Final answer:
To find the radius of curvature of the plano-convex lens, we use the relation between power, index of refraction, and radius of curvature based on the Lens Maker's Equation. We adjust the radius of curvature to achieve a power that is 1.5 times greater than the double convex lens with the same material and initial power.
Step-by-step explanation:
The student's question involves the concept of lens power and the relationships between focal length, radius of curvature, and power for optical lenses. According to the formula P = 1/f, where P is the power in diopters and f is the focal length in meters, if a double convex lens has power P and a plano-convex lens made of the same material has power 1.5P, we can relate their focal lengths. The formula for lens power derived from the Lens Maker's Equation is P = (n - 1)(1/R1 - 1/R2), where n is the index of refraction of the lens material and R1 and R2 are the radii of curvature of the lens surfaces.
For a double convex lens with equal radii of curvature r, the power P can be expressed as P = (n - 1)(2/r). For the plano-convex lens with power 1.5P and one flat surface (R1 = ∞, so 1/R1 is 0), we have 1.5P = (n - 1)(1/R2). Therefore, R2 has to be adjusted such that the power is 1.5 times more than the original power P.
By substituting the value of P from the double convex lens into the equation for the plano-convex lens, we can find the new radius of curvature R2 that will give the plano-convex lens a power of 1.5P.