Short Answer 
The Lensmaker’s formula, P = (n – 1)(1/R1 + 1/R2), is essential for calculating lens power. For a double-convex lens with equal radii of curvature, the power simplifies to P = 2(n – 1)/R, indicating the dependence of lens power on the refractive index and radius of curvature.
Step 1: Understand the Lensmaker’s Formula
The Lensmaker’s formula is crucial for calculating the power of a lens, particularly in optics. This formula is expressed as P = (n – 1)(1/R1 + 1/R2). Here, ‘P’ represents the power of the lens, ‘n’ is the refractive index of the lens material, and R1 and R2 are the radii of curvature for both lens surfaces.
Step 2: Apply the Formula for a Double-Convex Lens
For a double-convex lens with equal radii of curvature, we denote them as R. Thus, both surfaces are curved outward. In this case, the first radius (R1) is R and the second radius (R2) is -R, which indicates the opposite curvature direction. Plugging these values into the formula, we get:
- P = (n – 1)(1/R – 1/(-R))
- This simplifies to P = (n – 1)(2/R).
Step 3: Derive the Final Result
Once the calculations are complete, we can summarize the power of the lens. The derived power is P = 2(n – 1)/R, where ‘R’ is the radius of curvature and ‘n’ is the refractive index of the lens material. Thus, the answer to the problem is option (A): 2(n-1)/R, which reflects the relationship between lens power and its physical properties.