A hypothetical student decided to investigate on his own (as one should) the magnification of a spherical mirror<\/a><\/span>. He came up with this design<\/p>\n

<\/p>\n

and reasoning:<\/p>\n

The angles $\\theta$ and $\\theta’$ are equal as vertically opposite angles:<\/p>\n

\\begin{equation}
\n\\label{eq:Wed10Oct162927BST2018}
\n\\theta=\\theta’
\n\\end{equation}<\/p>\n

and they can be both related to the important quantities of the problem as follows:<\/p>\n

\\begin{align}
\n\\tan\\theta=\\frac{h}{s-R}\\\\
\n\\tan\\theta’=\\frac{h’}{s’-R}\\label{eq:Wed10Oct162841BST2018}
\n\\end{align}<\/p>\n

On the second line, I note that $h’$ is negative, which is okay as it is an algebraic quantity. Anyway, from the first equation, I can deduce that the magnification $m\\equiv\\displaystyle\\frac{h’}{h}$ is given by<\/p>\n

\\begin{equation}
\nm=\\frac{s’-R}{s-R}\\,.
\n\\end{equation}<\/p><\/blockquote>\n

However the formula which has been given in class for the magnification is:<\/p>\n

\\begin{equation}
\n\\label{eq:Wed10Oct163138BST2018}
\nm=-\\frac{s’}{s}\\,.
\n\\end{equation}<\/p>\n

Can you explain to this student what is going on? (before next tutorial and\/or next blog post, where an explanation will be proposed; you are welcome to share your suggestions in the comments below. If you figure it out, it should be clear what is going on).<\/p>\n","protected":false},"excerpt":{"rendered":"

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