[b]Translação no espelho plano[/b][br]A translação de imagens nos espelhos planos funciona da seguinte forma: quando nos aproximamos ou nos afastamos a uma certa distância do espelho, [b]nossa imagem percorre a mesma distância[/b].[br]Por exemplo, se nos aproximarmos 2 m em direção ao espelho, nossa imagem terá se aproximado 2 m com relação ao espelho, portanto teremos nos aproximado 4 m em relação à imagem.[br]A[b] mesma lógica se aplica à velocidade de aproximação ou afastamento[/b] entre o objeto e sua imagem. Basta duplicarmos a velocidade em que o objeto se aproxima ou se afasta e então obtemos a velocidade relativa entre eles.[b]Associação de espelhos planos[/b][br]A associação de espelhos planos é feita[b] alinhando-se dois espelhos com um certo ângulo α[/b], medido em relação à direção normal à superfície dos espelhos, como mostramos na figura a 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[/img][br][br]Nesse caso, observa-se a formação de um [b]número[/b] [b]progressivo[/b] [b]de[/b] [b]imagens[/b], à medida que o ângulo α diminui. A fórmula que nos permite calcular o número de imagens formadas pela associação de dois espelhos planos é a seguinte:[br][img]data:image/png;base64,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[/img][br][b]N[/b] – número de imagens[br][b]α[/b] – ângulo entre as direções normais a cada espelho[br][br][br]