{"id":2289,"date":"2016-06-20T03:43:00","date_gmt":"2016-06-20T03:43:00","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2289"},"modified":"2024-09-02T14:08:35","modified_gmt":"2024-09-02T14:08:35","slug":"instrumentos-opticos","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/optica\/optica-geometrica\/instrumentos-opticos\/","title":{"rendered":"Instrumentos \u00d3pticos"},"content":{"rendered":"

Instrumentos \u00d3pticos<\/b><\/span><\/span><\/span><\/p>\n

Instrumentos de proje\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

S\u00e3o <\/b><\/span><\/span><\/span><\/span>aqueles cuja imagem formada \u00e9 real<\/b><\/span><\/span><\/span><\/span>, pois pode ser <\/b><\/span><\/span><\/span><\/span>projetada sobre um filme, uma tela, um anteparo, etc.\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<\/b><\/span><\/span><\/span><\/span><\/p>\n

I – C\u00e2mera fotogr\u00e1fica<\/b><\/span><\/span><\/span><\/span> <\/b>ou m\u00e1quina fotogr\u00e1fica<\/b><\/span><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span><\/span> <\/b>dispositivo<\/b><\/span><\/span><\/span><\/span> utilizado para <\/b><\/span><\/span><\/span><\/span>capturar imagens. <\/b><\/span><\/span><\/span><\/span>Consiste b\u00e1sicamente de uma <\/b><\/span><\/span><\/span><\/span>caixa com orif\u00edcio no qual se encontram uma ou mais lentes convergentes (objetiva),<\/b><\/span><\/span><\/span><\/span> por <\/b><\/span><\/span><\/span><\/span>onde entram os raios de luz\u00a0 provenientes dos objetos que queremos<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

fotografar ou filmar <\/b><\/span><\/span><\/span><\/span>e que <\/b><\/span><\/span><\/span><\/span>produzem uma imagem real, menor e invertida sobre o filme <\/b><\/span><\/span><\/span><\/span>(c\u00e2mera comum) ou sobre um <\/b><\/span><\/span><\/span><\/span>censor que armazena as imagens em cart\u00f5es de mem\u00f3ria<\/b><\/span><\/span><\/span><\/span> (c\u00e2mera digital).<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"\u00a0Quando queremos <\/b><\/span><\/span><\/span><\/span>focalizar a imagem devemos variar a dist\u00e2ncia lente-filme <\/b><\/span><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span><\/span>variar a imagem P\u2019 <\/b><\/span><\/span><\/span><\/span>pois <\/b><\/span><\/span><\/span><\/span>P e o foco s\u00e3o constantes<\/b><\/span><\/span><\/span><\/span>. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Assim, quando o <\/b><\/span><\/span><\/span><\/span>objeto se aproxima devemos afastar a lente para que a imagem seja projetada novamente sobrfe o filme.<\/b><\/span><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

II-\u00a0<\/b><\/span><\/span><\/span><\/span>Projetor<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>consta de uma <\/b><\/span><\/span><\/span>fonte de luz <\/b><\/span><\/span><\/span>que, <\/b><\/span><\/span><\/span>atrav\u00e9s de uma intensa ilumina\u00e7\u00e3o <\/b><\/span><\/span><\/span>e de <\/b><\/span><\/span><\/span>uma lente convergente<\/b><\/span><\/span><\/span> (ou um sistema de lentes), <\/b><\/span><\/span><\/span>projeta a imagem de um objeto <\/b><\/span><\/span><\/span>(filme, slide, transpar\u00eancia) <\/b><\/span><\/span><\/span>em uma tela.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

\"\"\u00a0\u00a0Essa <\/b><\/span><\/span><\/span>imagem \u00e9 real, invertida e maior, desde que o objeto esteja entre o centro de curvatura da lente e o foco objeto. <\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

Instrumentos de observa\u00e7\u00e3o<\/b><\/span><\/span><\/span><\/p>\n

\u00a0A <\/b><\/span><\/span><\/span>imagem \u00e9 observada diretamente pelo observador e\u00a0<\/b><\/span><\/span><\/span>\u00e9 virtual e direita<\/b><\/span><\/span><\/span>.<\/b><\/span><\/span><\/span><\/p>\n

I-Lupa<\/b><\/span><\/span><\/span> \"\"<\/b><\/span><\/span><\/span>\u00a0Tamb\u00e9m <\/b><\/span><\/span><\/span>chamada de lente de aumento <\/b><\/span><\/span><\/span>\u00e9 uma <\/b><\/span><\/span><\/span>simples lente convergente <\/b><\/span><\/span><\/span>que <\/b><\/span><\/span><\/span>fornece <\/b><\/span><\/span><\/span>de um <\/b><\/span><\/span><\/span>objeto colocado entre seu foco F e seu centro \u00f3ptico O <\/b><\/span><\/span><\/span>uma <\/b><\/span><\/span><\/span>imagem virtual, direita e maior que o objeto observado.<\/b><\/span><\/span><\/span><\/p>\n

\"\"\u00a0Observe no <\/b><\/span><\/span><\/span>esquema abaixo a forma\u00e7\u00e3o da imagem A\u2019B\u2019 de um objeto AB em uma lupa, onde o objeto a ser observado tem que estar entre o foco objeto f<\/b><\/span><\/span><\/span>o<\/b><\/span><\/span><\/sub><\/span> e a lente.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Sendo a <\/b><\/span><\/span><\/span>imagem<\/b><\/span><\/span><\/span> formada <\/b><\/span><\/span><\/span>virtual<\/b><\/span><\/span><\/span>,<\/b><\/span><\/span><\/span> nas equa\u00e7\u00f5es <\/b><\/span><\/span><\/span>1\/f = 1\/P + 1\/P\u2019, i\/o = -P\u2019\/P e A = i\/o = -P\u2019\/P, <\/b><\/span><\/span><\/span>P\u2019<\/b><\/span><\/span><\/span> deve e ser <\/b><\/span><\/span><\/span>substitu\u00edda com sinal negativo, pois\u00a0<\/b><\/span><\/span><\/span>P\u2019<\u00a00.<\/b><\/span><\/span><\/span><\/p>\n

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

II- Microsc\u00f3pio composto<\/b><\/span><\/span><\/span> \"\" Utilizado na <\/b><\/span><\/span><\/span>observa\u00e7\u00e3o de regi\u00f5es de dimens\u00f5es microsc\u00f3picas <\/b><\/span><\/span><\/span>que o <\/b><\/span><\/span><\/span>olho humano n\u00e3o consegue perceber, <\/b><\/span><\/span><\/span>como por exemplo, na <\/b><\/span><\/span><\/span>histologia, anatomia, mineralogia, etc.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Consta de <\/b><\/span><\/span><\/span>duas lentes convergentes <\/b><\/span><\/span><\/span>(geralmente compostas) de <\/b><\/span><\/span><\/span>pequenas dist\u00e2ncias focais que s\u00e3o: <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/span> (sistema de lentes bastante sofisticado) que est\u00e1 <\/b><\/span><\/span><\/span>pr\u00f3xima ao objeto observado <\/b><\/span><\/span><\/span>e a <\/b><\/span><\/span><\/span>ocular<\/b><\/span><\/span><\/span> (com no m\u00ednimo duas lentes) com a qual <\/b><\/span><\/span><\/span>observamos a imagem fornecida pela objetiva.<\/b><\/span><\/span><\/span><\/p>\n

Veja o <\/b><\/span><\/span><\/span>esquema simplificado do microsc\u00f3pio composto.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span><\/span>dist\u00e2ncia focal da objetiva \u00e9 muito pequena<\/b><\/span><\/span><\/span> (mil\u00edmetros). A <\/b><\/span><\/span><\/span>objetiva forma <\/b><\/span><\/span><\/span>do <\/b><\/span><\/span><\/span>objeto AB<\/b><\/span><\/span><\/span> uma <\/b><\/span><\/span><\/span>imagem A\u2019B\u2019 real, invertida e maior<\/b><\/span><\/span><\/span> que o objeto e <\/b><\/span><\/span><\/span>essa imagem serve como objeto para a ocular <\/b><\/span><\/span><\/span>(de dist\u00e2ncia focal da ordem de cent\u00edmetros) que <\/b><\/span><\/span><\/span>fornece uma imagem final A\u2019\u2019B\u2019\u2019, virtual, maior e direita em rela\u00e7\u00e3o a A\u2019B\u2019. <\/b><\/span><\/span><\/span><\/p>\n

Observe que <\/b><\/span><\/span><\/span>A\u2019\u2019B\u2019\u2019 \u00e9 direita em rela\u00e7\u00e3o a A\u2019B\u2019 e invertida em rela\u00e7\u00e3o ao objeto AB.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>aumento linear transversal do microsc\u00f3pio<\/b><\/span><\/span><\/span> \u00e9 fornecido pela <\/b><\/span><\/span><\/span>express\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

A<\/b><\/span><\/span><\/span>microsc\u00f3pio <\/b><\/span><\/span><\/sub><\/span>= A<\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/sub><\/span>\u00a0. A<\/b><\/span><\/span><\/span>ocular<\/b><\/span><\/span><\/sub><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>aumento produzido <\/b><\/span><\/span><\/span>por esse microsc\u00f3pio chega at\u00e9 a <\/b><\/span><\/span><\/span>2000 vezes. <\/b><\/span><\/span><\/span>Atualmente existem <\/b><\/span><\/span><\/span>microsc\u00f3pios eletr\u00f4nicos que produzem amplia\u00e7\u00f5es de at\u00e9 cem mil vezes.<\/b><\/span><\/span><\/span><\/p>\n

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

III- Luneta astron\u00f4mica<\/b><\/span><\/span><\/span>\u00a0\"\"<\/b><\/span><\/span><\/span> utilizada na <\/b><\/span><\/span><\/span>observa\u00e7\u00e3o de astros ou de objetos distantes.<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Consta de <\/b><\/span><\/span><\/span>2 lentes convergentes, a objetiva e a ocular.\u00a0 <\/b><\/span><\/span><\/span>Ao contr\u00e1rio do microsc\u00f3pio composto, a <\/b><\/span><\/span><\/span>dist\u00e2ncia focal da objetiva \u00e9 muito grande <\/b><\/span><\/span><\/span>(da ordem de metros). A <\/b><\/span><\/span><\/span>ocular tem pequena dist\u00e2ncia focal.<\/b><\/span><\/span><\/span><\/p>\n

Devido ao fato de o <\/b><\/span><\/span><\/span>objeto estar muito afastado, a imagem (i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>) formada pela objetiva est\u00e1 praticamente sobre seu foco (f<\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/sub><\/span>) e \u00e9 real e invertida (veja figura).<\/b><\/span><\/span><\/span><\/p>\n

\"\"Essa <\/b><\/span><\/span><\/span>imagem (i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>) vai servir como objeto para a ocular <\/b><\/span><\/span><\/span>resultando numa <\/b><\/span><\/span><\/span>imagem final (i<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>), virtual <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>invertida em rela\u00e7\u00e3o ao objeto. <\/b><\/span><\/span><\/span><\/p>\n

Observe que os <\/b><\/span><\/span><\/span>focos da ocular (f<\/b><\/span><\/span><\/span>ocular<\/b><\/span><\/span><\/sub><\/span>) e da objetiva (f<\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/sub><\/span>) est\u00e3o muito pr\u00f3ximos, praticamente coincidindo.<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>aumento <\/b><\/span><\/span><\/span>desta luneta \u00e9 dado por\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>A =f<\/b><\/span><\/span><\/span>obj\u00a0<\/b><\/span><\/span><\/sub><\/span>\/ f<\/b><\/span><\/span><\/span>oc<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe <\/b><\/span><\/span><\/span>por essa express\u00e3o <\/b><\/span><\/span><\/span>que,<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub><\/span>para que o <\/b><\/span><\/span><\/span>aumento seja bem grande, a dist\u00e2ncia focal da ocular deve ser bem menor que a da objetiva, ou seja, <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>oc<\/b><\/span><\/span><\/sub><\/span>\u00a0< f<\/b><\/span><\/span><\/span>ob<\/b><\/span><\/span><\/sub><\/span>.<\/b><\/span><\/span><\/span>\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

No caso de uma\u00a0<\/b><\/span><\/span><\/span>luneta terrestre<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>onde a <\/b><\/span><\/span><\/span>imagem final n\u00e3o \u00e9 invertida <\/b><\/span><\/span><\/span>devemos <\/b><\/span><\/span><\/span>trocar a lente ocular convergente por uma lente divergente que tem dist\u00e2ncia focal negativa. <\/b><\/span><\/span><\/span><\/p>\n

Como o <\/b><\/span><\/span><\/span>aumento<\/b><\/span><\/span><\/span> \u00e9 dado por <\/b><\/span><\/span><\/span>A = f<\/b><\/span><\/span><\/span>obj\u00a0<\/b><\/span><\/span><\/sub><\/span>\/ f<\/b><\/span><\/span><\/span>oc<\/b><\/span><\/span><\/sub><\/span>, <\/b><\/span><\/span><\/span>\u00e9 claro <\/b><\/span><\/span><\/span>que maior ser\u00e1 o aumento quanto maior o m\u00f3dulo da objetiva for maior que o m\u00f3dulo da ocular.<\/b><\/span><\/span><\/span><\/p>\n

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

\"\" Entender o funcionamento de todos os dispositivos descritos acima.<\/b><\/span><\/span><\/span><\/p>\n

\"\" Se voc\u00ea quiser aprofundar mais, analise as resolu\u00e7\u00f5es dos exerc\u00edcios a seguir:<\/b><\/span><\/span><\/span><\/p>\n

01-<\/b><\/span><\/span><\/span> <\/b>Uma <\/b><\/span><\/span><\/span>pequena luneta <\/b><\/span><\/span><\/span>consiste em uma <\/b><\/span><\/span><\/span>lente objetiva convergente de dist\u00e2ncia focal f<\/b><\/span><\/span><\/span>ob<\/b><\/span><\/span><\/sub><\/span>\u00a0= 35 cm <\/b><\/span><\/span><\/span>e de uma <\/b><\/span><\/span><\/span>lente ocular divergente de dist\u00e2ncia focal f<\/b><\/span><\/span><\/span>oc<\/b><\/span><\/span><\/sub><\/span>\u00a0= – 5,0 cm. <\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>duas lentes est\u00e3o separadas por uma dist\u00e2ncia d = 30 cm,<\/b><\/span><\/span><\/span> como ilustrado na <\/b><\/span><\/span><\/span>figura 1. <\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span><\/span>objeto \u00e9 colocado sobre o eixo \u00f3ptico da luneta, \u00e0 esquerda da objetiva, distando x da mesma.<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Calcule a <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o da imagem final desse objeto, <\/b><\/span><\/span><\/span>medida em <\/b><\/span><\/span><\/span>rela\u00e7\u00e3o ao centro da lente ocular, quando x = 40 cm.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Considere um <\/b><\/span><\/span><\/span>feixe de raios paralelos de luz incidente na objetiva. <\/b><\/span><\/span><\/span><\/p>\n

Complete o diagrama de raios, na figura 2, representando<\/b><\/span><\/span><\/span> suas trajet\u00f3rias no <\/b><\/span><\/span><\/span>interior da luneta <\/b><\/span><\/span><\/span>e <\/b><\/span><\/span><\/span>indicando claramente a dire\u00e7\u00e3o em que emergem da ocular <\/b><\/span><\/span><\/span>(a figura foi ampliada na dire\u00e7\u00e3o transversal ao eixo \u00f3ptico da luneta para facilitar seu desenho)<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span><\/span>Localizando a<\/b><\/span><\/span><\/span> imagem P\u2019 formada pela objetiva com o objeto P colocado \u00e0 40 cm <\/b><\/span><\/span><\/span>da mesma tal que <\/b><\/span><\/span><\/span>P = 4 0cm, <\/b><\/span><\/span><\/span>sendo fornecida <\/b><\/span><\/span><\/span>a dist\u00e2ncia focal da objetiva f<\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/sub><\/span> = 35 cm.<\/b><\/span><\/span><\/span><\/p>\n

Aplicando a<\/b><\/span><\/span><\/span> equa\u00e7\u00e3o dos pontos conjugados\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>P = 40 cm\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>f = 35 cm\u00a0 \"\"<\/b><\/span><\/span><\/span> <\/b>1\/f = 1\/P + 1\/P\u2019 \u00a0\"\"<\/b><\/span><\/span><\/span><\/p>\n

1\/35 = 1\/40 + 1\/P\u2019\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>1\/35 \u2013 1\/40 = 1\/P\u2019\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>1\/P\u2019 = (8 \u2013 7)\/280\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>P\u2019 = 280cm (dist\u00e2ncia da objetiva at\u00e9 i<\/b><\/span><\/span><\/span>1 <\/b><\/span><\/span><\/sub><\/span> <\/b>conforme a<\/b><\/span><\/span><\/span> figura abaixo com i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> <\/b>localizada atrav\u00e9s dos <\/b><\/span><\/span><\/span>dois raios not\u00e1veis tra\u00e7ados).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Localiza\u00e7\u00e3o <\/b><\/span><\/span><\/span>da imagem i<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> de i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, que\u00a0<\/b><\/span><\/span><\/span>funciona como objeto para a ocular <\/b><\/span><\/span><\/span>sendo dados:<\/b><\/span><\/span><\/span><\/p>\n

P = 250cm\u00a0<\/b><\/span><\/span><\/span>(dist\u00e2ncia do objeto i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span> at\u00e9 a ocular) \"\" <\/b><\/span><\/span><\/span>f<\/b><\/span><\/span><\/span>ocular <\/b><\/span><\/span><\/sub><\/span>= – 5cm (divergente<\/b><\/span><\/span><\/span>)\u00a0 \"\"\u00a0equa\u00e7\u00e3o dos <\/b><\/span><\/span><\/span>pontos conjugados de Gauss \"\"<\/b><\/span><\/span><\/span> <\/b>1\/f = 1\/P + 1\/P\u2019 \"\"<\/b><\/span><\/span><\/span> 1\/-5 = 1\/250 + 1\/P\u2019\u00a0 \"\"\u00a0 1\/P\u2019 = – 1\/5 – 1\/250 \"\" \u00a01\/P\u2019 = (- 50 \u2013 1)\/250\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>P\u2019= – 4,9cm (dist\u00e2ncia pedida de i<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0at\u00e9 a ocular <\/b><\/span><\/span><\/span>conforme a figura abaixo <\/b><\/span><\/span><\/span>localizado por dois raios not\u00e1veis)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>os <\/b><\/span><\/span><\/span>raios que incidem paralelamente ao eixo da lente objetiva, <\/b><\/span><\/span><\/span>emergem desta, em <\/b><\/span><\/span><\/span>dire\u00e7\u00e3o ao foco<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

da lente ocular, emergindo<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>da ocular, paralelamente ao eixo principal das lentes.<\/b><\/span><\/span><\/span><\/p>\n

02- <\/b><\/span><\/span><\/span>A figura a <\/b><\/span><\/span><\/span>seguir \u00e9 a representa\u00e7\u00e3o esquem\u00e1tica de um sistema \u00f3ptico <\/b><\/span><\/span><\/span>formado por <\/b><\/span><\/span><\/span>duas lentes convergentes, separadas por 50 cm. <\/b><\/span><\/span><\/span><\/p>\n

As <\/b><\/span><\/span><\/span>dist\u00e2ncias focais das lentes 1 e 2 s\u00e3o, respectivamente, 10 cm e 15 cm.<\/b><\/span><\/span><\/span>\"\"<\/p>\n

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

Utiliza-se um <\/b><\/span><\/span><\/span>l\u00e1pis com 4 cm de comprimento como objeto,<\/b><\/span><\/span><\/span> o qual \u00e9 <\/b><\/span><\/span><\/span>posicionado a 15 cm da lente 1. <\/b><\/span><\/span><\/span>Com <\/b><\/span><\/span><\/span>base nesses dados:<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> <\/b>Determine a <\/b><\/span><\/span><\/span>posi\u00e7\u00e3o da imagem formada pelo sistema de lentes.<\/b><\/span><\/span><\/span><\/p>\n

b)<\/b><\/span><\/span><\/span> <\/b>Determine o <\/b><\/span><\/span><\/span>tamanho da imagem formada pelo sistema. <\/b><\/span><\/span><\/span>Ela \u00e9 <\/b><\/span><\/span><\/span>direita ou invertida, em rela\u00e7\u00e3o ao objeto? Justifique sua resposta.<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> <\/b>Empregando a <\/b><\/span><\/span><\/span>representa\u00e7\u00e3o de raios,<\/b><\/span><\/span><\/span> fa\u00e7a um <\/b><\/span><\/span><\/span>desenho em escala, <\/b><\/span><\/span><\/span>mostrando a <\/b><\/span><\/span><\/span>localiza\u00e7\u00e3o e o tamanho da imagem formada pelo sistema. <\/b><\/span><\/span><\/span>Utilize a <\/b><\/span><\/span><\/span>escala 10 para 1, <\/b><\/span><\/span><\/span>ou seja, <\/b><\/span><\/span><\/span>cada 10 cm no sistema real correspondem a 1 cm no seu desenho. <\/b><\/span><\/span><\/span>(Cada quadr\u00edcula tem 0,5 cm de lado).<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

a)<\/b><\/span><\/span><\/span> Dados\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>dist\u00e2ncia focal da <\/b><\/span><\/span><\/span>lente 1 (f<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0= 10 cm)\u00a0 \"\" <\/b><\/span><\/span><\/span>dist\u00e2ncia focal da <\/b><\/span><\/span><\/span>lente 2 (f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0= 15 cm) \"\" <\/b><\/span><\/span><\/span>dist\u00e2ncia entre as <\/b><\/span><\/span><\/span>duas lentes<\/b><\/span><\/span><\/span> <\/b>(d = 50 cm)\u00a0 \"\" <\/b><\/span><\/span><\/span>dist\u00e2ncia do objeto <\/b><\/span><\/span><\/span>(l\u00e1pis) \u00e0 lente 1<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(p<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0= 15 cm).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0C\u00e1lculo da dist\u00e2ncia (P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2019) da primeira imagem \u00e0 Lente 1<\/b><\/span><\/span><\/span>\u00a0aplicando a <\/b><\/span><\/span><\/span>equa\u00e7\u00e3o dos pontos conjugados <\/b><\/span><\/span><\/span>de <\/b><\/span><\/span><\/span>Gauss<\/b><\/span><\/span><\/span> \"\"\u00a0 1\/f = 1\/P + 1\/P\u2019\u00a0 \"\"\u00a0 1\/10 = 1\/15 + 1\/P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2019\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2019= + 30cm<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(a primeira imagem \u00e9 real e forma-se 30 cm \u00e0 direita da Lente 1).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Essa <\/b><\/span><\/span><\/span>primeira imagem funciona como objeto para a segunda lente\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 sendo a <\/b><\/span><\/span><\/span>dist\u00e2ncia entre as lentes \u00e9 d = 50 cm<\/b><\/span><\/span><\/span>, a <\/b><\/span><\/span><\/span>dist\u00e2ncia (p<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>) da primeira imagem \u00e0 lente 2<\/b><\/span><\/span><\/span> \u00e9\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0= d \u2013 P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2019<\/b><\/span><\/span><\/span>= 50 \u2013 30\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>p<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0=20 cm (dist\u00e2ncia da primeira imagem, agora objeto, para a lente 2).<\/b><\/span><\/span><\/span><\/p>\n

C\u00e1lculo da dist\u00e2ncia (P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u2019) da imagem final \u00e0 lente 2 de dist\u00e2ncia focal f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> = 15 cm\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 1<\/b><\/span><\/span><\/span>\/f<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> = 1\/P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> + 1\/P\u2019<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span><\/p>\n

\"\" 1\/15 = 1\/20 + 1\/ P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u2019\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u2019= + 60cm<\/b><\/span><\/span><\/span> <\/b>(<\/b><\/span><\/span><\/span>a imagem final \u00e9 real <\/b><\/span><\/span><\/span>e se forma <\/b><\/span><\/span><\/span>60 cm \u00e0 direita da lente 2 <\/b><\/span><\/span><\/span>ou <\/b><\/span><\/span><\/span>110 cm \u00e0 direita da Lente 1).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0b)<\/b><\/span><\/span><\/span> <\/b>O <\/b><\/span><\/span><\/span>aumento fornecido pelo sistema \u00e9 o produto dos aumentos<\/b><\/span><\/span><\/span> \"\" A = A<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0x A<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 A= P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u2019\/P<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>\u00a0x P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u2019\/P<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\" A = 30\/15 x 60\/20 \u00a0\"\" <\/b><\/span><\/span><\/span>A= +6 (a imagem final \u00e9 direita e 6 vezes maior que o objeto).<\/b><\/span><\/span><\/span><\/p>\n

\u00a0Altura h\u2019<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> da imagem final em rela\u00e7\u00e3o \u00e0 altura h = 4 cm do objeto \"\" <\/b><\/span><\/span><\/span>A=h\u2019<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/h\u00a0 \"\"\u00a0 6 = h\u2019<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span>\/4\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>h\u2019<\/b><\/span><\/span><\/span>2 <\/b><\/span><\/span><\/sub><\/span>= 24cm<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>(<\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>imagem final \u00e9 real, <\/b><\/span><\/span><\/span>tem <\/b><\/span><\/span><\/span>comprimento 24 cm e \u00e9 direita em rela\u00e7\u00e3o ao objeto, <\/b><\/span><\/span><\/span>pois o <\/b><\/span><\/span><\/span>aumento linear transversal \u00e9 positivo).<\/b><\/span><\/span><\/span><\/p>\n

c)<\/b><\/span><\/span><\/span> <\/b>Escala dada\u00a0 \"\"\u00a0 \u00a0<\/b><\/span><\/span><\/span>[10 cm : 1 cm : 2 quadr\u00edculas]\u00a0 \"\"<\/b><\/span><\/span><\/span> \u00a0<\/b><\/span><\/span><\/span>[5 cm : 1 cm : 1 quadr\u00edcula]\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 observe que<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

na figura acima, o lado de cada quadr\u00edcula representa 5 cm nas medidas dadas no enunciado.<\/b><\/span><\/span><\/span><\/p>\n

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

03-<\/b><\/span><\/span><\/span> <\/b>Um <\/b><\/span><\/span><\/span>microsc\u00f3pio composto \u00e9 formado por duas lentes convergentes. A lente que fica mais pr\u00f3xima <\/b><\/span><\/span><\/span>do objeto \u00e9 a <\/b><\/span><\/span><\/span>objetiva <\/b><\/span><\/span><\/span>e aquela <\/b><\/span><\/span><\/span>atrav\u00e9s da qual se observa a imagem \u00e9 a ocular. <\/b><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span><\/span>imagem I<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>, formada pela objetiva, funciona como um objeto para a ocular (figura)<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

Quando o <\/b><\/span><\/span><\/span>objeto \u00e9 colocado a 1cm da objetiva <\/b><\/span><\/span><\/span>a <\/b><\/span><\/span><\/span>imagem final <\/b><\/span><\/span><\/span>que se observa \u00e9 <\/b><\/span><\/span><\/span>100 vezes maior que o objeto e se encontra a 50cm da lente ocular. <\/b><\/span><\/span><\/span><\/p>\n

Se a <\/b><\/span><\/span><\/span>amplia\u00e7\u00e3o devido \u00e0 lente objetiva \u00e9 20 vezes<\/b><\/span><\/span><\/span>, <\/b><\/span><\/span><\/span>determine a dist\u00e2ncia D, <\/b><\/span><\/span><\/span>em <\/b><\/span><\/span><\/span>cent\u00edmetros.<\/b><\/span><\/span><\/span><\/p>\n

Resolu\u00e7\u00e3o:<\/b><\/span><\/span><\/span><\/p>\n

O <\/b><\/span><\/span><\/span>aumento<\/b><\/span><\/span><\/span> fornecido pela <\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/span> vale \"\"\u00a0 <\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>objetiva <\/b><\/span><\/span><\/sub><\/span>= – 20 <\/b><\/span><\/span><\/span>(negativo, a imagem \u00e9 invertida).<\/b><\/span><\/span><\/span><\/p>\n

Dist\u00e2ncia do objeto \u00e0 objetiva P = 1 cm\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 <\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>objetiva <\/b><\/span><\/span><\/sub><\/span>= – P\u2019\/P\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 -20 = – P\u2019\/1\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>P\u2019 = 20 cm <\/b><\/span><\/span><\/span>(dist\u00e2ncia da objetiva at\u00e9 a <\/b><\/span><\/span><\/span>imagem por ela formada que \u00e9 i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

A<\/b><\/span><\/span><\/span>final <\/b><\/span><\/span><\/sub><\/span>= A<\/b><\/span><\/span><\/span>objetiva<\/b><\/span><\/span><\/sub><\/span>.A<\/b><\/span><\/span><\/span>ocular<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"<\/b><\/span><\/span><\/span>\u00a0 -100 = – 20.A<\/b><\/span><\/span><\/span>ocular<\/b><\/span><\/span><\/sub><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>oc <\/b><\/span><\/span><\/sub><\/span>= 5\u00a0<\/b><\/span><\/span><\/span>(aumento fornecido pela ocular, positivo pois i<\/b><\/span><\/span><\/span>2<\/b><\/span><\/span><\/sub><\/span> \u00e9 direita em rela\u00e7\u00e3o \u00e0 i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>). <\/b><\/span><\/span><\/span><\/p>\n

Imagem<\/b><\/span><\/span><\/span> fornecida pela <\/b><\/span><\/span><\/span>ocular dista 50cm da mesma e P\u2019 \u00e9 negativa pois a imagem \u00e9 virtual) \"\" P\u2019 = – 50cm<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>A<\/b><\/span><\/span><\/span>ocular <\/b><\/span><\/span><\/sub><\/span>= – P\u2019\/P<\/b><\/span><\/span><\/span>\u00a0 \"\"\u00a0 5 = – (- 50)\/P\u00a0 \"\"\u00a0 <\/b><\/span><\/span><\/span>P = 10cm (dist\u00e2ncia da ocular at\u00e9 i<\/b><\/span><\/span><\/span>1<\/b><\/span><\/span><\/sub><\/span>).<\/b><\/span><\/span><\/span><\/p>\n

A dist\u00e2ncia D pedida vale\u00a0\"\"<\/b><\/span><\/span><\/span>\u00a0 D = 20 + 10\u00a0 \"\"\u00a0\u00a0<\/b><\/span><\/span><\/span>D = 30cm<\/b><\/span><\/span><\/span>.<\/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":"

Instrumentos \u00d3pticos Instrumentos de proje\u00e7\u00e3o S\u00e3o aqueles cuja imagem formada \u00e9 real, pois pode ser projetada sobre um filme, uma tela, um anteparo, etc.\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 I – C\u00e2mera fotogr\u00e1fica ou m\u00e1quina fotogr\u00e1fica\u00a0 dispositivo utilizado para capturar imagens. Consiste b\u00e1sicamente de uma caixa com orif\u00edcio no qual se encontram uma ou mais lentes convergentes (objetiva), por onde entram os raios de<\/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-2289","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2289","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=2289"}],"version-history":[{"count":2,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2289\/revisions"}],"predecessor-version":[{"id":2297,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2289\/revisions\/2297"}],"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=2289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}