This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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a) Step 1: Select the appropriate mirror. The most appropriate mirror for boda boda riders is a convex mirror.
Step 2: Provide the reason. A convex mirror is chosen because it provides a wide field of view, allowing the rider to see a larger area behind them. It forms a virtual, upright, and diminished image, which is essential for safety and observing traffic.
Step 3: Describe the illustration. An illustration would show a convex mirror with parallel incident rays diverging after reflection, appearing to originate from a virtual focal point behind the mirror. The image formed would be smaller and upright.
b) Step 1: Select the appropriate mirror and design the optical instrument. The appropriate optical instrument is a periscope, which uses two plane mirrors.
Step 2: Provide the reason. Plane mirrors are used because they produce an upright, true-sized image without distortion, allowing for accurate observation of objects over obstacles.
Step 3: Describe the design. A simple periscope consists of a tube with two plane mirrors placed parallel to each other at opposite ends. Each mirror is angled at to the line of sight. Light from the object hits the top mirror, reflects downwards to the bottom mirror, and then reflects horizontally into the observer's eye.
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a) Step 1: Select the appropriate mirror. The most appropriate mirror for boda boda riders is a convex mirror.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.