Final answer:
The focal length of a plano-convex lens can be found using the Lens Maker's Equation by considering the radius of curvature and the index of refraction. In the case of a lens with a radius of curvature of -35 cm and an index of refraction of 1.5, the focal length is computed to be 35 cm.
Step-by-step explanation:
The question involves using concepts of optics within physics to find the focal length of a plano-convex lens. To find the focal length of a thin plano-convex lens, one can use the Lens Maker's Equation, which takes into account the radius of curvature of the lens surface, the index of refraction of the material, and the lens's geometry. Here's an example of how to apply the Lens Maker's Equation:
To find the focal length of a plano-convex lens with a radius of curvature R₂ = -35 cm and an index of refraction of 1.5, we use the following equation:
focal length (f) = ×2/(n-1) * (1/R₁ - 1/R₂)
Since the lens is plano-convex, the radius of curvature for the flat surface (R₁) is infinity, and hence its reciprocal is zero. This simplifies the equation to:
f = 1/[(n-1) * (-1/R₂)] = 1/[(1.5-1) * (-1/(-35 cm))] = 35 cm
Therefore, the focal length of the lens is 35 cm.