Final answer:
The lens maker's formula for a thin double convex lens is derived from the thin-lens equation and relates the focal length to the lens's radii of curvature and indices of refraction in a thin-lens approximation.
Step-by-step explanation:
To derive the lens maker's formula for a thin double convex lens, we need to understand the thin-lens equation and how it can be used to analyze image formation through ray tracing. The lens maker's formula relates the focal length of a thin lens to its radii of curvature (R1 and R2) and the indices of refraction of the lens (n) and surrounding medium (usually air, n1=1).
Simplified for air, the lens maker's equation is 1/f = (n - 1)(1/R1 - 1/R2). When the lens is thin enough, the thickness t is negligible compared to R1 and R2, validating the thin-lens approximation. Ray tracing in this context refers to the method of drawing specific rays to determine the position and size of an image formed by a lens. The key rays include one that passes through the center of the lens and is not deviated, and others that strike the lens and refract according to the principles of optics.