A fancy thermometer is developed as shown in the figure in which a laser pointer placed $2 \mathrm{ft}$ away from a mirror and the distance of reflected radiation to the original source is measured as shown in the figure. The angular orientation, $\theta$, of a "rigid" mirror is controlled by the ambient temperature, the lengths of rods and their coefficient of thermal expansion. At the reference temperature, the rods are the same length: $\mathrm{L}_{1}=\mathrm{L}_{2}=10 \mathrm{in}$. The distance between the rods is $\mathrm{a}=5 \mathrm{in}$. (a) If the thermal coefficient of the rods (1) and (2) are $\mathrm{a}_{1}=7.2 \times 10-6 /{ }^{\circ} \mathrm{F}$ and $\mathrm{a}_{2}=12.5 \times 10-6 /{ }^{\circ} \mathrm{F}$, respectively. Determine an expression for the temperature change, $\Delta T\left({ }^{\circ} \mathrm{F}\right)$, as a function of distance $\mathrm{d}$ (in.). Assume that the rods are uniformly heated or cooled along their lengths.

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LT8PO0 The First Answerer