{"id":2260,"date":"2016-06-20T03:23:20","date_gmt":"2016-06-20T03:23:20","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2260"},"modified":"2024-09-02T14:22:31","modified_gmt":"2024-09-02T14:22:31","slug":"lentes-construcao-geometrica-de-imagens","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/optica\/optica-geometrica\/lentes-construcao-geometrica-de-imagens\/","title":{"rendered":"Lentes \u2013 Constru\u00e7\u00e3o Geom\u00e9trica de Imagens"},"content":{"rendered":"

Lentes \u2013 Constru\u00e7\u00e3o Geom\u00e9trica de Imagens<\/b><\/span><\/span><\/span><\/p>\n

Defini\u00e7\u00e3o de lente<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Uma lente \u00e9 um <\/b><\/span><\/span><\/span>dispositivo feito de material homog\u00eaneo e transparente<\/b><\/span><\/span><\/span> no qual <\/b><\/span><\/span><\/span>uma das superf\u00edcies\u00e9 plana e a outra esf\u00e9rica ou as duas superf\u00edcies s\u00e3o esf\u00e9ricas.<\/b><\/span><\/span><\/span><\/p>\n

Esse <\/b><\/span><\/span><\/span>sistema \u00f3ptico <\/b><\/span><\/span><\/span>\u00e9 constitu\u00eddo por<\/b><\/span><\/span><\/span>tr\u00eas meios homog\u00eaneos e transparentes,<\/b><\/span><\/span><\/span> cujas <\/b><\/span><\/span><\/span>superf\u00edcies<\/b><\/span><\/span><\/span> (plana ou esf\u00e9rica) que <\/b><\/span><\/span><\/span>os separam s\u00e3o denominadas faces.<\/b><\/span><\/span><\/span><\/p>\n

Lentes delgadas<\/b><\/span><\/span><\/span><\/p>\n

Ser\u00e3o <\/b><\/span><\/span><\/span>chamadas lentes delgadas <\/b><\/span><\/span><\/span>quando sua <\/b><\/span><\/span><\/span>espessura for desprez\u00edvel em rela\u00e7\u00e3o ao seu raio de<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

curvatura que \u00e9 o raio da(s) circunfer\u00eancias que as geraram.<\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>lentes biconvexas e bic\u00f4ncavas <\/b><\/span><\/span><\/span>podem ser <\/b><\/span><\/span><\/span>sim\u00e9tricas se seus raios de curvaturas forem iguais <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>assim\u00e9tricas se eles forem diferentes.<\/b><\/span><\/span><\/span><\/p>\n

Como <\/b><\/span><\/span><\/span>normalmente temos lentes de vidro imersas no ar<\/b><\/span><\/span><\/span>, ent\u00e3o, <\/b><\/span><\/span><\/span>neste caso, <\/b><\/span><\/span><\/span>as lentes <\/b><\/span><\/span><\/span>de bordas <\/b><\/span><\/span><\/span>(extremidades) <\/b><\/span><\/span><\/span>finas s\u00e3o lentes convergentes e lentes de <\/b><\/span><\/span><\/span>extremidades <\/b><\/span><\/span><\/span>grossas s\u00e3o lentes divergentes. <\/b><\/span><\/span><\/span><\/p>\n

Mas, <\/b><\/span><\/span><\/span>dependendo do \u00edndice de refra\u00e7\u00e3o da lente e do meio <\/b><\/span><\/span><\/span>voc\u00ea pode ter o <\/b><\/span><\/span><\/span>comportamento \u00f3ptico<\/b><\/span><\/span><\/span><\/p>\n

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

indicado nas figuras acima.<\/b><\/span><\/span><\/span><\/p>\n

Representa\u00e7\u00e3o esquem\u00e1tica de lentes delgadas<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Muitas vezes <\/b><\/span><\/span><\/span>costumamos representar lente delgada <\/b><\/span><\/span><\/span>(espessura desprez\u00edvel quando comparada com<\/b><\/span><\/span><\/span><\/p>\n

seu raio de curvatura) <\/b><\/span><\/span><\/span>pelas figuras ao lado.<\/b><\/span><\/span><\/span><\/p>\n

Elementos de uma lente esf\u00e9rica<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Eixo principal<\/b><\/span><\/span><\/span>definido pela uni\u00e3o dos<\/b><\/span><\/span><\/span>dois pontos C<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> e C<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>de uma <\/b><\/span><\/span><\/span>reta <\/b><\/span><\/span><\/span>que cont\u00eam\u00a0os <\/b><\/span><\/span><\/span>centros de curvatura dos dioptros (faces) da lente, que s\u00e3o os supostos esf\u00e9ricos.\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

ou, se <\/b><\/span><\/span><\/span>uma das faces for plana o eixo principal <\/b><\/span><\/span><\/span>deve ser <\/b><\/span><\/span><\/span>perpendicular \u00e0 superf\u00edcie da lente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Centro \u00f3ptico de uma lente esf\u00e9rica<\/b><\/span><\/span><\/span><\/p>\n

\u00a0<\/b><\/span><\/span><\/span>O centro \u00f3ptico O <\/b><\/span><\/span><\/span>de uma <\/b><\/span><\/span><\/span>lente esf\u00e9rica delgada <\/b><\/span><\/span><\/span>\u00e9 definido como <\/b><\/span><\/span><\/span>sendo o\u00a0ponto onde o eixo principal (ep)corta a lente <\/b><\/span><\/span><\/span>(convergente ou divergente).<\/b><\/span><\/span><\/span>\"\"<\/p>\n

\u00c9 <\/b><\/span><\/span><\/span>sempre v\u00e1lida a seguinte propriedade:<\/b><\/span><\/span><\/span><\/p>\n

Todo raio de luz que passa pela lente pelo seu centro \u00f3ptico (O) n\u00e3o sofre desvio.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Foco principal objeto f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\u00a0<\/span>Por ele (f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>) passam <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>raios incidentes na lente convergente <\/b><\/span><\/span><\/span>(figura 1) ou seus <\/b><\/span><\/span><\/span>prolongamentos na<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

lente divergente (figura 2).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Foco principal imagem f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span><\/p>\n

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

Por ele (f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>)<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>passam <\/b><\/span><\/span><\/span>os <\/b><\/span><\/span><\/span>raios que emergem na lente convergente <\/b><\/span><\/span><\/span>quando <\/b><\/span><\/span><\/span>nela os raios incidem <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

paralelamente ao eixo principal <\/b><\/span><\/span><\/span>(figura 1) e por ele <\/b><\/span><\/span><\/span>passam os prolongamentos dos raios emergentes quando na lente divergente incide um feixe de raios paralelos. (figura 2).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Dist\u00e2ncia focal (f) da lente<\/b><\/span><\/span><\/span><\/p>\n

A\u00a0<\/b><\/span><\/span><\/span>dist\u00e2ncia focal (f)\u00a0da lente\u00a0<\/b><\/span><\/span><\/span>corresponde <\/b><\/span><\/span><\/span>\u00e0 dist\u00e2ncia de f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0a O ou de f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0a O, para as duas lentes<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

(convergentes e divergentes).<\/b><\/span><\/span><\/span><\/p>\n

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

Ponto antiprincipal objeto A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e imagem A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span><\/p>\n

Os <\/b><\/span><\/span><\/span>pontos antiprincipal objeto A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e imagem A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>s\u00e3o aqueles<\/b><\/span><\/span><\/span>cuja dist\u00e2ncia ao centro \u00f3ptico O da lente<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00e9 o dobro da dist\u00e2ncia focal.\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

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

Raios not\u00e1veis<\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o e o tamanho das imagens<\/b><\/span><\/span><\/span> formadas pelos <\/b><\/span><\/span><\/span>espelhos esf\u00e9ricos<\/b><\/span><\/span><\/span> podem ser <\/b><\/span><\/span><\/span>determinados a partir do comportamento dos raios que <\/b><\/span><\/span><\/span>saem do objeto e incidem no<\/b><\/span><\/span><\/span> <\/b>espelho<\/b><\/span><\/span><\/span> e<\/b><\/span><\/span><\/span> nos fornecem as caracter\u00edsticas da imagem formada.<\/b><\/span><\/span><\/span> S\u00e3o eles:<\/b><\/span><\/span><\/span><\/p>\n

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

Todo raio de luz<\/b><\/span><\/span><\/span> que <\/b><\/span><\/span><\/span>incide<\/b><\/span><\/span><\/span> na <\/b><\/span><\/span><\/span>lente passando pelo foco objeto emerge paralelamente ao eixo<\/b><\/span><\/span><\/span> <\/b>principal<\/b><\/span><\/span><\/span> (lente convergente) e <\/b><\/span><\/span><\/span>todo raio de luz <\/b><\/span><\/span><\/span>que incide <\/b><\/span><\/span><\/span>na lente de modo que seu prolongamento passe pelo foco objeto emerge paralelamente ao eixo principal <\/b><\/span><\/span><\/span>(lente divergente).<\/b><\/span><\/span><\/span>\"\"<\/p>\n

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

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

\"\"<\/p>\n

Todo raio de luz<\/b><\/span><\/span><\/span> que incide <\/b><\/span><\/span><\/span>paralelamente ao eixo principal<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>refratado passando (ou seu prolongamento) pelo foco imagem (f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Todo raio de luz<\/b><\/span><\/span><\/span> que <\/b><\/span><\/span><\/span>incide passando pelo centro \u00f3ptico da lente<\/b><\/span><\/span><\/span> <\/b>n\u00e3o sofre desvio<\/b><\/span><\/span><\/span> ao se refratar.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

Todo raio de luz que incide na <\/b><\/span><\/span><\/span>lente passando pelo <\/b><\/span><\/span><\/span>ponto antiprincipal<\/b><\/span><\/span><\/span> (objeto ou imagem) <\/b><\/span><\/span><\/span>se refrata<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

passando pelo ponto antiprincipal (imagem ou objeto).<\/b><\/span><\/span><\/span><\/p>\n

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

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

Constru\u00e7\u00e3o geom\u00e9trica de imagens<\/b><\/span><\/span><\/span><\/p>\n

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

Lente convergente<\/b><\/span><\/span><\/span><\/p>\n

Temos cinco casos:<\/b><\/span><\/span><\/span><\/p>\n

Em cada um desses 5 casos a seguir<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span>cada um dos infinitos raios de <\/b><\/span><\/span><\/span>luz que saem de cada um dos<\/b><\/span><\/span><\/span><\/p>\n

infinitos pontos do objeto<\/b><\/span><\/span><\/span> <\/b>chega at\u00e9 a lente e <\/b><\/span><\/span><\/span>s\u00e3o refratados convergindo para os mesmos infinitos pontos da imagem, formando-a, como pixels. <\/b><\/span><\/span><\/span>\"\"<\/p>\n

Um <\/b><\/span><\/span><\/span>observador ao receber esses raios que saem da imagem<\/b><\/span><\/span><\/span> tem a <\/b><\/span><\/span><\/span>impress\u00e3o de que eles est\u00e3o partindo do local onde ela \u00e9 formada, como voc\u00ea pode observar na figura<\/b><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0caso<\/b><\/span><\/span><\/span>:<\/b><\/span><\/span><\/span> <\/b>Objeto O antes de A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/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<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Caracter\u00edsticas da imagem <\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/span>:<\/b><\/span><\/span><\/span><\/p>\n

Natureza<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>Real (<\/b><\/span><\/span><\/span>obtida no <\/b><\/span><\/span><\/span>cruzamento do pr\u00f3prio raio luminoso<\/b><\/span><\/span><\/span> (linha cheia)<\/b><\/span><\/span><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\" entre <\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>menor que o objeto<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>invertida <\/b><\/span><\/span><\/span>em rela\u00e7\u00e3o ao mesmo<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Utilidades<\/b><\/span><\/span><\/span><\/p>\n

\"\" Uma m\u00e1quina fotogr\u00e1fica e uma filmadora (digitais ou n\u00e3o) t\u00eam seu sistema<\/b><\/span><\/span><\/span> <\/b>\u00f3ptico<\/b><\/span><\/span><\/span> como nesse <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

caso onde <\/b><\/span><\/span><\/span>a imagem formada no filme<\/b><\/span><\/span><\/span> (ou censor na m\u00e1quina digital) \u00e9 <\/b><\/span><\/span><\/span>real, invertida e menor.<\/b><\/span><\/span><\/span><\/p>\n

\"\" O <\/b><\/span><\/span><\/span>mesmo<\/b><\/span><\/span><\/span> acontece numa <\/b><\/span><\/span><\/span>m\u00e1quina de x\u00e9rox<\/b><\/span><\/span><\/span> quando queremos <\/b><\/span><\/span><\/span>reduzir um documento.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

O <\/b><\/span><\/span><\/span>globo ocular<\/b><\/span><\/span><\/span> funciona tamb\u00e9m de <\/b><\/span><\/span><\/span>modo semelhante,<\/b><\/span><\/span><\/span> pois seus <\/b><\/span><\/span><\/span>v\u00e1rios componentes transparentes funcionam como uma lente convergente<\/b><\/span><\/span><\/span> formando na <\/b><\/span><\/span><\/span>retina uma imagem real, menor e invertida.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

2<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0caso: Objeto O sobre A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> (centro de curvatura).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Caracter\u00edsticas da imagem <\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/span>:<\/b><\/span><\/span><\/span><\/p>\n

Natureza<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>real.<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>sob A<\/b><\/span><\/span><\/span>i <\/b><\/span><\/span><\/sub><\/span>(centro de curvatura).<\/b><\/span><\/span><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>mesmo tamanho<\/b><\/span><\/span><\/span> que o do objeto e <\/b><\/span><\/span><\/span>invertida em rela\u00e7\u00e3o a ele<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Utilidade:<\/b><\/span><\/span><\/span> <\/b>X\u00e9rox \"\" tamanho normal<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

3<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0caso: Objeto O entre A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\"<\/p>\n

Natureza \"\"<\/b><\/span><\/span><\/span> <\/b>real.<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>depois de A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> maior que o objeto<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>invertida em rela\u00e7\u00e3o a ele.<\/b><\/span><\/span><\/span><\/p>\n

Utilidades<\/b><\/span><\/span><\/span><\/p>\n

\"\" Projetores de filmes e de slides<\/b><\/span><\/span><\/span> que <\/b><\/span><\/span><\/span>fornecem do filme ou slide<\/b><\/span><\/span><\/span> (objetos) uma <\/b><\/span><\/span><\/span>imagem real, invertida e maior, projetada numa tela.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" x\u00e9rox \"\"<\/b><\/span><\/span><\/span> <\/b>amplia\u00e7\u00e3o.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

4<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0caso: Objeto O sobre o foco f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\"<\/p>\n

Neste caso dizemos que a <\/b><\/span><\/span><\/span>imagem \u00e9\u00a0<\/b><\/span><\/span><\/span>impr\u00f3pria<\/b><\/span><\/span><\/span> (est\u00e1 no infinito).<\/b><\/span><\/span><\/span><\/p>\n

Aplica\u00e7\u00e3o <\/b><\/span><\/span><\/span> <\/b>gera\u00e7\u00e3o de feixes de raios paralelos, microsc\u00f3pios, etc.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

5<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/span>\u00a0caso: Objeto O entre f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e O<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Natureza \"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Virtual<\/b><\/span><\/span><\/span> (obtida no <\/b><\/span><\/span><\/span>cruzamento dos prolongamentos<\/b><\/span><\/span><\/span> dos raios luminosos).<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o \"\" <\/b><\/span><\/span><\/span>Antes de f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o \"\" maior <\/b><\/span><\/span><\/span>que o objeto e <\/b><\/span><\/span><\/span>direita <\/b><\/span><\/span><\/span>em rela\u00e7\u00e3o a ele.<\/b><\/span><\/span><\/span><\/p>\n

Utilidade<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

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

Lente divergente<\/b><\/span><\/span><\/span><\/p>\n

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

Neste caso, <\/b><\/span><\/span><\/span>independente <\/b><\/span><\/span><\/span>da <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o do objeto O,<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>imagem i<\/b><\/span><\/span><\/span> ter\u00e1 <\/b><\/span><\/span><\/span>sempre <\/b><\/span><\/span><\/span>as seguintes caracter\u00edsticas:\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Natureza\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>virtual (obtida pelo prolongamento do raio refratado).<\/b><\/span><\/span><\/span><\/p>\n

Localiza\u00e7\u00e3o\u00a0<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> entre O e f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

Tamanho e orienta\u00e7\u00e3o<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>menor<\/b><\/span><\/span><\/span> que o objeto e <\/b><\/span><\/span><\/span>direita<\/b><\/span><\/span><\/span> em rela\u00e7\u00e3o a ele.<\/b><\/span><\/span><\/span><\/p>\n

Utilidades<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\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\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0Para <\/b><\/span><\/span><\/span>qualquer posi\u00e7\u00e3o do objeto<\/b><\/span><\/span><\/span> a <\/b><\/span><\/span><\/span>imagem <\/b><\/span><\/span><\/span>ser\u00e1 sempre <\/b><\/span><\/span><\/span>virtual, direita e menor,<\/b><\/span><\/span><\/span> mas estar\u00e1 <\/b><\/span><\/span><\/span>sempre entre f<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span> e 0.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

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

\"\"<\/p>\n

Voc\u00ea deve <\/b><\/span><\/span><\/span>conhecer os tipos de raios not\u00e1veis<\/b><\/span><\/span><\/span>, e <\/b><\/span><\/span><\/span>todos os casos<\/b><\/span><\/span><\/span> dos <\/b><\/span><\/span><\/span>tipos de imagens<\/b><\/span><\/span><\/span> formadas para <\/b><\/span><\/span><\/span>cada posi\u00e7\u00e3o do objeto nas lentes convergentes e divergentes.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Toda <\/b><\/span><\/span><\/span>imagem virtual \u00e9 direita<\/b><\/span><\/span><\/span> e toda <\/b><\/span><\/span><\/span>imagem real \u00e9 invertida.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Toda <\/b><\/span><\/span><\/span>imagem real<\/b><\/span><\/span><\/span> pode ser <\/b><\/span><\/span><\/span>projetada numa tela, anteparo ou parede. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Entre o <\/b><\/span><\/span><\/span>objeto e a imagem,<\/b><\/span><\/span><\/span> o <\/b><\/span><\/span><\/span>elemento que se encontra <\/b><\/span><\/span><\/span>mais afastado da lente tem maior tamanho.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0<\/span>Guarde apenas<\/b><\/span><\/span><\/span> que a <\/b><\/span><\/span><\/span>imagem fornecida por uma lente divergente \u00e9 sempre virtual, direita e menor<\/b><\/span><\/span><\/span> que o objeto. <\/b><\/span><\/span><\/span>Para qualquer outro tipo de imagem, a lente \u00e9 convergente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\u00a0<\/span>N\u00e3o \u00e9 poss\u00edvel queimar papel<\/b><\/span><\/span><\/span> com uma <\/b><\/span><\/span><\/span>lente divergente,<\/b><\/span><\/span><\/span> somente com <\/b><\/span><\/span><\/span>lente convergente<\/b><\/span><\/span><\/span> , pois os <\/b><\/span><\/span><\/span>raios efetivos de luz<\/b><\/span><\/span><\/span> (n\u00e3o seus prolongamentos) <\/b><\/span><\/span><\/span>provenientes do sol devem convergir para o papel, tendo intensidade m\u00e1xima no foco.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\"<\/p>\n

Se <\/b><\/span><\/span><\/span>uma lente quebrar<\/b><\/span><\/span><\/span>, cada <\/b><\/span><\/span><\/span>caco funciona como uma lente semelhante \u00e0 inteira,<\/b><\/span><\/span><\/span> com a <\/b><\/span><\/span><\/span>mesma dist\u00e2ncia focal,<\/b><\/span><\/span><\/span> pois os <\/b><\/span><\/span><\/span>raios de curvatura de cada face permanecem os mesmos<\/b><\/span><\/span><\/span> e fornecem imagem com as <\/b><\/span><\/span><\/span>mesmas caracter\u00edsticas da inteira,<\/b><\/span><\/span><\/span> apenas <\/b><\/span><\/span><\/span>com menor brilho,<\/b><\/span><\/span><\/span> pois a <\/b><\/span><\/span><\/span>quantidade dos raios de luz recebidos \u00e9 menor.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Lentes de bordas<\/b><\/span><\/span><\/span> (extremidades) <\/b><\/span><\/span><\/span>delgadas (finas)<\/b><\/span><\/span><\/span> \"\" \u00a0se <\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span>lente <\/b><\/span><\/span><\/sub><\/span>> n<\/b><\/span><\/span><\/span>meio<\/b><\/span><\/span><\/sub><\/span>, a lente \u00e9 <\/b><\/span><\/span><\/span>convergente <\/b><\/span><\/span><\/span>como, por exemplo, <\/b><\/span><\/span><\/span>lentes de vidro no ar<\/b><\/span><\/span><\/span> \u00a0e <\/b><\/span><\/span><\/span>caso contr\u00e1rio, divergente<\/b><\/span><\/span><\/span>, como, por exemplo, <\/b><\/span><\/span><\/span>lentes de ar no vidro.<\/b><\/span><\/span><\/span><\/p>\n

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

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

\"\"<\/p>\n

Lentes de bordas<\/b><\/span><\/span><\/span> (extremidades) <\/b><\/span><\/span><\/span>espessas (grossas)<\/b><\/span><\/span><\/span> \"\" se \u00a0<\/b><\/span><\/span><\/span>n<\/b><\/span><\/span><\/span>lente <\/b><\/span><\/span><\/sub><\/span>> n<\/b><\/span><\/span><\/span>meio<\/b><\/span><\/span><\/sub><\/span>,<\/b><\/span><\/span><\/span> a lente \u00e9 <\/b><\/span><\/span><\/span>divergente,<\/b><\/span><\/span><\/span> como por exemplo<\/b><\/span><\/span><\/span>, lentes de vidro no ar<\/b><\/span><\/span><\/span> e <\/b><\/span><\/span><\/span>caso contr\u00e1rio, convergente<\/b><\/span><\/span><\/span>, como por exemplo, <\/b><\/span><\/span><\/span>lentes de ar no vidro.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span><\/span>eixo secund\u00e1rio <\/b><\/span><\/span><\/span>de uma lente \u00e9 <\/b><\/span><\/span><\/span>toda reta que cont\u00e9m o centro \u00f3tico (0)<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>inclinada em rela\u00e7\u00e3o ao plano da lente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Assim, quando <\/b><\/span><\/span><\/span>um feixe de raios paralelos incide numa lente convergente<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>paralelamente<\/b><\/span><\/span><\/span> a um de <\/b><\/span><\/span><\/span>seus eixos secund\u00e1rios<\/b><\/span><\/span><\/span>, se <\/b><\/span><\/span><\/span>refrata convergindo em um ponto Fi\u2019<\/b><\/span><\/span><\/span> que pertence ao <\/b><\/span><\/span><\/span>plano focal secund\u00e1rio imagem dessa lente. <\/b><\/span><\/span><\/span>O mesmo ocorre com<\/b><\/span><\/span><\/span> lente divergente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Para <\/b><\/span><\/span><\/span>determinar a imagem A\u2019B\u2019C\u2019 de um corpo extenso ABC<\/b><\/span><\/span><\/span> voc\u00ea deve <\/b><\/span><\/span><\/span>localizar a imagem de cada<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

ponto e depois uni-las. <\/b><\/span><\/span><\/span>Veja o exemplo da figura acima.<\/b><\/span><\/span><\/span><\/p>\n

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

Dados um objeto AB, sua imagem A\u2019B\u2019 e o eixo principal (ep) de uma lente, localizar a lente, seu foco f, seu ponto anti-principal (A) \u00a0e esquematizar dois raios de luz que determinam a imagem<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Etapas:<\/b><\/span><\/span><\/span><\/p>\n

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span> \"\" Identificar a lente<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span> \u00e9 <\/b><\/span><\/span><\/span>divergente <\/b><\/span><\/span><\/span>pois a imagem \u00e9 direita e menor que o objeto.<\/b><\/span><\/span><\/span><\/p>\n

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>– \"\" <\/b><\/span><\/span><\/span>Tra\u00e7ar uma <\/b><\/span><\/span><\/span>reta que, passando por A e A\u2019 ir\u00e1 <\/b><\/span><\/span><\/span>interceptar<\/b><\/span><\/span><\/span> o ep e neste ponto est\u00e1 o eixo<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00f3ptico 0 da lente e, consequentemente a mesma.<\/b><\/span><\/span><\/span><\/p>\n

3<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>– \"\" <\/b><\/span><\/span><\/span> <\/b>A <\/b><\/span><\/span><\/span>partir de A, <\/b><\/span><\/span><\/span>tra\u00e7ar um <\/b><\/span><\/span><\/span>raio de luz que, incidindo paralelamente ao eixo principal <\/b><\/span><\/span><\/span>sofra<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

refra\u00e7\u00e3o na lente, divergindo<\/b><\/span><\/span><\/span>, de modo que <\/b><\/span><\/span><\/span>seu prolongamento<\/b><\/span><\/span><\/span> passe por A\u2019 e intercepte o ep no foco F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

4<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span> \"\" <\/b><\/span><\/span><\/span> <\/b>A <\/b><\/span><\/span><\/span>dist\u00e2ncia de A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0a O \u00e9 o dobro da dist\u00e2ncia de F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0a O.<\/b><\/span><\/span><\/span> <\/b>Os raios de luz que determinam a imagem s\u00e3o os raios 1 e 2 da figura abaixo.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Lembre-se de que f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0s\u00e3o sim\u00e9tricos a fi e Ai e est\u00e3o do outro lado da lente.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Se a <\/b><\/span><\/span><\/span>lente for\u00a0<\/b><\/span><\/span><\/span>convergente,<\/b><\/span><\/span><\/span> as etapas s\u00e3o as mesmas.<\/b><\/span><\/span><\/span><\/p>\n

Exemplo:<\/b><\/span><\/span><\/span><\/p>\n

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

1<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span> A <\/b><\/span><\/span><\/span>lente \u00e9 convergente <\/b><\/span><\/span><\/span>pois <\/b><\/span><\/span><\/span>a imagem \u00e9 maior que o objeto e \u00e9 invertida.<\/b><\/span><\/span><\/span><\/p>\n

2<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\" <\/b><\/span><\/span><\/span>Unir A com A\u2019 e localizar a lente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a03<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Tra\u00e7ar um raio de luz <\/b><\/span><\/span><\/span>que, <\/b><\/span><\/span><\/span>partindo de A, intercepte o ep no F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0e passe por A\u2019.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

4<\/b><\/span><\/span><\/span>a<\/b><\/span><\/span><\/sup><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> <\/b>Localizar A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0tal que OF<\/b><\/span><\/span><\/span>i <\/b><\/span><\/span><\/sub><\/span>= F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>A<\/b><\/span><\/span><\/span>i\u00a0<\/b><\/span><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span><\/span>e lembrar que <\/b><\/span><\/span><\/span>F<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span>\u00a0s\u00e3o sim\u00e9tricos a F<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0e A<\/b><\/span><\/span><\/span>i<\/b><\/span><\/span><\/sub><\/span>\u00a0e tra\u00e7ar os dois<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

raios de luz 1 e 2 que determinam a imagem.<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Confira os exerc\u00edcios com resolu\u00e7\u00e3o comentada<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Lentes \u2013 Constru\u00e7\u00e3o Geom\u00e9trica de Imagens Defini\u00e7\u00e3o de lente Uma lente \u00e9 um dispositivo feito de material homog\u00eaneo e transparente no qual uma das superf\u00edcies\u00e9 plana e a outra esf\u00e9rica ou as duas superf\u00edcies s\u00e3o esf\u00e9ricas. Esse sistema \u00f3ptico \u00e9 constitu\u00eddo portr\u00eas meios homog\u00eaneos e transparentes, cujas superf\u00edcies (plana ou esf\u00e9rica) que os separam s\u00e3o denominadas faces. Lentes delgadas Ser\u00e3o<\/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-2260","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2260","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=2260"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2260\/revisions"}],"predecessor-version":[{"id":2268,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2260\/revisions\/2268"}],"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=2260"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}