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Question

Explain mirror formula $$\dfrac{1}{u} + \dfrac{1}{v} = \dfrac{1}{f}$$.


Solution

$$\dfrac{AB}{A'B'} = \dfrac{AC}{A'C'}$$

$$\dfrac{BP}{A'B'} = \dfrac{PF}{A'F'}$$

$$\therefore \dfrac{AB}{A'B'} = \dfrac{PF}{A'F}$$

$$PF = -f$$          $$AP = -u$$
$$A'P = -v$$

$$\dfrac{(-2f) - (-v)}{-u - (-2f)} = \dfrac{-v - (-f)}{-f}$$

$$\therefore uv = fv + uf$$

$$\therefore \dfrac{1}{f} = \dfrac{1}{u} + \dfrac{1}{v}$$

$$\dfrac{n_2}{n_1} = \dfrac{A'B'}{AB}$$

$$= \dfrac{A'P}{AP}$$

$$= \dfrac{-v}{u}$$

1077580_1162102_ans_abe4b4f7b6e94f0b87d786a05a98dba2.png

Physics

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