{"id":5135,"date":"2022-03-24T20:34:43","date_gmt":"2022-03-24T20:34:43","guid":{"rendered":"https:\/\/10minuteschool.com\/content\/?p=5135"},"modified":"2022-03-24T14:53:36","modified_gmt":"2022-03-24T14:53:36","slug":"distance-between-two-centers-of-bands","status":"publish","type":"post","link":"https:\/\/10minuteschool.com\/content\/distance-between-two-centers-of-bands\/","title":{"rendered":"\u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09ac\u09be \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac"},"content":{"rendered":"

\u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09ac\u09be \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/b>
\n<\/b>(Distance of bright or dark bands)<\/b><\/h2>\n

\u099a\u09bf\u09a4\u09cd\u09b0 \u09ed.\u09e7\u09e6 \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987,<\/span><\/p>\n

\u00a0\\left(S_{1} P\\right)^{2}=D^{2}+\\left(x_{n}-d\\right)^{2} ; x_{n} =\u00a0 <\/span><\/span>\u00a0\u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u0993 \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09aa\u099f\u09cd\u099f\u09bf\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\n

\u098f\u09ac\u0982 \\left(S_{2} P\\right)=D^{2}+\\left(x_{n}+d\\right)^{2} <\/span><\/span><\/p>\n\\therefore \\left(S_{2} P\\right)^{2} - \\left(S_{1} P\\right)^{2} = \\left[D^{2} + \\left(x_{n}+d\\right)^{2} \\right] - \\left[D^{2}+\\left(x_{n}-d\\right)^{2}\\right] <\/span>\n

\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0=\\left(x_{n}+d\\right)^{2}-\\left(x_{n}-d\\right)^{2} <\/span><\/span><\/p>\n

\u09ac\u09be,\u00a0 \\left(S_{2} P+S_{1} P\\right)\\left(S_{2} P-S_{1} P\\right)=4 x_{n} d <\/span><\/span><\/p>\n

\u098f\u0996\u09a8 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 M \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0996\u09c1\u09ac\u0987 \u09b8\u09a8\u09cd\u09a8\u09bf\u0995\u099f\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09ac\u09b2\u09c7\u00a0<\/span><\/p>\n

S_{1} p=S_{2} P=D <\/span> \u09a7\u09b0\u09be \u09af\u09be\u09df\u0964<\/span><\/p>\n

\u0985\u09a4\u098f\u09ac, \\left(S_{2} \\mathrm{P}-S_{1} P\\right)=\\frac{4 x_{n} d}{\\left(S_{2} \\mathrm{P}+S_{1} P\\right)}=\\frac{4 x_{n} d}{2 D}=\\frac{2 x_{n} d}{D} <\/span><\/span><\/p>\n

\u098f\u0996\u09a8 S_1 <\/span><\/span> \u09b9\u09a4\u09c7 S_2 P <\/span><\/span> \u098f\u09b0 \u0993\u09aa\u09b0 S_1 Q <\/span><\/span>\u00a0\u09b2\u09ae\u09cd\u09ac \u099f\u09be\u09a8\u09bf\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u098f\u0987 \u09a6\u09c1\u099f\u09bf \u09a4\u09b0\u0999\u09cd\u0997\u09c7\u09b0 \u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af<\/span><\/p>\n

\\sigma=S_{2} Q=\\left(S_{2} P-S_{1} P\\right)=\\frac{2 x_{n} d}{D} <\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\n

\u098f\u0996\u09a8 \u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (7.15) \u09b9\u09a4\u09c7 \u099c\u09be\u09a8\u09bf, n-\u09a4\u09ae \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09cb\u09b0\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af n\\lambda <\/span><\/span>-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964<\/span>
\n<\/span>\\therefore \\frac{2 x_{n} d}{D}=n \\lambda <\/span>, <\/span>\u098f\u0996\u09be\u09a8\u09c7 <\/span>n<\/span> = 0,1,2,3 … …<\/span><\/p>\n

\u09ac\u09be, x_{n}=\\frac{D}{2 d} n \\lambda <\/span><\/span><\/p>\n

\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7 M \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 \u09b9\u09a4\u09c7 (<\/span>n<\/span>+ 1)-\u09a4\u09ae \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09cb\u09b0\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\nx_{n}+1=\\frac{D}{2 d}(n+1) \\lambda <\/span>\n

\u2234<\/span>\u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09cb\u09b0\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u09ac\u09be \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce \\beta=x_{n+1}-x_{n} <\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0=\\frac{D}{2 d}(n+1) \\lambda-\\frac{D}{2 d} n \\lambda <\/span><\/span><\/p>\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0=\\frac{D}{2 d} \\lambda <\/span><\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09af\u09c7\u0995\u09cb\u09a8\u09cb \u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09be\u09cb\u09b0\u09be\u09b0 \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8, \\beta=\\frac{D \\lambda}{2 d} <\/span><\/span><\/p>\n

\u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09ac\u09be \u09a1\u09cb\u09b0\u09be\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 (Position of Bright Bands)<\/b><\/h2>\n\n\n\n\n\n\n\n\n
\u099d\u09b2\u09b0 \u09ac\u09be \u09a1\u09cb\u09b0\u09be<\/b><\/td>\nn<\/span><\/td>\n\u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af<\/b><\/td>\n\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac, <\/b>x<\/span><\/td>\n<\/tr>\n
\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09af\u09bc<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n0<\/span><\/td>\n<\/tr>\n
\u09aa\u09cd\u09f0\u09a5\u09ae<\/span><\/td>\n1<\/span><\/td>\n\\lambda <\/span><\/td>\n\u00a0\\frac{ D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n
\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc<\/span><\/td>\n2<\/span><\/td>\n\u00a02 \\lambda <\/span><\/td>\n\u00a0\\frac{2 D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n
\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n<\/tr>\n
?<\/span>-\u09a4\u09ae<\/span><\/td>\n?<\/span><\/td>\n\u00a0n \\lambda <\/span><\/td>\n\\frac{n D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

\u0986\u09ac\u09be\u09b0, \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u099c\u09a8\u09cd\u09af \u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af (2 n+1) \\frac{\\lambda}{2} <\/span><\/span>\u00a0-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8 \u09b9\u09a4\u09c7 \u09b9\u09ac\u09c7\u00a0<\/span><\/p>\n

\\frac{2 x_{n} d}{D}=(2 n+1) \\frac{\\lambda}{2} <\/span>
\n<\/span>\u0985\u09a8\u09c1\u09b0\u09c2\u09aa\u09ad\u09be\u09ac\u09c7, M \u09b9\u09a4\u09c7 (n + 1)-\u09a4\u09ae \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span>
\n<\/span>x_{n+1}=\\frac{D}{2 d}\\left[(2(n+1)+1] \\frac{\\lambda}{2}\\right. <\/span><\/p>\n

=\\frac{D}{2 d}(2 n+3) \\frac{\\lambda}{2}<\/span><\/span><\/p>\n


\n<\/span>\\therefore <\/span><\/span> \u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac<\/span><\/p>\n

\u0985\u09b0\u09cd\u09a5\u09be\u09ce, \\beta=\\left(x_{n+1}\\right)-x_{n} <\/span><\/span>
\n<\/span>= \\frac{D}{2 d}(2 n+3) \\frac{\\lambda}{2}-\\frac{D}{2 d}(2 n+1) \\frac{\\lambda}{2} <\/span>
\n<\/span>= \\frac{D}{2 d} \\lambda <\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0<\/span><\/p>\n

 <\/p>\n

\u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09ac\u09be \u09a1\u09cb\u09b0\u09be\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 (Position of Dark Bands)<\/b><\/h2>\n\n\n\n\n\n\n\n\n
\u099d\u09b2\u09b0 \u09ac\u09be \u09a1\u09cb\u09b0\u09be<\/b><\/td>\nn<\/span><\/td>\n\u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af<\/b><\/td>\n\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0 \u09b9\u09a4\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac, <\/b>x<\/span><\/td>\n<\/tr>\n
\u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09af\u09bc<\/span><\/td>\n1<\/span><\/td>\n\\frac{1}{2} \\lambda <\/span><\/td>\n\\frac{1}{2} \\frac{D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n
\u09aa\u09cd\u09f0\u09a5\u09ae<\/span><\/td>\n2<\/span><\/td>\n\\frac{3}{2} \\lambda <\/span><\/span><\/td>\n\\frac{3}{2} \\frac{D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n
\u09a6\u09cd\u09ac\u09bf\u09a4\u09c0\u09af\u09bc<\/span><\/td>\n3<\/span><\/td>\n\\frac{5}{2} \\lambda <\/span><\/td>\n\\frac{5}{2} \\frac{D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n
\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n\u2026\u2026\u2026\u2026\u2026\u2026……<\/span><\/td>\n<\/tr>\n
m<\/span>–<\/span>\u09a4\u09ae<\/span><\/td>\nm<\/span><\/td>\n\\left(m+ \\frac{1}{2}\\right)\\lambda <\/span><\/td>\n\\left(\\frac{2 m+1}{2}\\right) \\frac{D \\lambda}{2 d} <\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

 <\/p>\n

\u09a1\u09cb\u09b0\u09be\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5<\/b>
\n<\/b>(Width of bands)<\/b><\/h2>\n

\u098f\u0996\u09a8 \u098f\u0995\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09ac\u09be \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 \u09ac\u09be \u09ac\u09c7\u09a7 (width) \u09a6\u09c1\u099f\u09bf \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be \u09ac\u09be \u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09cb\u09b0\u09be\u09b0 <\/span>\u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8\u09c7\u09b0 \u0985\u09b0\u09cd\u09a7\u09c7\u0995\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u09a1\u09cb\u09b0\u09be\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 \u09ac\u09be \u09ac\u09c7\u09a7,<\/span>
\n<\/span>b=\\frac{\\lambda D \/ 2 d}{2}=\\frac{\\lambda D}{4 d} <\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0\u00a0<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (7.18) \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7\u2014<\/span>
\n<\/span>(i) <\/b>b \u098f\u09b0 \u09b0\u09be\u09b6\u09bf\u09ae\u09be\u09b2\u09be\u09af\u09bc n \u09a8\u09c7\u0987\u0964 \u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u098f\u099f\u09bf \u09b8\u09cd\u09aa\u09b7\u09cd\u099f \u09af\u09c7 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a5 \u099d\u09be\u09b2\u09b0 \u09b8\u0982\u0996\u09cd\u09af\u09be\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u09b8\u0995\u09b2 \u099d\u09be\u09b2\u09b0 \u098f\u0995\u0987 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0\u0964<\/span>
\n<\/span>(ii) <\/b>\u099d\u09be\u09b2\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 \u0986\u09b2\u09cb\u09b0 \u09a4\u09b0\u0999\u09cd\u0997\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \\lambda <\/span> <\/span>-\u098f\u09b0 \u09b8\u09ae\u09be\u09a8\u09c1\u09aa\u09be\u09a4\u09bf\u0995\u0964 \u09a4\u09b0\u0999\u09cd\u0997\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09c7\u09b6\u09bf \u09b9\u09b2\u09c7 b \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u099d\u09be\u09b2\u09b0\u09c7\u09b0<\/span>
\n<\/span>\u09aa\u09cd\u09f0\u09b8\u09cd\u09a5 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7 \u09ac\u09be \u09ae\u09cb\u099f\u09be \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 b \u0995\u09ae \u09b9\u09b2\u09c7 \u099d\u09be\u09b2\u09b0 \u09b8\u09b0\u09c1 \u09b9\u09ac\u09c7\u0964 \u09a4\u09be\u0987 \u09b2\u09be\u09b2 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a5 \u09ac\u09c7\u09b6\u09bf, \u09aa\u0995\u09cd\u09b7\u09be\u09a8\u09cd\u09a4\u09b0\u09c7 \u09ac\u09c7\u0997\u09c1\u09a8\u09bf \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 \u0995\u09ae\u0964<\/span>
\n<\/span>(iii) <\/b>D-\u098f\u09b0 \u09ae\u09be\u09a8 \u09ac\u09c7\u09b6\u09bf \u09b9\u09b2\u09c7 \u098f\u09ac\u0982 d \u098f\u09b0 \u09ae\u09be\u09a8 \u0995\u09ae \u09b9\u09b2\u09c7 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5 \u09ac\u09c7\u09b6\u09bf \u09b9\u09ac\u09c7\u0964<\/span>
\n<\/span>(iv) <\/b>\u09aa\u09be\u09a8\u09bf \u09ac\u09be \u0995\u09cb\u09a8\u09cb \u09a4\u09b0\u09b2\u09c7 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09a3 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u099f\u09bf \u09a1\u09c1\u09ac\u09be\u09b2\u09c7 \u09a4\u09b0\u0999\u09cd\u0997\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09be\u09af\u09bc \\left(\\lambda^{\\prime}=\\frac{\\lambda}{\\mu}\\right) <\/span><\/span>\u00a0\u09b8\u09c1\u09a4\u09b0\u09be\u0982 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09aa\u09cd\u09f0\u09b8\u09cd\u09a5 \u0995\u09ae\u09c7\u0964<\/span><\/p>\n

\u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7<\/b>
\n<\/b>(Angular width of the fringe)<\/b><\/h2>\n

\u09aa\u09b0\u09cd\u09a6\u09be\u09af\u09bc n-\u09a4\u09ae \u099d\u09be\u09b2\u09b0 \u09ac\u09be \u09a1\u09cb\u09b0\u09be\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8 <\/span>n<\/span> \u09b9\u09b2\u09c7, \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987<\/span>
\n<\/span>\\theta_{n}=\\frac{x_{n}}{D}=\\frac{D n \\lambda \/ 2 d}{D}=\\frac{n \\lambda}{2 d} <\/span>
\n<\/span>\u098f\u09ac\u0982 (n + 1)-\u09a4\u09ae \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8,<\/span>
\n<\/span>\\theta_{n+1}=\\frac{(n+1) \\lambda}{2 d} <\/span><\/p>\n

\u09b8\u09c1\u09a4\u09b0\u09be\u0982, \u09aa\u09b0\u09aa\u09b0 \u09a6\u09c1\u099f\u09bf \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7\u09b0 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af \u09ac\u09be \u09ac\u09cd\u09af\u09ac\u09a7\u09be\u09a8 \u0985\u09b0\u09cd\u09a5\u09be\u09ce \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7,<\/span>
\n<\/span>\\theta=\\theta_{n+1}-\\theta_{n}=\\frac{(n+1) \\lambda}{2 d}-\\frac{n \\lambda}{2 d}=\\frac{\\lambda}{2 d} <\/span>\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(i)<\/span><\/p>\n

\u09b8\u09ae\u09c0\u0995\u09b0\u09a3 (i) \u09b9\u09a4\u09c7 \u09a6\u09c7\u0996\u09be \u09af\u09be\u09af\u09bc \u09af\u09c7-<\/span>
\n<\/span>(\u0995) <\/b>\u098f\u0987 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7 \u09aa\u09b0\u09cd\u09a6\u09be\u09b0 \u0985\u09ac\u09b8\u09cd\u09a5\u09be\u09a8\u09c7\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09c7 \u09a8\u09be\u0964<\/span>
\n<\/span>(\u0996) <\/b>\u09b8\u09c1\u09b8\u0982\u0997\u09a4 \u0989\u09ce\u09b8 \u09a6\u09c1\u099f\u09bf\u09b0 \u09ae\u09a7\u09cd\u09af\u09c7 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac (2d) \u09ac\u09be\u09a1\u09bc\u09b2\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7 \u0995\u09ae\u09ac\u09c7 \u098f\u09ac\u0982 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u0995\u09ae\u09b2\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7<\/span>
\n<\/span>\u09ac\u09be\u09a1\u09bc\u09ac\u09c7\u0964<\/span>
\n<\/span>(\u0997) <\/b>\u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7 \u09a4\u09b0\u0999\u09cd\u0997\u09c7\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af\u09c7\u09b0 \u0993\u09aa\u09b0 \u09a8\u09bf\u09b0\u09cd\u09ad\u09b0 \u0995\u09b0\u09ac\u09c7\u0964 \u09a4\u09b0\u0999\u09cd\u0997\u09a6\u09c8\u09b0\u09cd\u0998\u09cd\u09af \u09ac\u09be\u09a1\u09bc\u09b2\u09c7 \\theta <\/span> <\/span>\u09ac\u09be\u09a1\u09bc\u09ac\u09c7, \u0986\u09ac\u09be\u09b0 <\/span> \u0995\u09ae\u09b2\u09c7 theta <\/span> <\/span>\u0995\u09ae\u09ac\u09c7\u0964 \u09af\u09a6\u09bf \u09b8\u09ae\u0997\u09cd\u09b0 \u09aa\u09b0\u09c0\u0995\u09cd\u09b7\u09a3 \u09ac\u09cd\u09af\u09ac\u09b8\u09cd\u09a5\u09be\u099f\u09bf <\/span> \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09b0\u09be\u0999\u09cd\u0995\u09c7\u09b0 \u09a4\u09b0\u09b2\u09c7 \u09a8\u09bf\u09ae\u099c\u09cd\u099c\u09bf\u09a4 \u0995\u09b0\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u0995\u09cc\u09a3\u09bf\u0995 \u09ac\u09c7\u09a7<\/span>
\n<\/span>\u0995\u09ae\u09ac\u09c7, \u0995\u09c7\u09a8\u09a8\u09be \u09a4\u09c7\u09b2 < <\/span>\u09a4\u09b0\u09b2<\/span> <\u00a0<\/span>\u09ac\u09be\u09df\u09c1<\/span> !<\/span><\/p>\n

\u09a6\u09c1\u099f\u09bf \u098f\u0995\u0987 \u09a7\u09b0\u09a8\u09c7\u09b0 \u0986\u09b2\u09cb\u0995 \u0989\u09ce\u09b8 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be- \u09ac\u09cd\u09af\u09be\u0996\u09cd\u09af\u09be \u0995\u09b0\u0964 (Two light sources of the same type can not produce interference pattern)<\/b><\/h3>\n

\u0986\u09b2\u09cb\u09b0 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0<\/a> \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u09b0 \u09b6\u09b0\u09cd\u09a4 \u09b9\u09b2\u09cb\u2014(\u09e7) \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u0995\u09be\u09b0\u09c0 \u0989\u09ce\u09b8 \u09a6\u09c1\u099f\u09bf\u0995\u09c7 \u09b8\u09c1\u09b8\u0982\u0997\u09a4 \u09b9\u09a4\u09c7 \u09b9\u09ac\u09c7 \u098f\u09ac\u0982 (\u09e8) \u09af\u09c7 \u09a6\u09c1\u099f\u09bf <\/span>\u09a4\u09b0\u0999\u09cd\u0997\u09c7\u09b0 \u0989\u09aa\u09b0\u09bf\u09aa\u09be\u09a4\u09c7\u09b0 \u09ab\u09b2\u09c7 \u099d\u09be\u09b2\u09b0 \u09a4\u09c8\u09b0\u09bf \u09b9\u09ac\u09c7 \u09a4\u09be\u09a6\u09c7\u09b0 \u09a6\u09b6\u09be \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af \u09b8\u09b0\u09cd\u09ac\u0995\u09cd\u09b7\u09a3\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u0985\u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09bf\u09a4 \u09a5\u09be\u0995\u09a4\u09c7 \u09b9\u09ac\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09a6\u09c1\u099f\u09bf \u098f\u0995\u0987 \u0986\u09b2\u09cb\u09b0 \u0989\u09ce\u09b8 \u0993\u09aa\u09b0\u09c7\u09b0 \u09b6\u09b0\u09cd\u09a4 \u09aa\u09c2\u09b0\u09a3 \u0995\u09b0\u09c7 \u09a8\u09be, \u09a4\u09be\u0987 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u0995\u09b0\u09a4\u09c7 \u09aa\u09be\u09b0\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n

\u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u0995\u09be\u09b0\u09c0 \u09a6\u09c1\u099f\u09bf \u09a4\u09b0\u0999\u09cd\u0997\u09c7\u09b0 \u098f\u0995\u099f\u09bf\u09b0 \u09aa\u09a5\u09c7 \u098f\u0995\u099f\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u0995\u09be\u099a \u09aa\u09cd\u09b2\u09c7\u099f \u09b0\u09be\u0996\u09b2\u09c7 \u099d\u09be\u09b2\u09b0\u09c7\u09b0 \u0995\u09bf \u09aa\u09b0\u09bf\u09ac\u09b0\u09cd\u09a4\u09a8 <\/b>\u09b9\u09ac\u09c7 ?<\/b><\/h3>\n

\u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf\u0995\u09be\u09b0\u09c0 \u09a6\u09c1\u099f\u09bf \u09a4\u09b0\u0999\u09cd\u0997\u09c7\u09b0 \u09af\u09c7 \u0995\u09cb\u09a8\u09cb \u098f\u0995\u099f\u09bf\u09b0 \u09aa\u09a5\u09c7 <\/span>t<\/span> \u09ac\u09c7\u09a7\u09c7\u09b0 \u098f\u0995\u099f\u09bf \u09aa\u09be\u09a4\u09b2\u09be \u0995\u09be\u099a \u09aa\u09cd\u09b2\u09c7\u099f \u09b0\u09be\u0996\u09b2\u09c7 \u09a4\u09b0\u0999\u09cd\u0997\u09a6\u09cd\u09ac\u09af\u09bc\u09c7\u09b0 <\/span>\u09ae\u09a7\u09cd\u09af\u09c7 (\\mu - 1)t <\/span><\/span> \u09aa\u09b0\u09bf\u09ae\u09be\u09a3 \u0985\u09a4\u09bf\u09b0\u09bf\u0995\u09cd\u09a4 \u09aa\u09a5 \u09aa\u09be\u09b0\u09cd\u09a5\u0995\u09cd\u09af\u09c7\u09b0 \u09b8\u09c3\u09b7\u09cd\u099f\u09bf \u09b9\u09ac\u09c7\u0964 \u098f\u0996\u09be\u09a8\u09c7 \\mu <\/span><\/span>= \u0995\u09be\u099a\u09c7\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u09b8\u09b0\u09be\u0999\u09cd\u0995\u0964 \u09ab\u09b2\u09c7 \u09b8\u09ae\u0997\u09cd\u09b0 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u099d\u09be\u09b2\u09b0, \u0995\u09be\u099a \u09aa\u09cd\u09b2\u09c7\u099f\u09c7\u09b0 \u09af\u09c7\u09a6\u09bf\u0995\u09c7 \u09b0\u09be\u0996\u09be \u09b9\u09af\u09bc\u09c7\u099b\u09c7 \u09b8\u09c7\u09a6\u09bf\u0995\u09c7 \u09b8\u09b0\u09c7 \u09af\u09be\u09ac\u09c7\u0964 \u0995\u09bf\u09a8\u09cd\u09a4\u09c1 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u099d\u09be\u09b2\u09b0\u09c7 \u09b8\u09b0\u09a3 \u0998\u099f\u09b2\u09c7\u0993 \u099d\u09be\u09b2\u09b0 \u09aa\u09cd\u09b0\u09b8\u09cd\u09a5\u09c7\u09b0 \u0995\u09cb\u09a8\u09cb \u09aa\u09b0\u09bf\u09b0\u09cd\u09ac\u09a4\u09a8 \u09b9\u09ac\u09c7 \u09a8\u09be\u0964<\/span><\/p>\n

\u09a6\u09c1\u099f\u09bf \u098f\u0995\u0987 \u09a7\u09b0\u09a8\u09c7\u09b0 \u099b\u09bf\u09a6\u09cd\u09b0 \u09a6\u09cd\u09ac\u09be\u09b0\u09be \u0997\u09a0\u09bf\u09a4 \u09ac\u09cd\u09af\u09a4\u09bf\u099a\u09be\u09b0 \u099d\u09be\u09b2\u09b0\u09c7 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09af\u09bc \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09aa\u09a1\u09bf\u09b0 \u09a4\u09c0\u09ac\u09cd\u09b0\u09a4\u09be I\u0964 \u09af\u09a6\u09bf \u098f\u0995\u099f\u09bf \u099a\u09bf\u09a1\u09bc \u09ac\u09a8\u09cd\u09a7 <\/b>\u0995\u09b0\u09c7 \u09a6\u09c7\u0993\u09af\u09bc\u09be \u09b9\u09af\u09bc \u09a4\u09ac\u09c7 \u0993\u0987 \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09a4\u09c0\u09ac\u09cd\u09b0\u09a4\u09be \u0995\u09a4 \u09b9\u09ac\u09c7 ?<\/b><\/h3>\n

\u09a7\u09b0\u09be \u09af\u09be\u0995, \u09a4\u09b0\u0999\u09cd\u0997 \u09a6\u09c1\u099f\u09bf\u09b0 \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf\u09b0 \u09ac\u09bf\u09b8\u09cd\u09a4\u09be\u09b0, <\/span>A<\/span><\/p>\n

\\therefore A_{max} = A+A=2A <\/span>
\n<\/span>\u09b8\u09c1\u09a4\u09b0\u09be\u0982,<\/span> I_{max}= A^{2}_{max} =(2A)^2 = 4A^2 = 4I_0 <\/span><\/span> [\u098f\u0996\u09be\u09a8\u09c7, I_0 <\/span><\/span> \u09aa\u09cd\u09b0\u09a4\u09bf\u099f\u09bf \u099a\u09bf\u09a1\u09bc\u09c7\u09b0 \u099c\u09a8\u09cd\u09af \u09a4\u09c0\u09ac\u09cd\u09b0\u09a4\u09be]<\/span>
\n<\/span>\u098f\u0996\u09a8, \u098f\u0995\u099f\u09bf \u099a\u09bf\u09a1\u09bc \u09ac\u09a8\u09cd\u09a7 \u0995\u09b0\u09c7 \u09a6\u09bf\u09b2\u09c7 \u0993\u0987 \u09b8\u09cd\u09a5\u09be\u09a8\u09c7 \u09a4\u09c0\u09ac\u09cd\u09b0\u09a4\u09be \u09b9\u09ac\u09c7,<\/span><\/p>\n

I_{0}=\\frac{\\operatorname{Imax}}{4} <\/span>
\n<\/span>\u0985\u09b0\u09cd\u09a5\u09be\u09ce \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c0\u09af\u09bc \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09a1\u09cb\u09b0\u09be\u09b0 \u09a4\u09c0\u09ac\u09cd\u09b0\u09a4\u09be 4 \u0997\u09c1\u09a3 \u09b9\u09cd\u09b0\u09be\u09b8 \u09aa\u09be\u09ac\u09c7\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

\u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u09ac\u09be \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09a1\u09cb\u09b0\u09be\u09b0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac (Distance of bright or dark bands) \u099a\u09bf\u09a4\u09cd\u09b0 \u09ed.\u09e7\u09e6 \u09b9\u09a4\u09c7 \u0986\u09ae\u09b0\u09be \u09aa\u09be\u0987, \u00a0\u00a0\u09a6\u09c1\u099f\u09bf \u0989\u099c\u09cd\u099c\u09cd\u09ac\u09b2 \u0993 \u0985\u09a8\u09cd\u09a7\u0995\u09be\u09b0 \u09aa\u099f\u09cd\u099f\u09bf\u09b0 \u0995\u09c7\u09a8\u09cd\u09a6\u09cd\u09b0\u09c7\u09b0 \u09ae\u09a7\u09cd\u09af\u09ac\u09b0\u09cd\u09a4\u09c0 \u09a6\u09c2\u09b0\u09a4\u09cd\u09ac \u098f\u09ac\u0982 \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0= \u09ac\u09be,\u00a0 \u098f\u0996\u09a8 P \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1 M \u09ac\u09bf\u09a8\u09cd\u09a6\u09c1\u09b0 \u0996\u09c1\u09ac\u0987 \u09b8\u09a8\u09cd\u09a8\u09bf\u0995\u099f\u09c7 \u0985\u09ac\u09b8\u09cd\u09a5\u09bf\u09a4 \u09ac\u09b2\u09c7\u00a0 \u09a7\u09b0\u09be \u09af\u09be\u09df\u0964 \u0985\u09a4\u098f\u09ac, \u098f\u0996\u09a8<\/p>\n

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