Question #43563

A composite rod of uniform cross-sectional area $A$ is placed perfectly between two rigid, immovable walls located at $x=0$ and $x=3L$. The rod consists of Section A (from $x=0$ to $x=L$) and Section B (from $x=L$ to $x=3L$). Section A has Young's modulus $Y$ and coefficient of linear thermal expansion $3\alpha$. Section B has Young's modulus $2Y$ and coefficient of linear thermal expansion $\alpha$. Two thin convex lenses, each of optical power $P$, are mounted such that their principal axes are collinear. Lens 1 is fixed to the wall at $x=0$, and Lens 2 is rigidly attached to the junction of the two sections at $x=L$. When the temperature of the entire system is uniformly increased by $\Delta T$, thermal stress develops in the rod. Assuming the walls remain perfectly rigid and the lenses themselves do not undergo thermal expansion, what is the change in the effective optical power ($\Delta P_{\text{eff}}$) of the two-lens system?