雨过天晴，人们常看到天空中出现彩虹，它是由阳光照射到空中弥漫的水珠上时出现的现象．在说明这个现象时
\uff085\u5206\uff09\u96e8\u8fc7\u5929\u6674\uff0c\u4eba\u4eec\u5e38\u770b\u5230\u5929\u7a7a\u4e2d\u51fa\u73b0\u5f69\u8679\uff0c\u5b83\u662f\u7531\u9633\u5149\u7167\u5c04\u5230\u7a7a\u4e2d\u5f25\u6f2b\u7684\u6c34\u73e0\u4e0a\u65f6\u51fa\u73b0\u7684\u73b0\u8c61\uff0e\u5728\u8bf4\u660e\u8fd9\uff081\uff09\u5982\u56fe\u6240\u793a \uff082\uff0932 0 \u8bd5\u9898\u5206\u6790\uff1a\uff081\uff09\u6839\u636e\u5149\u7684\u6298\u5c04\u5b9a\u5f8b\uff0c\u5149\u8def\u56fe\u5982\u56fe\u6240\u793a\uff1a \uff082\uff09\u7531\u51e0\u4f55\u5173\u7cfb\u5f97\uff1a \uff0c\u6240\u4ee5 \uff1b\u518d\u6839\u636e\u6298\u5c04\u5b9a\u5f8b\uff1a \uff0c\u5f97 \uff0c\u6240\u4ee5 \uff0c\u6240\u4ee5\u5149\u7ebf\u504f\u8f6c\u7684\u89d2\u5ea6
\uff081\uff09\u5149\u8def\u5982\u56fe\uff08a\uff09\u6240\u793a\uff0e\uff082\uff09\u4ee5i\u3001r\u8868\u793a\u5165\u5c04\u5149\u7ebf\u7684\u5165\u5c04\u89d2\u3001\u6298\u5c04\u89d2\uff0c\u7531\u6298\u5c04\u5b9a\u5f8b\u6709?sini=nsinr\uff0c?\u4ee5\u03b4 1 \u3001\u03b4 2 \u3001\u03b4 3 \u8868\u793a\u6bcf\u4e00\u6b21\u504f\u8f6c\u7684\u89d2\u5ea6\uff0c\u5982\u56fe\uff08b\uff09\u6240\u793a\uff0c\u7531\u53cd\u5c04\u5b9a\u5f8b\u3001\u6298\u5c04\u5b9a\u5f8b\u548c\u51e0\u4f55\u5173\u7cfb\u53ef\u77e5? sini= d R \uff0c?\u03b4 1 =i-r\uff0c\u03b4 2 =\u03c0-2r\uff0c\u03b4 3 =i-r\uff0e?\u7531\u4ee5\u4e0a\u5404\u5f0f\u89e3\u5f97\uff1a\u6545\u8fd9\u675f\u5149\u7ebf\u4ece\u5c04\u5411\u6c34\u73e0\u5230\u5c04\u51fa\u6c34\u73e0\u6bcf\u4e00\u6b21\u504f\u8f6c\u7684\u89d2\u5ea6\u4e3a\uff1a? \u03b4 1 = (sin -1 d R )-( sin -1 d nR ) ? \u03b4 2 =\u03c0-2 sin -1 d nR ? \u03b4 3 =( sin -1 d R ) -( sin -1 d nR )
当光沿AB进入圆形水球时，发生折射，首先过球心和入射点B做出法线，确定了入射角，由于是从空气进入水中，折射角小于入射角，由此可以做出折射光线BC．光线BC射到水球的内表面发生反射，连接OC，做出法线，根据光的反射规律再做出入射光线BC的反射光线CD．
光线CD射到水球的内表面，又发生折射，连接OD，做出法线，根据光的折射规律做出对应的折射光线DE．
答案如下图所示：
绛旓細鈶犲厜绾垮皠鍏ユ按鐝犲悗锛岀涓娆′粠姘寸彔涓皠鍑虹殑鍏夎矾鍥惧鍥炬墍绀猴紟鈶＄敱鍑犱綍鍏崇郴寰梥in胃1=dR=0.8鍗澄1=53掳鐢辨姌灏勫畾寰嬪緱sin胃1=nsin胃2瑙ｅ緱sin胃2=0.6鍗澄2=37掳鍒櫹=2锛埼1-胃2锛=32掳锛庣瓟锛氣憼鍏夎矾鍥惧鍥炬墍绀猴紟鈶″厜绾垮亸杞殑瑙掑害涓32掳锛
绛旓細褰撳厜娌緼B杩涘叆鍦嗗舰姘寸悆鏃讹紝鍙戠敓鎶樺皠锛岄鍏堣繃鐞冨績鍜屽叆灏勭偣B鍋氬嚭娉曠嚎锛岀‘瀹氫簡鍏ュ皠瑙掞紝鐢变簬鏄粠绌烘皵杩涘叆姘翠腑锛屾姌灏勮灏忎簬鍏ュ皠瑙掞紝鐢辨鍙互鍋氬嚭鎶樺皠鍏夌嚎BC锛庡厜绾緽C灏勫埌姘寸悆鐨勫唴琛ㄩ潰鍙戠敓鍙嶅皠锛岃繛鎺C锛屽仛鍑烘硶绾匡紝鏍规嵁鍏夌殑鍙嶅皠瑙勫緥鍐嶅仛鍑哄叆灏勫厜绾緽C鐨勫弽灏勫厜绾緾D锛庡厜绾緾D灏勫埌姘寸悆鐨勫唴琛ㄩ潰锛屽張鍙戠敓鎶樺皠锛岃繛鎺D锛...
绛旓細鍏夌嚎缁忎簩娆℃姌灏勫拰涓娆″弽灏勮搴︿箣闂村叧绯诲鍥炬墍绀猴細 锛3鍒嗭級鐢卞嚑浣曞叧绯诲緱sini锛漝/R 锛1鍒嗭級绗竴娆℃姌灏勫簲鐢ㄦ姌灏勫畾寰嬪緱锛歴ini锛漬sinr 锛1鍒嗭級瑙ｅ緱sinr锛漝/nR浠庡浘涓彲浠ョ湅鍑猴紝绗竴娆℃姌灏勫厜绾垮亸杞 锛1鍒嗭級绗簩娆℃姌灏勫厜绾垮亸杞 锛1鍒嗭級鍙嶅皠鍋忚浆 锛1鍒嗭級鎵浠ヤ粠鍏夌嚎灏勫叆鍒板皠鍑哄叡鍋忚浆瑙掑害...
绛旓細銆愯В绛斻戠瓟锛氬澶锛岄洦杩囧ぉ鏅鏃讹紝甯稿湪澶╃┖鍑虹幇褰╄櫣锛岃繖鏄お闃冲厜閫氳繃鎮诞鍦ㄧ┖姘斾腑缁嗗皬鐨勬按鐝犳姌灏勮屾垚鐨勶紝鐧藉厜缁忔按鐝犳姌灏勪互鍚庯紝鍒嗚В鎴愮孩銆佹銆侀粍銆佺豢銆佽摑銆侀潧銆佺传涓冪鑹插厜锛屽洜姝ゅ僵铏圭殑涓婅竟缂樺彲鑳藉憟绾㈣壊锛岃繖绉嶇幇璞″彨鍋氬厜鐨勮壊鏁ｇ幇璞★紟绛旈瑕佺偣锛氣憼闆ㄦ淮涓崟鑹插厜鐨勫舰鎴愶紱 鈶″厜鍦ㄩ洦婊村唴鍙戠敓浜嗗弽灏勶紱 鈶㈠崟鑹插厜...
绛旓細閭ｆ槸鍥犱负闆ㄥ悗澶╃┖涓婕傛诞杩欏ぇ閲忕殑缁嗗皬姘寸彔锛屽綋澶槼鐓у皠鍒拌繖浜涙按鐝犱笂锛屽氨鍙戠敓浜嗗厜鐨勮壊鏁ｏ紝鎶婂畠浠垎瑙ｆ垚浜嗙粴涓界殑涓冭壊鍏夛紝濡傛灉杩欎簺鍏夊垰濂借繘鍏ユ垜浠殑鐪肩潧锛屾垜浠氨鐪嬪埌浜嗗僵铏广傛槸鍥犱负澶槼鍙戠敓浜 鍏夌殑鑹叉暎
绛旓細1. 闆ㄨ繃澶╂櫞涔嬪悗锛屼汉浠粡甯鍙互鍦澶╃┖涓湅鍒缇庝附鐨勫僵铏广2. 杩欐槸鍥犱负澶槼鍏夊湪缁忚繃姘存淮鏃跺彂鐢熶簡鎶樺皠鍜岃壊鏁ｃ3. 鐧藉厜鐢卞绉嶉鑹茬殑鍏夌粍鎴愶紝褰撳お闃冲厜灏勫叆姘存淮鏃讹紝杩欎簺棰滆壊浼氬洜鎶樺皠瑙掑害涓嶅悓鑰屽垎绂汇4. 褰╄櫣鐨勪竷绉嶉鑹叉槸鐢变簬涓嶅悓娉㈤暱鐨勫厜鎶樺皠瑙掑害涓嶅悓閫犳垚鐨勩5. 褰╄櫣閫氬父鍑虹幇鍦ㄥお闃崇殑瀵归潰锛屽綋澶槼鍏夊湪...
绛旓細褰闆ㄨ繃澶╂櫞锛屽ぉ绌哄父甯浼鍑虹幇褰╄櫣銆傝繖鏄敱浜庡お闃冲厜绾跨┛杩囩┖姘斾腑鎮诞鐨勫皬姘寸彔鏃跺彂鐢熸姌灏勶紝骞跺洜姝や骇鐢熻壊鏁ｏ紝灏嗙櫧鍏夊垎瑙ｆ垚澶氱褰╄壊鍏夌嚎銆傝繖绉嶇幇璞¤绉颁负鍏夌殑鑹叉暎銆傚僵铏圭殑褰㈡垚鏄洜涓洪槼鍏夊皠鍏ユ帴杩戠悆褰㈢殑姘存淮锛屽厜绾夸互涓嶅悓瑙掑害杩涘叆鍜屽弽灏勶紝鍏朵腑浠ュぇ绾40鑷42搴︾殑鍙嶅皠鏈涓烘樉钁楋紝浠庤屽舰鎴愪簡鎴戜滑鐪嬪埌鐨勫僵铏广
绛旓細鍏跺疄鍙绌烘皵涓湁姘存淮,鑰岄槼鍏夋鍦ㄨ瀵熻呯殑鑳屽悗浠ヤ綆瑙掑害鐓у皠,渚垮彲鑳戒骇鐢熷彲浠ヨ瀵熷埌鐨勫僵铏圭幇璞.褰╄櫣鏈甯稿湪涓嬪崍,闆ㄥ悗鍒氳浆澶╂櫞鏃鍑虹幇.杩欐椂绌烘皵鍐呭皹鍩冨皯鑰屽厖婊″皬姘存淮,澶╃┖鐨勪竴杈瑰洜涓轰粛鏈夐洦浜戣岃緝鏆.鑰岃瀵熻呭ご涓婃垨鑳屽悗宸叉病鏈変簯鐨勯伄鎸¤屽彲瑙侀槼鍏,杩欐牱褰╄櫣渚夸細杈冨鏄撹鐪嬪埌.鍙︿竴涓缁忓父鍙鍒板僵铏圭殑鍦版柟鏄戝竷...
绛旓細澶忔棩鐨勫崍鍚庯紝澶╂皵闂风儹锛屼箤浜戝瘑甯冿紝闆风數浜ゅ姞锛屾帴鐫灏变笅璧蜂簡鐡㈡臣澶ч洦銆闆ㄨ繃澶╂櫞锛屽ぉ绌轰腑甯稿父浼鍑虹幇涓鏉″褰㈢殑褰╁甫锛岃繖灏辨槸閫氬父鎵璇寸殑褰╄櫣銆傚湪鍙や唬锛屾浘娴佷紶杩囪澶氭湁鍏冲僵铏圭殑浼犺銆傛湁鐨勮瀹冩槸娆箰濂崇鐨勭瑧瀹癸紝鏈夌殑璇村畠鏄厜鏄庝箣绁炵殑瀹濆紦鈥︹︽讳箣锛屽僵铏硅钂欎笂浜嗕竴灞傜绉樼殑鑹插僵銆傚灏戝勾鏉ワ紝褰╄櫣鐨勫舰鎴...
绛旓細澶ч洦杩囧悗 澶槼鍏夌嚎绌胯繃绌烘皵涓殑姘存淮 鍙戠敓鍏夌殑鑹叉暎锛屽舰鎴愬僵铏 闃冲厜灏勫叆灏忔按婊达紝鍗充粠绌烘皵杩欑濯掕川杩涘叆姘磋繖绉嶅獟璐紝鍙戠敓涓娆℃姌灏勶紝鐢变簬鏋勬垚鐧藉厜鐨勫悇绉嶅崟鑹插厜鐨勬姌灏勭巼涓嶅悓锛岀传鍏夋尝闀挎渶鐭紝鍏舵姌灏勭巼鏈澶э紝绾㈠厜娉㈤暱杈冮暱锛屽叾鎶樺皠鐜囨渶灏忥紝鍏朵綑鍚勮壊鍏夊垯浠嬩箮鍏堕棿銆傚洜姝わ紝鍏夌嚎鍦ㄥ皬姘存淮鍐呬骇鐢熷垎鍏夌幇璞★紝鍚勮壊鍏夊悓鏃跺湪灏...
