Question

show analytically from the lens equation that when the object is at the principal focus, the image is formed at infinity

Answer 1

we know, the lens formula is
$$\begin{gathered} \frac{1}{f}=\frac{1}{v}-\frac{1}{u} \\ \Rightarrow \frac{1}{v}=\frac{1}{f}+\frac{1}{u} \\ \Rightarrow \frac{1}{v}=\frac{-f+f}{-f^2} \\ \Rightarrow \frac{1}{v}=\frac{0}{-f^2} \\ \Rightarrow v=\infty \end{gathered}$$

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