{"id":2624,"date":"2016-11-11T02:37:23","date_gmt":"2016-11-11T02:37:23","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2624"},"modified":"2024-09-02T14:59:26","modified_gmt":"2024-09-02T14:59:26","slug":"espelhos-esfericos","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/raciocinio-logico\/espelhos-esfericos\/","title":{"rendered":"Espelhos Esf\u00e9ricos"},"content":{"rendered":"

Racioc\u00ednio L\u00f3gico<\/b><\/span><\/span><\/span><\/span><\/p>\n

Espelhos Esf\u00e9ricos<\/span><\/span><\/span><\/span><\/span><\/p>\n

Como esse conte\u00fado envolve muita teoria, voc\u00ea pode encontr\u00e1-la em <\/b><\/span><\/span><\/span>fisicaevestibular.com.br \u2013 \u00d3ptica Geom\u00e9trica \u2013 Espelhos Esf\u00e9ricos<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

Exerc\u00edcios comentados de vestibulares que exigem, al\u00e9m da aplica\u00e7\u00e3o de f\u00f3rmulas, racioc\u00ednio l\u00f3gico, sobre <\/b><\/span><\/span><\/span>Espelhos Esf\u00e9ricos.<\/b><\/span><\/span><\/span><\/span><\/span><\/p>\n

 <\/p>\n

01- (PUC-SP)\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Em um <\/b><\/span><\/span>farol de autom\u00f3vel tem-se um refletor constitu\u00eddo por um espelho esf\u00e9rico <\/b><\/span><\/span>e um <\/b><\/span><\/span>filamento <\/b><\/span><\/span>de <\/b><\/span><\/span>pequenas\u00a0 dimens\u00f5es <\/b><\/span><\/span>que <\/b><\/span><\/span>pode emitir luz.<\/b><\/span><\/span> <\/b><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span>farol funciona bem quando o espelho <\/b><\/span><\/span>\u00e9:<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) c\u00f4ncavo<\/b><\/span><\/span> e o filamento est\u00e1 no <\/b><\/span><\/span>centro do espelho;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

b) c\u00f4ncavo<\/b><\/span><\/span> e o filamento est\u00e1 no <\/b><\/span><\/span>foco do espelho;<\/b><\/span><\/span><\/span><\/span><\/p>\n

c) convexo<\/b><\/span><\/span> e o filamento est\u00e1 no <\/b><\/span><\/span>centro do espelho;\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

d) convexo<\/b><\/span><\/span> e o filamento est\u00e1 no <\/b><\/span><\/span>foco do espelho;<\/b><\/span><\/span><\/span><\/span><\/p>\n

e) convexo<\/b><\/span><\/span> e o filamento est\u00e1 no <\/b><\/span><\/span>ponto m\u00e9dio entre o foco e o centro do espelho.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

02-(UFMA-MA)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Mary Scondy, <\/b><\/span><\/span>uma <\/b><\/span><\/span>ilusionista amadora, <\/b><\/span><\/span>fez a <\/b><\/span><\/span>m\u00e1gica conhecida como l\u00e2mpada fantasma. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Instalou <\/b><\/span><\/span>uma <\/b><\/span><\/span>l\u00e2mpada incandescente <\/b><\/span><\/span>no <\/b><\/span><\/span>interior de uma caixa,<\/b><\/span><\/span> aberta em <\/b><\/span><\/span>um dos lados. <\/b><\/span><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span>parte aberta da caixa <\/b><\/span><\/span>estava <\/b><\/span><\/span>voltada para frente <\/b><\/span><\/span>de um <\/b><\/span><\/span>espelho c\u00f4ncavo,<\/b><\/span><\/span> <\/b>habilmente colocado <\/b><\/span><\/span>para que a <\/b><\/span><\/span>imagem da l\u00e2mpada pudesse ser formada na parte superior da caixa, <\/b><\/span><\/span>conforme <\/b><\/span><\/span>representado <\/b><\/span><\/span>esquematicamente na <\/b><\/span><\/span>figura.<\/b><\/span><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span>l\u00e2mpada tinha uma pot\u00eancia de 40W <\/b><\/span><\/span>e inicialmente estava <\/b><\/span><\/span>desligada.<\/b><\/span><\/span> <\/b><\/span><\/span>\"\"<\/p>\n

Quando Mary <\/b><\/span><\/span>ligou o interruptor escondido, <\/b><\/span><\/span>a <\/b><\/span><\/span>l\u00e2mpada acendeu, <\/b><\/span><\/span>e <\/b><\/span><\/span>Josu\u00e9,<\/b><\/span><\/span> um dos <\/b><\/span><\/span>espectadores, <\/b><\/span><\/span>tomou um <\/b><\/span><\/span>susto<\/b><\/span><\/span>, pois <\/b><\/span><\/span>viu uma l\u00e2mpada aparecer magicamente sobre a caixa.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Com <\/b><\/span><\/span>base na figura <\/b><\/span><\/span>e no que <\/b><\/span><\/span>foi descrito, <\/b><\/span><\/span>pode-se <\/b><\/span><\/span>concluir que, ao ser ligada a l\u00e2mpada, <\/b><\/span><\/span>ocorreu a <\/b><\/span><\/span>forma\u00e7\u00e3o <\/b><\/span><\/span>de<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>uma <\/b><\/span><\/span>imagem real, <\/b><\/span><\/span>e a pot\u00eancia irradiada <\/b><\/span><\/span>era de 40W.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>uma <\/b><\/span><\/span>imagem real,<\/b><\/span><\/span> e a pot\u00eancia irradiada <\/b><\/span><\/span>era de 80W<\/b><\/span><\/span>.<\/b><\/span><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span>uma <\/b><\/span><\/span>imagem virtual, <\/b><\/span><\/span>e a pot\u00eancia irradiada <\/b><\/span><\/span>era de 40W.\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span>uma <\/b><\/span><\/span>imagem virtual, <\/b><\/span><\/span>e a pot\u00eancia irradiada <\/b><\/span><\/span>era de 80W.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

03-(PUC-MG)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Na <\/b><\/span><\/span>figura <\/b><\/span><\/span>o<\/b><\/span><\/span> e <\/b><\/span><\/span>i<\/b><\/span><\/span>\u00a0 representam, <\/b><\/span><\/span>respectivamente, o <\/b><\/span><\/span>objeto e a imagem <\/b><\/span><\/span>de um <\/b><\/span><\/span>corpo extenso <\/b><\/span><\/span>apoiados <\/b><\/span><\/span>sobre o eixo principal (ep) de um espelho esf\u00e9rico.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a) <\/b><\/span><\/span>O espelho <\/b><\/span><\/span>\u00e9 c\u00f4ncavo ou convexo? Justifique.<\/b><\/span><\/span><\/span><\/span><\/p>\n

b) Localize <\/b><\/span><\/span>o <\/b><\/span><\/span>espelho, o foco e o centro de curvatura.<\/b><\/span><\/span><\/span><\/span><\/p>\n

c) Trace dois raios not\u00e1veis <\/b><\/span><\/span>que <\/b><\/span><\/span>determinam a imagem, identificando-os.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

04-(Olimp\u00edada Brasileira de F\u00edsica)\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span>quadrado est\u00e1 localizado sobre o eixo principal <\/b><\/span><\/span>de um <\/b><\/span><\/span>espelho esf\u00e9rico c\u00f4ncavo <\/b><\/span><\/span>conforme <\/b><\/span><\/span>figura.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Sabe-se que o <\/b><\/span><\/span>v\u00e9rtice inferior esquerdo do quadrado est\u00e1 localizado exatamente sobre o centro de curvatura do espelho.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Pode-se <\/b><\/span><\/span>afirmar que a imagem do quadrado<\/b><\/span><\/span> tem a <\/b><\/span><\/span>forma de um:<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>quadrado\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>tri\u00e2ngulo\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span>ret\u00e2ngulo\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span>trap\u00e9zio\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

e) <\/b><\/span><\/span>losango<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

05-(UNIFESP-SP)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Os <\/b><\/span><\/span>elevados custos da energia, <\/b><\/span><\/span>aliados \u00e0 <\/b><\/span><\/span>conscientiza\u00e7\u00e3o da necessidade de reduzir<\/b><\/span><\/span> o <\/b><\/span><\/span>aquecimento<\/b><\/span><\/span> <\/b>global, <\/b><\/span><\/span>fazem <\/b><\/span><\/span>ressurgir antigos projetos, <\/b><\/span><\/span>como \u00e9 o <\/b><\/span><\/span>caso do fog\u00e3o solar.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Utilizando <\/b><\/span><\/span>as <\/b><\/span><\/span>propriedades reflexivas <\/b><\/span><\/span>de um <\/b><\/span><\/span>espelho esf\u00e9rico c\u00f4ncavo, <\/b><\/span><\/span>devidamente <\/b><\/span><\/span>orientado<\/b><\/span><\/span> para o <\/b><\/span><\/span>Sol,<\/b><\/span><\/span> \u00e9 <\/b><\/span><\/span>poss\u00edvel produzir aquecimento <\/b><\/span><\/span>suficiente para <\/b><\/span><\/span>cozinhar ou fritar alimentos.<\/b><\/span><\/span> <\/b><\/span><\/span><\/p>\n

Suponha que um <\/b><\/span><\/span>desses fog\u00f5es <\/b><\/span><\/span>seja <\/b><\/span><\/span>constitu\u00eddo de um espelho esf\u00e9rico c\u00f4ncavo ideal <\/b><\/span><\/span>e que, num <\/b><\/span><\/span>dado momento, tenha seu eixo principal alinhado com o Sol.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Na <\/b><\/span><\/span>figura, P<\/b><\/span><\/span>1<\/b><\/span><\/sub><\/span>\u00a0a P<\/b><\/span><\/span>5<\/b><\/span><\/sub><\/span>\u00a0<\/b><\/span><\/span>representam <\/b><\/span><\/span>cinco posi\u00e7\u00f5es igualmente espa\u00e7adas <\/b><\/span><\/span>sobre o <\/b><\/span><\/span>eixo principal <\/b><\/span><\/span>do <\/b><\/span><\/span>espelho,<\/b><\/span><\/span> nas quais <\/b><\/span><\/span>uma pequena frigideira pode ser colocada.<\/b><\/span><\/span> <\/b><\/span><\/span><\/p>\n

P<\/b><\/span><\/span>2<\/b><\/span><\/sub><\/span>\u00a0coincide com o centro de curvatura do espelho e P<\/b><\/span><\/span>4<\/b><\/span><\/sub><\/span>, com o foco. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Considerando que o <\/b><\/span><\/span>aquecimento em cada posi\u00e7\u00e3o dependa exclusivamente da quantidade de raios <\/b><\/span><\/span>de <\/b><\/span><\/span>luz refletidos pelo espelho <\/b><\/span><\/span>que <\/b><\/span><\/span>atinja a frigideira, <\/b><\/span><\/span>a <\/b><\/span><\/span>ordem decrescente de temperatura que a frigideira pode atingir em cada posi\u00e7\u00e3o \u00e9:<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

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

06-(FUVEST-SP)\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span>holofote <\/b><\/span><\/span>\u00e9 <\/b><\/span><\/span>constitu\u00eddo<\/b><\/span><\/span> por <\/b><\/span><\/span>dois espelhos c\u00f4ncavos E\u2019 e E\u2019\u2019<\/b><\/span><\/span> de modo que a <\/b><\/span><\/span>quase totalidade da luz emitida por uma l\u00e2mpada L, seja projetada pelo espelho maior E\u2019, <\/b><\/span><\/span>formando um <\/b><\/span><\/span>feixe de raios quase paralelos.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Nesse <\/b><\/span><\/span>arranjo, os espelhos devem ser posicionados de forma que a l\u00e2mpada esteja aproximadamente:<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>nos <\/b><\/span><\/span>focos<\/b><\/span><\/span> dos <\/b><\/span><\/span>espelhos E\u2019 e\u00a0 E\u2019\u2019\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>no <\/b><\/span><\/span>centro de curvatura de E\u2019\u2019 <\/b><\/span><\/span>e no <\/b><\/span><\/span>v\u00e9rtice de E\u2019\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span>no <\/b><\/span><\/span>foco de E\u2019\u2019 <\/b><\/span><\/span>e no <\/b><\/span><\/span>centro de curvatura de E\u2019\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

d) nos centros de curvatura de E\u2019 e E\u2019\u2019.\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

e) <\/b><\/span><\/span>no <\/b><\/span><\/span>foco de E\u2019 <\/b><\/span><\/span>e no <\/b><\/span><\/span>centro de curvatura de E\u2019\u2019.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

07-(ENEM-MEC)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Os <\/b><\/span><\/span>espelhos retrovisores, <\/b><\/span><\/span>que <\/b><\/span><\/span>deveriam auxiliar os motoristas na hora de estacionar <\/b><\/span><\/span>ou <\/b><\/span><\/span>mudar de pista, <\/b><\/span><\/span>muitas vezes <\/b><\/span><\/span>causam problemas.<\/b><\/span><\/span> <\/b><\/span><\/span><\/p>\n

\u00c9 que o <\/b><\/span><\/span>espelho retrovisor do lado direito, <\/b><\/span><\/span>em <\/b><\/span><\/span>alguns modelos, distorce a imagem, <\/b><\/span><\/span>dando a<\/b><\/span><\/span><\/span><\/span><\/p>\n

impress\u00e3o de que o ve\u00edculo est\u00e1 a uma dist\u00e2ncia maior do que a real.<\/b><\/span><\/span><\/span><\/span>\"\"<\/p>\n

Este <\/b><\/span><\/span>tipo de espelho,<\/b><\/span><\/span> chamado <\/b><\/span><\/span>convexo,<\/b><\/span><\/span> \u00e9 <\/b><\/span><\/span>utilizado com o objetivo de ampliar o campo visual <\/b><\/span><\/span>do <\/b><\/span><\/span>motorista,<\/b><\/span><\/span> j\u00e1 que no <\/b><\/span><\/span>Brasil se adota a dire\u00e7\u00e3o do lado esquerdo<\/b><\/span><\/span> e, assim, o <\/b><\/span><\/span>espelho da direita fica muito mais distante dos olhos do condutor.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Dispon\u00edvel em: http:\/\/noticias.vrum.com.br. Acesso em: 3 nov. 2010 (adaptado).<\/b><\/span><\/span><\/span><\/span><\/p>\n

Sabe-se que, em um espelho convexo, <\/b><\/span><\/span>a <\/b><\/span><\/span>imagem formada <\/b><\/span><\/span>est\u00e1 <\/b><\/span><\/span>mais pr\u00f3xima do espelho <\/b><\/span><\/span>do que <\/b><\/span><\/span>este est\u00e1 do objeto, <\/b><\/span><\/span>o que <\/b><\/span><\/span>parece estar em conflito com a informa\u00e7\u00e3o apresentada na reportagem. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Essa <\/b><\/span><\/span>aparente contradi\u00e7\u00e3o<\/b><\/span><\/span> \u00e9 <\/b><\/span><\/span>explicada pelo fato <\/b><\/span><\/span>de<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>a <\/b><\/span><\/span>imagem<\/b><\/span><\/span> projetada na <\/b><\/span><\/span>retina do motorista <\/b><\/span><\/span>ser <\/b><\/span><\/span>menor do que o objeto.\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>a <\/b><\/span><\/span>velocidade <\/b><\/span><\/span>do autom\u00f3vel afetar a <\/b><\/span><\/span>percep\u00e7\u00e3o da dist\u00e2ncia.\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span>o <\/b><\/span><\/span>c\u00e9rebro humano <\/b><\/span><\/span>interpretar como <\/b><\/span><\/span>distante uma imagem pequena<\/b><\/span><\/span>.\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span>o <\/b><\/span><\/span>espelho convexo <\/b><\/span><\/span>ser capaz de <\/b><\/span><\/span>aumentar o campo visual do motorista.\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

e) <\/b><\/span><\/span>o <\/b><\/span><\/span>motorista perceber a luz <\/b><\/span><\/span>vinda do espelho com a <\/b><\/span><\/span>parte lateral do olho.\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

08-(ACAFE-SC)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Acoplados nos espelhos <\/b><\/span><\/span>de alguns carros <\/b><\/span><\/span>s\u00e3o colocados espelhos esf\u00e9ricos convexos\u00a0<\/b><\/span><\/span>para o <\/b><\/span><\/span>motorista observar os carros de tr\u00e1s.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span>alternativa correta <\/b><\/span><\/span>que <\/b><\/span><\/span>mostra a vantagem<\/b><\/span><\/span> de se <\/b><\/span><\/span>usar<\/b><\/span><\/span> um <\/b><\/span><\/span>espelho desse tipo em rela\u00e7\u00e3o a um espelho plano est\u00e1 no fato <\/b><\/span><\/span>de que:<\/b><\/span><\/span><\/span><\/span><\/p>\n

A) <\/b><\/span><\/span>o <\/b><\/span><\/span>campo visual <\/b><\/span><\/span>\u00e9 <\/b><\/span><\/span>maior.\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

B) <\/b><\/span><\/span>as <\/b><\/span><\/span>imagens <\/b><\/span><\/span>dos carros <\/b><\/span><\/span>ficam maiores.\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

C) <\/b><\/span><\/span>as <\/b><\/span><\/span>imagens<\/b><\/span><\/span> dos carros <\/b><\/span><\/span>s\u00e3o reais.<\/b><\/span><\/span><\/span><\/span><\/p>\n

D) <\/b><\/span><\/span>as <\/b><\/span><\/span>dist\u00e2ncias das imagens ao espelho <\/b><\/span><\/span>s\u00e3o <\/b><\/span><\/span>maiores do que as <\/b><\/span><\/span>dist\u00e2ncias dos carros <\/b><\/span><\/span>ao espelho.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

\u00a009-(UNICAMP-SP)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Uma das <\/b><\/span><\/span>primeiras aplica\u00e7\u00f5es militares <\/b><\/span><\/span>da <\/b><\/span><\/span>\u00f3tica ocorreu <\/b><\/span><\/span>no s\u00e9culo III a.C. quando <\/b><\/span><\/span>Siracusa estava sitiada pelas for\u00e7as navais romanas. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Na v\u00e9spera da batalha, <\/b><\/span><\/span>Arquimedes ordenou que 60 soldados polissem seus escudos retangulares de bronze, <\/b><\/span><\/span>medindo <\/b><\/span><\/span>0,5m de largura por 1,0m de altura. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Quando o <\/b><\/span><\/span>primeiro navio romano <\/b><\/span><\/span>se encontrava a <\/b><\/span><\/span>aproximadamente 30m da praia para atacar, \u00e0 luz <\/b><\/span><\/span>do <\/b><\/span><\/span>sol nascente,<\/b><\/span><\/span> foi dada a <\/b><\/span><\/span>ordem para que os soldados se colocassem formando um arco<\/b><\/span><\/span> e <\/b><\/span><\/span>empunhassem seus escudos, como representado esquematicamente na figura a seguir.<\/b><\/span><\/span> <\/b><\/span><\/span><\/p>\n

Em <\/b><\/span><\/span>poucos minutos as velas do navio estavam ardendo em chamas.<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0Isso foi <\/b><\/span><\/span>repetido para cada navio, <\/b><\/span><\/span>e assim n\u00e3o foi dessa vez que <\/b><\/span><\/span>Siracusa caiu. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Uma forma <\/b><\/span><\/span>de entendermos o que ocorreu consiste em tratar o conjunto de espelhos como um espelho c\u00f4ncavo. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Suponha que os <\/b><\/span><\/span>raios do sol cheguem paralelos ao espelho e sejam focalizados na vela do navio.<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) Qual deve ser o raio do espelho c\u00f4ncavo <\/b><\/span><\/span>para que a <\/b><\/span><\/span>intensidade do sol concentrado seja m\u00e1xima?<\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>Considere a <\/b><\/span><\/span>intensidade da radia\u00e7\u00e3o solar no momento da batalha como 500 W\/m<\/b><\/span><\/span>2<\/b><\/span><\/sup><\/span>. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Considere que a <\/b><\/span><\/span>refletividade efetiva do bronze sobre todo o espectro solar \u00e9 de 0,6, ou seja, 60% da intensidade incidente \u00e9 refletida. Estime a pot\u00eancia total incidente na regi\u00e3o do foco.<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

10- (UFES-ES)\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span>objeto desloca-se ao longo do eixo principal,<\/b><\/span><\/span> em <\/b><\/span><\/span>dire\u00e7\u00e3o<\/b><\/span><\/span> ao <\/b><\/span><\/span>v\u00e9rtice de um espelho esf\u00e9rico c\u00f4ncavo Gaussiano,\u00a0com velocidade constante de 4cm\/s<\/b><\/span><\/span>. <\/b><\/span><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span>dist\u00e2ncia focal do espelho \u00e9 de 10cm. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Em <\/b><\/span><\/span>certo instante<\/b><\/span><\/span>, o <\/b><\/span><\/span>objeto est\u00e1 a 50cm do v\u00e9rtice.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Ap\u00f3s 5s, <\/b><\/span><\/span>a <\/b><\/span><\/span>dist\u00e2ncia percorrida pela imagem do objeto <\/b><\/span><\/span>\u00e9 de:<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>50,83 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

b) <\/b><\/span><\/span>49,58 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

c) <\/b><\/span><\/span>30,00 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

d) <\/b><\/span><\/span>12,50 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

e) <\/b><\/span><\/span>2,50 cm<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

11- (MACKENZIE-SP)\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Disp\u00f5e-se de <\/b><\/span><\/span>dois espelhos esf\u00e9ricos, <\/b><\/span><\/span>um <\/b><\/span><\/span>convexo e um c\u00f4ncavo, <\/b><\/span><\/span>com <\/b><\/span><\/span>raios de curvatura 20,0 cm cada um, <\/b><\/span><\/span>e que <\/b><\/span><\/span>obedecem \u00e0s condi\u00e7\u00f5es de Gauss. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Quando um <\/b><\/span><\/span>objeto real \u00e9 colocado perpendicularmente ao eixo principal do espelho convexo,<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

a 6,0 cm de seu v\u00e9rtice,<\/b><\/span><\/span> obt\u00e9m-se uma <\/b><\/span><\/span>imagem conjugada de 1,5 cm de altura. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Para que <\/b><\/span><\/span>seja obtida uma imagem conjugada, tamb\u00e9m de 1,5 cm de altura, <\/b><\/span><\/span>colocando <\/b><\/span><\/span>esse objeto perpendicularmente ao eixo principal do espelho c\u00f4ncavo, sua dist\u00e2ncia at\u00e9 o v\u00e9rtice desse espelho <\/b><\/span><\/span>dever\u00e1 ser<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

12-(UNESP-SP)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

A <\/b><\/span><\/span>imagem do Sol <\/b><\/span><\/span>\u00e9 <\/b><\/span><\/span>formada em um espelho esf\u00e9rico c\u00f4ncavo,<\/b><\/span><\/span> de <\/b><\/span><\/span>dist\u00e2ncia focal igual a 1 metro. Considerando<\/b><\/span><\/span> a\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

dist\u00e2ncia do Sol \u00e0 Terra 250 vezes maior que o di\u00e2metro do Sol, <\/b><\/span><\/span>o <\/b><\/span><\/span>di\u00e2metro da imagem formada <\/b><\/span><\/span>ser\u00e1:<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

13-(ITA-SP)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span>espelho plano<\/b><\/span><\/span> est\u00e1 <\/b><\/span><\/span>colocado na frente de um espelho c\u00f4ncavo, <\/b><\/span><\/span>perpendicularmente ao <\/b><\/span><\/span>eixo principal. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Uma <\/b><\/span><\/span>fonte luminosa A, centrada <\/b><\/span><\/span>no <\/b><\/span><\/span>eixo principal entre os dois espelhos, emite raios <\/b><\/span><\/span>que\u00a0 se <\/b><\/span><\/span>refletem<\/b><\/span><\/span> <\/b>sucessivamente sobre os dois espelhos e formam, sobre a pr\u00f3pria fonte A, <\/b><\/span><\/span>uma <\/b><\/span><\/span>imagem real <\/b><\/span><\/span>da <\/b><\/span><\/span>mesma. <\/b><\/span><\/span><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span>raio de curvatura do espelho \u00e9 40cm <\/b><\/span><\/span>e a <\/b><\/span><\/span>dist\u00e2ncia do centro da fonte A at\u00e9 o centro do espelho esf\u00e9rico \u00e9 de 30cm.<\/b><\/span><\/span><\/span><\/span><\/p>\n

A <\/b><\/span><\/span>dist\u00e2ncia d do espelho plano at\u00e9 o centro do espelho c\u00f4ncavo <\/b><\/span><\/span>\u00e9, ent\u00e3o:<\/b><\/span><\/span><\/span><\/span><\/p>\n

a) <\/b><\/span><\/span>20cm\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

b) <\/b><\/span><\/span>30cm\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

c) <\/b><\/span><\/span>40cm\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

d) <\/b><\/span><\/span>45cm\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

e) <\/b><\/span><\/span>50cm<\/b><\/span><\/span><\/span><\/span><\/p>\n

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

14-(MACKENZIE-SP)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

Um <\/b><\/span><\/span>pequeno objeto <\/b><\/span><\/span>foi <\/b><\/span><\/span>colocado sobre o eixo principal <\/b><\/span><\/span>de um <\/b><\/span><\/span>espelho esf\u00e9rico c\u00f4ncavo<\/b><\/span><\/span>, que obedece \u00e0s <\/b><\/span><\/span>condi\u00e7\u00f5es de Gauss, <\/b><\/span><\/span>conforme ilustra a <\/b><\/span><\/span>figura.<\/b><\/span><\/span> <\/b><\/span><\/span>\"\"<\/p>\n

O <\/b><\/span><\/span>raio da esfera, <\/b><\/span><\/span>da qual <\/b><\/span><\/span>foi retirada a calota que constitui o espelho, mede 1,00 m. <\/b><\/span><\/span><\/span><\/span><\/p>\n

Nessas condi\u00e7\u00f5es, <\/b><\/span><\/span>a <\/b><\/span><\/span>dist\u00e2ncia entre esse objeto e sua respectiva imagem conjugada <\/b><\/span><\/span>\u00e9 de<\/b><\/span><\/span><\/span><\/span><\/p>\n

a)\u00a0 <\/b><\/span><\/span>240 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/b><\/span><\/span><\/span><\/span><\/p>\n

b)\u00a0<\/b><\/span><\/span>150 cm\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

c)\u00a0 <\/b><\/span><\/span>75 cm\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

d)\u00a0 <\/b><\/span><\/span>60 cm \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0<\/b><\/span><\/span><\/span><\/span><\/p>\n

e)\u00a0 <\/b><\/span><\/span>50 cm<\/b><\/span><\/span><\/span><\/span><\/p>\n

<\/a> 15-(CEFET-MG)<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

\"\"<\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

 <\/p>\n

A <\/b><\/span><\/span>figura abaixo representa um objeto a frente de um espelho esf\u00e9rico convexo <\/b><\/span><\/span>de <\/b><\/span><\/span>raio de curvatura de 60 cm.<\/b><\/span><\/span><\/span><\/span><\/p>\n

Se <\/b><\/span><\/span>esse objeto est\u00e1 em repouso a 20 cm do v\u00e9rtice <\/b><\/span><\/span>sobre o <\/b><\/span><\/span>eixo principal do espelho <\/b><\/span><\/span>e, em seguida, <\/b><\/span><\/span>oscila em torno da posi\u00e7\u00e3o inicial com amplitude de 10 cm,<\/b><\/span><\/span> ent\u00e3o <\/b><\/span><\/span>as m\u00e1ximas dist\u00e2ncias a direita e a esquerda em rela\u00e7\u00e3o \u00e0 imagem inicial ser\u00e3o, respectivamente, em cm,<\/b><\/span><\/span> iguais a<\/b><\/span><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

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

Racioc\u00ednio L\u00f3gico Espelhos Esf\u00e9ricos Como esse conte\u00fado envolve muita teoria, voc\u00ea pode encontr\u00e1-la em fisicaevestibular.com.br \u2013 \u00d3ptica Geom\u00e9trica \u2013 Espelhos Esf\u00e9ricos Exerc\u00edcios comentados de vestibulares que exigem, al\u00e9m da aplica\u00e7\u00e3o de f\u00f3rmulas, racioc\u00ednio l\u00f3gico, sobre Espelhos Esf\u00e9ricos.   01- (PUC-SP)\u00a0 Em um farol de autom\u00f3vel tem-se um refletor constitu\u00eddo por um espelho esf\u00e9rico e um filamento de pequenas\u00a0 dimens\u00f5es que<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2508,"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-2624","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2624","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=2624"}],"version-history":[{"count":3,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2624\/revisions"}],"predecessor-version":[{"id":2630,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2624\/revisions\/2630"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2508"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2624"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}