{"id":2252,"date":"2016-05-24T00:03:13","date_gmt":"2016-05-24T00:03:13","guid":{"rendered":"http:\/\/fisicaevestibular.com.br\/novo\/?page_id=2252"},"modified":"2024-09-02T14:29:33","modified_gmt":"2024-09-02T14:29:33","slug":"resolucao-comentada-dos-exercicios-de-vestibulares-sobre-prismas-opticos","status":"publish","type":"page","link":"https:\/\/fisicaevestibular.com.br\/novo\/optica\/optica-geometrica\/prismas\/resolucao-comentada-dos-exercicios-de-vestibulares-sobre-prismas-opticos\/","title":{"rendered":"Prismas \u00f3pticos – Resolu\u00e7\u00e3o"},"content":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre <\/b><\/span><\/span><\/span><\/p>\n

Prismas \u00f3pticos<\/b><\/span><\/span><\/span><\/p>\n

 <\/p>\n

01-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Veja figura abaixo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

R- B<\/b><\/span><\/span><\/p>\n

02-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe a figura abaixo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

d=i + r\u2019 \u2013 A\u00a0 —\u00a0 d=50 + 30 -60\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>d=20<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 R- A<\/b><\/span><\/span><\/p>\n

03-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Se o raio emergir rasante, teremos que o \u00e2ngulo de incid\u00eancia i\u2019 na segunda face \u00e9 igual ao <\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00e2ngulo limite L que \u00e9 igual ao \u00e2ngulo de refring\u00eancia A, fornecido pela express\u00e3o \u2013 senL=n<\/b><\/span><\/span>menor<\/b><\/span><\/span><\/sub>\/n<\/b><\/span><\/span>maior\u00a0<\/b><\/span><\/span><\/sub>\u00a0\u00ae\u00a0senL=n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\/n\u00a0\u00aesenL=1\/n<\/b><\/span><\/span><\/p>\n

Como i\u2019=L\u00a0\u00ae\u00a0sen i\u2019=sen L\u00a0\u00a0\u00ae\u00a0sen i\u2019=senA=1\/n\u00a0\u00a0 —\u00a0 senA=1\/\u221a2\u00a0 —\u00a0 senA=\u221a2\/2\u00a0 —\u00a0 A=45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0<\/b><\/span><\/span>R- D.<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/p>\n

04-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>A=60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 i=45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 i\u2019=30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 A=r + i\u2019\u00a0 —\u00a0 60=r + 30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 r=30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 Aplicando Snell-Descartes na face onde o raio incide\u00a0 —\u00a0 n<\/b><\/span><\/span>ar.<\/b><\/span><\/span><\/sub>seni=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.senr\u00a0 —\u00a0 1.sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 1.\u221a2\/2=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.1\/2\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>=\u221a2<\/b><\/span><\/span><\/p>\n

05-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Veja a figura abaixo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Como o raio de luz incide perpendicularmente na primeira fase, ele n\u00e3o sofre desvio at\u00e9 atingir a segunda face quando emerge rasante, onde, aplicando Snell-Descartes\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.sen60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.sen90<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.1,73\/2=1.1\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>=1,15\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>R- B<\/b><\/span><\/span><\/p>\n

06-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>I- Como ele incide normalmente no l\u00edquido ele n\u00e3o sofre desvio at\u00e9 atingir a interface l\u00edquido-<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0prisma com \u00e2ngulo de 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup> (sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=\u221a2\/2=0,7) e, nessa interface\u00a0 —\u00a0 c\u00e1lculo do \u00e2ngulo limite\u00a0 —\u00a0\u00a0 senL=n<\/b><\/span><\/span>menor<\/b><\/span><\/span><\/sub>\/n<\/b><\/span><\/span>maior<\/b><\/span><\/span><\/sub>=\u221a2\/\u221a3=0,8\u00a0 —\u00a0 como seni<senL\u00a0 —\u00a0 i<L\u00a0 —\u00a0 assim, n\u00e3o haver\u00e1 reflex\u00e3o total e sim,\u00a0 refra\u00e7\u00e3o, penetrando no prisma\u00a0 —\u00a0<\/b><\/span><\/span>\u00a0Falsa<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/p>\n

II- Aplicando Snell-Descartes na interface l\u00edquido-prisma\u00a0 —\u00a0 n\u2019.sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n.senr\u00a0 —\u00a0 \u221a3. \u221a2\/2=\u221a2.senr\u00a0 —\u00a0 senr=\u221a3\/2\u00a0 —\u00a0 r=60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0<\/b><\/span><\/span>\u00a0Falsa<\/b><\/span><\/span><\/p>\n

III \u2013 C\u00e1lculo de i\u2019\u00a0 —\u00a0 A=r + i\u2019\u00a0 —\u00a0 90=60 + i\u2019\u00a0 —\u00a0 i\u2019=30<\/b><\/span><\/span>o\u00a0<\/b><\/span><\/span><\/sup>\u00a0—\u00a0 Aplicando Snell-Descartes na face em que o raio emerge para o ar<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0—\u00a0 n.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.senr\u2019\u00a0 —\u00a0 \u221a2. 1\/2=1.senr\u2019\u00a0 —\u00a0 senr\u2019=\u221a2\/2\u00a0 —\u00a0 r\u2019=45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>Verdadeira<\/b><\/span><\/span><\/p>\n

IV- Verdadeira\u00a0 —\u00a0 veja que os raios incidente e emergente possuem o mesmo \u00e2ngulo (45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>), portanto possuem dire\u00e7\u00f5es paralelas.<\/b><\/span><\/span><\/p>\n

R- D<\/b><\/span><\/span><\/p>\n

07-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Visualizando a figura de frente:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Observe que na face AB e CD ele n\u00e3o sofre desvio, pois incide e emerge perpendicularmente e nas outras duas faces sofre reflex\u00e3o total, pois incide com 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>, que \u00e9 superior ao \u00e2ngulo limite que \u00e9 42<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>.\u00a0\u00a0<\/b><\/span><\/span>R- D<\/b><\/span><\/span><\/p>\n

08-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe na sequ\u00eancia de figuras abaixo que \u00e0 medida que i diminui no sentido anti-hor\u00e1rio, r <\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

tamb\u00e9m diminui, mas no sentido hor\u00e1rio\u00a0\u00a0<\/b><\/span><\/span>R- E<\/b><\/span><\/span><\/p>\n

09-<\/b><\/span><\/span><\/span> <\/b>R- A<\/b><\/span><\/span>\u00a0\u2013 veja figura abaixo<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

10-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Veja a figura abaixo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.sen60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>P<\/b><\/span><\/span><\/sub>.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 1.\u221a3\/2=n<\/b><\/span><\/span>P<\/b><\/span><\/span><\/sub>.1\/2\u00a0 —\u00a0 n<\/b><\/span><\/span>P<\/b><\/span><\/span><\/sub>=\u221a3=1,7<\/b><\/span><\/span><\/p>\n

11-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Como o raio incide perpendicularmente na face A ele n\u00e3o sofre desvio at\u00e9 atingir a face B, onde incide com \u00e2ngulo i=45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0e sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=\u00a0\u00a0sen45<\/b><\/span><\/span>o <\/b><\/span><\/span><\/sup>= \u221a2\/2 = 070\u00a0 —\u00a0\u00a0\u00a0\u00a0 o \u00e2ngulo limite na interface prisma-\u00e1gua vale senL=n<\/b><\/span><\/span>menor<\/b><\/span><\/span><\/sub>\/n<\/b><\/span><\/span>maior<\/b><\/span><\/span><\/sub>\u00a0 —\u00a0 senL=1,33\/1,52\u00a0 —\u00a0 senL=8,87\u00a0 —\u00a0 sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup><senL\u00a0 —\u00a0\u00a0 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup><L\u00a0 —\u00a0 incide na face B com \u00e2ngulo inferior ao \u00e2ngulo limite, ou seja, n\u00e3o sofre reflex\u00e3o total em B, mas sim refra\u00e7\u00e3o, passando para a \u00e1gua<\/b><\/span><\/span>.\u00a0 R- A<\/b><\/span><\/span>\"\"<\/p>\n

12-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Quando o raio de luz se refrata paralelo \u00e0 base o desvio (d) tem valor m\u00ednimo e o \u00e2ngulo de incid\u00eancia \u00e9 igual ao \u00e2ngulo de emerg\u00eancia, ou seja, i = r\u2019. Mas, se isso ocorre\u00a0\u00ae\u00a0i\u2019 = r e i=r, veja figura abaixo.<\/b><\/span><\/span>\"\"<\/p>\n

A=2r\u00a0 —\u00a0 \u00a0aplicando Snell-Descartes na primeira face\u00a0 —\u00a0 n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.seni=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.senr\u00a0 —\u00a0 1.\u221a2\/2=\u221a2.senr\u00a0 —\u00a0 senr=1\/2\u00a0 —\u00a0 r=30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 A=2r=2.30\u00a0 —\u00a0 A=60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 d<\/b><\/span><\/span>min<\/b><\/span><\/span><\/sub>=d=i + r\u2019 \u2013 A=2i \u2013 A\u00a0 d=2.45 \u2013 60\u00a0 —\u00a0 d=90 \u2013 60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>d=30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup><\/p>\n

13-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>As trajet\u00f3rias dos raios incidente, no interior do prisma e emergente se deslocam como se voc\u00ea estivesse girando um \u201csaca-rolhas\u201d no sentido hor\u00e1rio, ou seja, o raio incidente sobe, e os outros dois descem conforme as figuras abaixo.<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

R- A\u00a0\u00a0<\/b><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/p>\n

14-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Refra\u00e7\u00e3o no pontoA\u00a0 —\u00a0 n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.sen60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.senr\u00a0 —\u00a0 1.\u221a3\/2=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 1.\u221a3\/2=n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.1\/2\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>=\u221a3\u00a0 —\u00a0 incide no ponto B onde sofre refra\u00e7\u00e3o, pois sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=1\/2 e senL=n<\/b><\/span><\/span>menor<\/b><\/span><\/span><\/sub>\/n<\/b><\/span><\/span>maior<\/b><\/span><\/span><\/sub>=1\/\u221a3= \u221a3\/3\u00a0 —\u00a0 assim, como seni<senL\u00a0 —\u00a0 i<L\u00a0 —\u00a0 ele n\u00e3o sofre reflex\u00e3o total\u00a0 —\u00a0<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

Aplicando Snell-Descartes no ponto B\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>.senr\u00a0 —\u00a0 \u221a3.1\/2=1.senr\u00a0 —\u00a0 senr=\u221a3\/2\u00a0 —\u00a0 r=60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>R- A<\/b><\/span><\/span><\/p>\n

15-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe na figura abaixo que os dois raios de luz incidem com \u00e2ngulo de 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 o \u00e2ngulo limite para o raio azul (a) \u00e9 de 44<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>e, como ele incide com 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0que \u00e9\u00a0 superior ao \u00e2ngulo limite, ele sofre reflex\u00e3o total, retornando ao prisma. O raio vermelho (v) incide tamb\u00e9m com 45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>, que \u00e9 inferior ao seu \u00e2ngulo limite (46<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>), sofrendo refra\u00e7\u00e3o e passando para o ar<\/b><\/span><\/span>.\u00a0 R- E<\/b><\/span><\/span>\"\"<\/p>\n

16-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Veja a figura abaixo:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

R- D<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

Pelo princ\u00edpio da reversibilidade dos raios de luz, o caminho na \u201cida\u201d \u00e9 o mesmo que na \u201cvolta\u201d<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

b) No ponto A\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.sen30<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>=n<\/b><\/span><\/span>ar.<\/b><\/span><\/span><\/sub>sen60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>.1\/2=1.\u221a3\/2\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>n<\/b><\/span><\/span>v<\/b><\/span><\/span><\/sub>=\u221a3<\/b><\/span><\/span><\/p>\n

18-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe que a luz incide na face interna\u00a0 com \u00e2ngulo i=45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0 —\u00a0 c\u00e1lculo do \u00e2ngulo limite\u00a0 nessa face\u00a0 —\u00a0 senL=n<\/b><\/span><\/span>menor<\/b><\/span><\/span><\/sub>\/n<\/b><\/span><\/span>maior<\/b><\/span><\/span><\/sub>=1\/n\u00a0\u00a0<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0para que ocorra reflex\u00e3o total ele deve incidir com \u00e2ngulo superior ao \u00e2ngulo limite, ou seja i>L, ou ainda seni > senL\u00a0 —\u00a0 sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0> senL\u00a0 —\u00a0 \u221a2\/2 > 1\/n\u00a0\u00a0<\/b><\/span><\/span>—\u00a0 n > \u221a2\u00a0 R- A<\/b><\/span><\/span><\/p>\n

19-<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span>R- C<\/b><\/span><\/span>\u00a0 (veja resolu\u00e7\u00e3o da quest\u00e3o anterior)<\/b><\/span><\/span><\/p>\n

20-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>a)<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

b)\u00a0 seni > senL\u00a0 —\u00a0 sen45<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0> senL\u00a0 —\u00a0 \u221a2\/2 > 1\/n\u00a0\u00a0<\/b><\/span><\/span>—\u00a0 n > \u221a2<\/b><\/span><\/span><\/p>\n

21- <\/b><\/span><\/span><\/span>Veja figura abaixo:\u00a0<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0para que haja reflex\u00e3o total\u00a0 —\u00a0 i > L\u00a0 —\u00a0 seni > senL\u00a0 —\u00a0 sen60<\/b><\/span><\/span>o<\/b><\/span><\/span><\/sup>\u00a0> 1\/n\u00a0 —\u00a0 \u221a3\/2 > 1\/n\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>n > 2\u221a3\/3<\/b><\/span><\/span><\/p>\n

22-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Observe a figura abaixo:<\/b><\/span><\/span><\/p>\n

 <\/p>\n

\"\"<\/p>\n

 <\/p>\n

R- D<\/b><\/span><\/span><\/p>\n

23-<\/b><\/span><\/span><\/span>\u00a0<\/b><\/span><\/span><\/span>Dados\u00a0 —\u00a0\u00a0 n<\/b><\/span><\/span>p<\/b><\/span><\/span><\/sub>\u00a0= 1,5\u00a0 —\u00a0 n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0= 1\u00a0 —\u00a0 sen 6\u00b0 = 0,104 e sen 9\u00b0 = 0,157\u00a0 —\u00a0 afigura a seguir ilustra a situa\u00e7\u00e3o, mostrando a trajet\u00f3ria do raio at\u00e9 a reflex\u00e3o no espelho plano\u00a0 —\u00a0 na primeira face, a incid\u00eancia \u00e9 normal, portanto n\u00e3o h\u00e1 desvio\u00a0 —\u00a0 a segunda face,<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

\u00a0aplicando a lei de Snell\u00a0 —\u00a0 n<\/b><\/span><\/span>p<\/b><\/span><\/span><\/sub>\u00a0sen i = n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0sen r\u00a0 —\u00a0 1,5 sen 6\u00b0 = 1 sen r\u00a0 —\u00a0 1,5 (0,104) = sen r\u00a0 —\u00a0 sen r = 0,157\u00a0\u00a0 —\u00a0\u00a0 r = 9\u00ba\u00a0 —\u00a0 \u00a0partir da\u00ed, acompanhando a figura, voc\u00ea conclui que o \u00e2ngulo de reflex\u00e3o no espelho plano \u00e9 3\u00b0\u00a0 —\u00a0\u00a0<\/b><\/span><\/span>R- B<\/b><\/span><\/span><\/p>\n

24-\u00a0<\/b><\/span><\/span><\/span>\u00a0\u00a0<\/b><\/span><\/span><\/span><\/p>\n

a) Dado\u00a0 —\u00a0 \u00a0n<\/b><\/span><\/span>vi<\/b><\/span><\/span><\/sub>\u00a0= 1,532\u00a0 —\u00a0 a\u00a0<\/b><\/span><\/span>Fig 1<\/b><\/i><\/span><\/span>\u00a0\u00a0mostra a refra\u00e7\u00e3o sofrida pelo raio violeta\u00a0 —\u00a0 lei de Snell\u00a0 —\u00a0 n<\/b><\/span><\/span>vi\u00a0<\/b><\/span><\/span><\/sub>sen<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub>30\u00b0 = n<\/b><\/span><\/span>ar\u00a0<\/b><\/span><\/span><\/sub>sen<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub>\u03b8<\/b><\/span><\/span>vi\u00a0 —\u00a0<\/b><\/span><\/span><\/sub><\/p>\n

\"\"<\/p>\n

\u00a01,532<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub>(0,5) = 1<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/sub>(senq<\/b><\/span><\/span>vi<\/b><\/span><\/span><\/sub> \u03b8<\/b><\/span><\/span>vi\u00a0<\/b><\/span><\/span><\/sub>)\u00a0 — sen \u03b8<\/b><\/span><\/span>vi\u00a0<\/b><\/span><\/span><\/sub>\u00a0= 0,766\u00a0 —\u00a0 da tabela dada, \u03b8<\/b><\/span><\/span>vi\u00a0<\/b><\/span><\/span><\/sub> <\/b>\u00a0= 50\u00b0<\/b><\/span><\/span>\u00a0—\u00a0 na\u00a0<\/b><\/span><\/span>Fig 2<\/b><\/i><\/span><\/span>\u00a0 —\u00a0 a + 30\u00b0 = 50\u00b0 \u00a0— \u00a0<\/b><\/span><\/span>\u03b1 = 20\u00b0<\/b><\/span><\/span>.<\/b><\/span><\/span><\/p>\n

 <\/p>\n

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

\"\"<\/p>\n

 <\/p>\n

c) Na refra\u00e7\u00e3o, o desvio angular cresce do vermelho para o violeta o que pode ser provado aplicando a lei de Snell para as demais radia\u00e7\u00f5es envolvidas\u00a0 —\u00a0 o \u00e2ngulo de incid\u00eancia \u00e9 \u03b8<\/b><\/span><\/span>rad<\/b><\/span><\/span><\/sub>\u00a0= 30\u00b0 para todas as radia\u00e7\u00f5es\u00a0 —\u00a0 n<\/b><\/span><\/span>rad<\/b><\/span><\/span><\/sub>\u00a0sen 30\u00b0 = n<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0sen\u03b8<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0 —\u00a0<\/b><\/span><\/span><\/p>\n

1.sen\u03b8<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0= n<\/b><\/span><\/span>rad<\/b><\/span><\/span><\/sub>. (0,5)\u00a0 —\u00a0 .sen\u03b8<\/b><\/span><\/span>ar<\/b><\/span><\/span><\/sub>\u00a0= n<\/b><\/span><\/span>rad<\/b><\/span><\/span><\/sub>.(0,5)\u00a0 —\u00a0 para cada radia\u00e7\u00e3o (cor) envolvida\u00a0 —\u00a0 sen\u03b8<\/b><\/span><\/span>azul<\/b><\/span><\/span><\/sub>=1,528.0,5=0,764\u00a0 —\u00a0 sen\u03b8<\/b><\/span><\/span>verde<\/b><\/span><\/span><\/sub>=1,519.0,5=0,760\u00a0 —\u00a0 sen\u03b8<\/b><\/span><\/span>amarelo<\/b><\/span><\/span><\/sub>=1,515.0,5=0,758\u00a0 —\u00a0 no intervalo de 0\u00b0 a 90\u00b0, quanto menor o seno do \u00e2ngulo, menor \u00e9 o \u00e2ngulo o que implica que o raio amarelo \u00e9 o que sofre menor desvio, depois, nessa ordem, verde, azul e violeta\u00a0 —\u00a0 observe o esquema:<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

25-\u00a0<\/b><\/span><\/span><\/span><\/p>\n

\"\"<\/p>\n

 <\/p>\n

26- <\/b><\/span><\/span><\/span>Observe no gr\u00e1fico que ambos os \u00e2ngulos v\u00e3o aumentando at\u00e9 que, a refra\u00e7\u00e3o acontece quando \u03b8r=90o\u00a0(\u00e2ngulo critico) e, nesse caso \u03b8r=30o\u00a0 —\u00a0 alicando a lei de Snell-Descartes\u00a0 —\u00a0 ni.sen \u03b8i\u00a0= nar.sen \u03b8r\u00a0—\u00a0 ni.sen30o=1.sen90o\u00a0 —\u00a0 ni.1\/2=1.1\u00a0 —\u00a0\u00a0ni=2.\u00a0<\/b><\/span><\/span><\/p>\n

 <\/p>\n

27- <\/b><\/span><\/span><\/span>Observe a figura abaixo que mostra a luz entrando e saindo de uma gota de chuva\u00a0 —\u00a0 nesta\u00a0 figura, em 1 ocorre refra\u00e7\u00e3o, em<\/b><\/span><\/span><\/p>\n

\"\"<\/p>\n

2 reflex\u00e3o, e em 3 nova refra\u00e7\u00e3o\u00a0 —\u00a0 entre 1 e 2, ocorre dispers\u00e3o\u00a0 —\u00a0<\/b><\/span><\/span>\u00a0R- A<\/b><\/span><\/span>\u00a0<\/b><\/span><\/span><\/p>\n

 <\/p>\n

Voltar para os exerc\u00edcios<\/span><\/a><\/h3>\n","protected":false},"excerpt":{"rendered":"

Resolu\u00e7\u00e3o comentada dos exerc\u00edcios de vestibulares sobre Prismas \u00f3pticos   01-\u00a0Veja figura abaixo: R- B 02-\u00a0Observe a figura abaixo: d=i + r\u2019 \u2013 A\u00a0 —\u00a0 d=50 + 30 -60\u00a0 —\u00a0\u00a0d=20o\u00a0 R- A 03-\u00a0Se o raio emergir rasante, teremos que o \u00e2ngulo de incid\u00eancia i\u2019 na segunda face \u00e9 igual ao \u00e2ngulo limite L que \u00e9 igual ao \u00e2ngulo de refring\u00eancia<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":2248,"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-2252","page","type-page","status-publish","hentry"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2252","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=2252"}],"version-history":[{"count":4,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2252\/revisions"}],"predecessor-version":[{"id":10954,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2252\/revisions\/10954"}],"up":[{"embeddable":true,"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/pages\/2248"}],"wp:attachment":[{"href":"https:\/\/fisicaevestibular.com.br\/novo\/wp-json\/wp\/v2\/media?parent=2252"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}