b) I I o12.
5.102. (a)Il ^ 946 /0, I2 = 114 10 , 13 = 1 /1610, /4 = /2, I ;:,-;
(1 — 0231) 2 / 0 ; (b) /5 (^25) /18'0, - 1 8 'X' 9 /4 '07 1.7 ';`.1 4946. 107 I 8 =
= /6, / (1 + cp/II) 2 / 0. Here p is the angle covered by the
screen.
5.103. (a) h (k 3/8)/(n — 1)
= 1.2 (k + 7/8) 1AM, (c) h = 1.2k or
= 0, 1, 2,...
5.104. h = (k + 3/4)/(n — 1),
(b) /max x 8/ 0.
5.105. Izm ir, X, (k + 5/8)/(n — 1)
5.106. r= likXfbl(b — f) = 0.90 -VT
5.107. b' = b/T1 2 = 1.0 m.
5.108. (a) y' = yb/a = 9 mm;
= 0.1.0 mm.
5.109. f = abl(a b) = 0.6 m. This value corresponds to the
principal focal point, apart from which there are other points as
well.
5.110. (a) h = 0.60 (2k + 1) pm; (b) h = 0.30 (2k 1) 1.1,m.
Here k = 0, 1, 2,...
5.111. (a) /fliagrnin 1.7, (b) a = 2 (Ax) 2 /b(v 2 — v1) 2 =
= 0.711m, where v^1 and v^2 are the corresponding values of the para-
meter along Cornu's spiral.
5.112. Icentr.11 edge. ^ 2.6.
5.113. X ----- (Ah) 2 /2b (v 2 — v 1 ) = 2 0.55 pm, where vl and v 2 are
the corresponding values of the parameter along Cornu's spiral.
5.114. h (k + 3/4)/(n — 1), where k = 0, 1, 2,...
5.115. / 2 // 1 1.9.
5.116. I 2.84.
5.117. / 1 : : ,--:.-, 1 : 4 : 7.
5.118. I I,.
5.119. Ie C'D (sine a)/a 2 , where a —(3tblX) sin 0; b sin 0 = kX,
k = 1, 2, 3,...
5.120. The condition for a maximum leads to the transcendental
equation tan a = a, where a = (Tcb/X) sin 0. The solution of this
equation (by means of plotting or selection) provides the following
root values: a 1 = 1.433t, a 2 = 2.46 t, a 3 = 3.47n. Hence b sin Al =
= 1.43A,, b sin 0 2 = 2.46X, b sin 0 3 = 3.47k.
5.121. b (sin 0 — sin 0 0 ) = k?.; for k = + 1 and k = —1 the
angles 0 are equal to 33° and 27° respectively.
1.2 (k + 3/8) gm; (b) h =
1.2 (k + 3/4) gm. Here k =where k = 0, 1, 2,..= 2.5 gm, where k = 2.
mm, where k= 1, 3, 5, ...(b) hmin abXID (a b)