{"id":2217,"date":"2016-05-14T23:56:22","date_gmt":"2016-05-14T23:56:22","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2217"},"modified":"2024-09-02T14:10:59","modified_gmt":"2024-09-02T14:10:59","slug":"laminas-de-faces-paralelas","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/optica\/optica-geometrica\/laminas-de-faces-paralelas\/","title":{"rendered":"L\u00e2minas de faces paralelas"},"content":{"rendered":"

L\u00e2minas de faces paralelas<\/b><\/span><\/span><\/span><\/p>\n

Comportamento \u00f3ptico de uma l\u00e2mina de faces paralelas<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Considere um <\/b><\/span><\/span><\/span>raio de luz se propagando num meio 1 de \u00edndice de refra\u00e7\u00e3o n<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e incidindo numa <\/b><\/span><\/span><\/span>l\u00e2mina de faces paralelas de material de \u00edndice\u00a0de refra\u00e7\u00e3o n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Esse <\/b><\/span><\/span><\/span>raio de luz sofre duas refra\u00e7\u00f5es, <\/b><\/span><\/span><\/span>uma quando <\/b><\/span><\/span><\/span>entra na l\u00e2mina <\/b><\/span><\/span><\/span>e outra quando <\/b><\/span><\/span><\/span>sai dela, <\/b><\/span><\/span><\/span>fazendo com que a <\/b><\/span><\/span><\/span>luz seja desviada sem alterar sua dire\u00e7\u00e3o de propaga\u00e7\u00e3o (veja que os raios de luz incidente e emergente s\u00e3o paralelos).<\/b><\/span><\/span><\/span><\/p>\n

Exemplos de l\u00e2minas de faces paralelas:<\/b><\/span><\/span><\/span> vidros de: uma vidra\u00e7a, uma estufa, uma cobertura, para-<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

brisa de um carro, moldura de vidro de um quadro, etc.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0\u00a0\u00a0 <\/span><\/p>\n

Equa\u00e7\u00e3o do desvio lateral de um raio de luz ao atravessar uma l\u00e2mina de faces paralelas<\/b><\/span><\/span><\/span><\/p>\n

Na <\/b><\/span><\/span><\/span>figura abaixo<\/b><\/span><\/span><\/span> temos uma <\/b><\/span><\/span><\/span>l\u00e2mina de faces paralelas <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>\u00edndice de refra\u00e7\u00e3o n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>, imersa num <\/b><\/span><\/span><\/span>meio <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

de \u00edndice de refra\u00e7\u00e3o n<\/b><\/span><\/span><\/span>1\u00ad\u00a0<\/b><\/span><\/span><\/sub><\/span>e sendo atravessada por <\/b><\/span><\/span><\/span>um raio de luz monocrom\u00e1tico.<\/b><\/span><\/span><\/span><\/p>\n

Aplicando a <\/b><\/span><\/span><\/span>lei de Snell Descartes\u00a0<\/b><\/span><\/span><\/span>nas <\/b><\/span><\/span><\/span>duas refra\u00e7\u00f5es <\/b><\/span><\/span><\/span>da figura:<\/b><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0refra\u00e7\u00e3o \"\" <\/b><\/span><\/span><\/span> entrando na l\u00e2mina\u00a0\"\" <\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.sen i = n<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>.sen r<\/b><\/span><\/span><\/span>\"\"<\/p>\n

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0refra\u00e7\u00e3o \"\" <\/b><\/span><\/span><\/span> saindo da l\u00e2mina \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span>2.<\/b><\/span><\/span><\/sub><\/span>sen r = n<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>.sen i<\/b><\/span><\/span><\/span><\/p>\n

N\u00e3o existe <\/b><\/span><\/span><\/span>desvio angular<\/b><\/span><\/span><\/span> que \u00e9 nulo, <\/b><\/span><\/span><\/span>pois os <\/b><\/span><\/span><\/span>raios incidente e emergente s\u00e3o paralelos<\/b><\/span><\/span><\/span>, mas <\/b><\/span><\/span><\/span>sim <\/b><\/span><\/span><\/span>desvio\u00a0lateral (d)\u00a0<\/b><\/span><\/span><\/span>que corresponde \u00e0 <\/b><\/span><\/span><\/span>dist\u00e2ncia entre as retas que cont\u00e9m os raios incidente (seu prolongamento) e emergente.<\/b><\/span><\/span><\/span><\/p>\n

C\u00e1lculo do <\/b><\/span><\/span><\/span>desvio (d):<\/b><\/span><\/span><\/span><\/p>\n

Tri\u00e2ngulo <\/b><\/span><\/span><\/span>XYZ\u00a0<\/b><\/span><\/span><\/span> \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>sen \u03b8 = d\/XY \"\" sen<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u03b8 =<\/b><\/span><\/span><\/span> sen (i – r) <\/b><\/span><\/span><\/span>= d\/XY \"\" XY = sen (i \u2013 r)\/d<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(I).<\/b><\/span><\/span><\/span><\/p>\n

Tri\u00e2ngulo <\/b><\/span><\/span><\/span>KXY <\/b><\/span><\/span><\/span>\u00a0\"\"\u00a0 <\/b><\/span><\/span><\/span>cos r = e\/XY\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0 <\/b><\/span><\/span><\/span>XY = cos r\/e<\/b><\/span><\/span><\/span> <\/b>(II).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

O que voc\u00ea deve saber, informa\u00e7\u00f5es e dicas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe na <\/b><\/span><\/span><\/span>express\u00e3o do desvio lateral <\/b><\/span><\/span><\/span>que, <\/b><\/span><\/span><\/span>quanto maior for a espessura <\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span> da l\u00e2mina, maior ser\u00e1<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

o desvio sofrido.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0<\/span><\/p>\n

\"\"<\/p>\n

Se o <\/b><\/span><\/span><\/span>raio incidente na l\u00e2mina for perpendicular <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>uma de suas faces o desvio lateral ser\u00e1 nulo. A incid\u00eancia normal ocorre sem desvio do raio de luz.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Os <\/b><\/span><\/span><\/span>prolongamentos dos raios incidente e emergente s\u00e3o sempre retas paralelas.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

A <\/b><\/span><\/span><\/span>imagem de um objeto vista atrav\u00e9s de uma l\u00e2mina de faces paralelas<\/b><\/span><\/span><\/span> (placa de vidro no ar) <\/b><\/span><\/span><\/span>\u00e9 sempre virtual <\/b><\/span><\/span><\/span>e est\u00e1 <\/b><\/span><\/span><\/span>sempre mais pr\u00f3xima da l\u00e2mina que o objeto, <\/b><\/span><\/span><\/span>pois ao <\/b><\/span><\/span><\/span>penetrarem na l\u00e2mina os raios de luz se aproximam da normal.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

Assim, a <\/b><\/span><\/span><\/span>imagem \u00e9 vista pelo observador como sendo maior que o objeto por estar mais pr\u00f3xima (aumenta o campo visual).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Se <\/b><\/span><\/span><\/span>o raio de luz sofrer reflex\u00e3o e refra\u00e7\u00e3o em ambas as faces <\/b><\/span><\/span><\/span>e,<\/b><\/span><\/span><\/span> nelas, retornar ao ar, os seguintes \u00e2ngulos ser\u00e3o iguais <\/b><\/span><\/span><\/span>a = b = g = h e c = d = e = f.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Podemos tamb\u00e9m <\/b><\/span><\/span><\/span>decompor uma luz policrom\u00e1tica fazendo-a atravessar uma l\u00e2mina de vidro de<\/b><\/span><\/span><\/span> <\/b>faces paralelas. <\/b><\/span><\/span><\/span><\/p>\n

No interior da l\u00e2mina cada cor se move com velocidades diferentes <\/b><\/span><\/span><\/span>e ao <\/b><\/span><\/span><\/span>sa\u00edrem da mesma sofrer\u00e3o desvios laterais diferentes, sofrendo assim, dispers\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>cor que sofre menor desvio ao penetrar no vidro \u00e9 o vermelho (maior velocidade) e menor desvio \u00e9 o violeta (maior velocidade).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Associa\u00e7\u00e3o de l\u00e2minas de faces paralelas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Considere as <\/b><\/span><\/span><\/span>duas l\u00e2minas da figura, imersas no ar, uma de vidro e a outra de diamante<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>\u00edndice de refra\u00e7\u00e3o do diamante \u00e9 maior que o do vidro, <\/b><\/span><\/span><\/span>que por sua <\/b><\/span><\/span><\/span>vez \u00e9 maior que o do ar.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Observe que, <\/b><\/span><\/span><\/span>quanto mais refringente for o meio <\/b><\/span><\/span><\/span>(maior \u00edndice de refra\u00e7\u00e3o)<\/b><\/span><\/span><\/span>, mais o raio de luz se aproxima da normal, <\/b><\/span><\/span><\/span><\/p>\n

menor ser\u00e1 a velocidade da luz nesse meio e maior ser\u00e1 o desvio sofrido.<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/span><\/p>\n

\"\"\"\"<\/p>\n

Tem-se um <\/b><\/span><\/span><\/span>aparelho que emite um feixe colimado<\/b><\/span><\/span><\/span>, estreito, de <\/b><\/span><\/span><\/span>luz verde. <\/b><\/span><\/span><\/span>Mas o <\/b><\/span><\/span><\/span>feixe \u00e9<\/b><\/span><\/span><\/span>, na\u00a0verdade, <\/b><\/span><\/span><\/span><\/p>\n

mistura de luz amarela com azul. <\/b><\/span><\/span><\/span><\/p>\n

Pode-se <\/b><\/span><\/span><\/span>descobrir tal fato, fazendo-se incidir o feixe numa\u00a0l\u00e2mina de\u00a0vidro de faces paralelas <\/b><\/span><\/span><\/span>e<\/b><\/span><\/span><\/span> <\/b>assim<\/b><\/span><\/span><\/span> <\/b>uma das <\/b><\/span><\/span><\/span>cores sofreria um deslocamento paralelo maior que a outra, numa incid\u00eancia obl\u00edqua.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

D<\/b><\/span><\/span><\/span>iferentes cores sofrem desvios diferentes <\/b><\/span><\/span><\/span>e, consequentemente, <\/b><\/span><\/span><\/span>deslocamentos paralelos diferentes<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Veja um exerc\u00edcio de aplica\u00e7\u00e3o sobre desvio lateral nas l\u00e2minas de faces paralelas:<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>espessura de uma l\u00e2mina de vidro<\/b><\/span><\/span><\/span> de faces paralelas \u00e9 de <\/b><\/span><\/span><\/span>2,0 cm. <\/b><\/span><\/span><\/span><\/p>\n

Um <\/b><\/span><\/span><\/span>raio monocrom\u00e1tico de luz <\/b><\/span><\/span><\/span>incide numa de suas faces com <\/b><\/span><\/span><\/span>\u00e2ngulo de 60<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0<\/b><\/span><\/span><\/span>e se <\/b><\/span><\/span><\/span>refrata com \u00e2ngulo de 45<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>. <\/b><\/span><\/span><\/span><\/p>\n

Considerando <\/b><\/span><\/span><\/span>cos75<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= sen15<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= 0,25, sen60<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= cos30<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= \u221a3\/2 = 0,8, \u00a0n<\/b><\/span><\/span><\/span>ar <\/b><\/span><\/span><\/sub><\/span>= 1,0 e sen45<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= cos45<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= \u221a2\/2 = 0,7, \u00a0pede-se:<\/b><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span><\/span>Esbo\u00e7ar o <\/b><\/span><\/span><\/span>trajeto do raio de luz <\/b><\/span><\/span><\/span>ao <\/b><\/span><\/span><\/span>atravessar a l\u00e2mina<\/b><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span><\/span>Determinar o <\/b><\/span><\/span><\/span>\u00edndice de refra\u00e7\u00e3o do vidro<\/b><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span><\/span>Determinar o <\/b><\/span><\/span><\/span>desvio lateral (d) e o desvio angular (\u03b2)<\/b><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span><\/span>Determinar o <\/b><\/span><\/span><\/span>valor do \u00e2ngulo de emerg\u00eancia<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

n<\/b><\/span><\/span><\/span>vidro<\/b><\/span><\/span><\/sub><\/span> = 1,2.<\/b><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span><\/span>d = e.sen(i \u2013 r)\/cosr\u00a0 \"\"\u00a0 d = 2.sen(60<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span> \u2013 45<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span> )\/cos45<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\" d = 2.sen(15<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>)\/cos45<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"\u00a0 d = 2.0,25\/0,7\u00a0 \"\" \u00a0<\/b><\/span><\/span><\/span>d = 0,71cm (desvio lateral)\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 o <\/b><\/span><\/span><\/span>desvio angular \u00e9 nulo,\u00a0<\/b><\/span><\/span><\/span>pois o<\/b><\/span><\/span><\/span>\u00a0prolongamento do raio incidente <\/b><\/span><\/span><\/span>e o<\/b><\/span><\/span><\/span> raio emergente tem a mesma dire\u00e7\u00e3o, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>s\u00e3o paralelos\u00a0 \"\"\u00a0\u00a0\u03b2 = 0.<\/b><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span><\/span>Aplicando <\/b><\/span><\/span><\/span>Snell-Descartes <\/b><\/span><\/span><\/span>na face <\/b><\/span><\/span><\/span>inferior da l\u00e2mina\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span>vidro<\/b><\/span><\/span><\/sub><\/span>.senr = n<\/b><\/span><\/span><\/span>ar<\/b><\/span><\/span><\/sub><\/span>.senr\u2019\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 1,2.sen45<\/b><\/span><\/span><\/span>o <\/b><\/span><\/span><\/sup><\/span>= 1.senr\u2019\u00a0 \"\" 1,2.0,7 = 1.senr\u2019\u00a0 \"\"\u00a0 senr\u2019 = 0,8\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0\u00a0r\u2019 = 60<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>observe que i = r\u2019 = 60<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0(por essa raz\u00e3o que o raio incidente e o prolongamento do raio incidente s\u00e3o paralelos).<\/b><\/span><\/span><\/span><\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00f5es comentadas<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

L\u00e2minas de faces paralelas Comportamento \u00f3ptico de uma l\u00e2mina de faces paralelas \u00a0Considere um raio de luz se propagando num meio 1 de \u00edndice de refra\u00e7\u00e3o n1\u00a0e incidindo numa l\u00e2mina de faces paralelas de material de \u00edndice\u00a0de refra\u00e7\u00e3o n2. Esse raio de luz sofre duas refra\u00e7\u00f5es, uma quando entra na l\u00e2mina e outra quando sai dela, fazendo com que a<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2137,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"class_list":["post-2217","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2217","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/comments?post=2217"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2217\/revisions"}],"predecessor-version":[{"id":10943,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2217\/revisions\/10943"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2137"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2217"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}