The focal length of a lens is related to its radius of curvature and refractive index. In this case, we are given that the radius of curvature for each surface of the convex lens is 40 cm, and the refractive index is 1.5. We need to find the focal length of the lens.

1. Calculating the focal length using the lens formula:
The lens formula is given by:
1/f = (n - 1) * (1/R1 - 1/R2)
where f is the focal length, n is the refractive index, R1 is the radius of curvature of the first surface, and R2 is the radius of curvature of the second surface.

2. Substituting the given values:
In this case, the radius of curvature for both surfaces is 40 cm, and the refractive index is 1.5. Therefore, we can substitute these values into the lens formula:
1/f = (1.5 - 1) * (1/40 - 1/40)

3. Simplifying the equation:
1/f = (0.5) * (0 - 0)
1/f = 0

4. Solving for the focal length:
To solve for the focal length, we can take the reciprocal of both sides of the equation:
f = 1/0

However, dividing by zero is undefined, so the focal length cannot be determined using the lens formula in this case.

5. Understanding the result:
The reason we cannot determine the focal length using the lens formula is because the radius of curvature for both surfaces is the same. This creates a special case known as "zero power lens" or "plano-convex lens." In this case, the lens has equal curvature on both sides, resulting in a focal length of infinity. This means that parallel rays of light will become parallel rays after passing through the lens, without any convergence or divergence.

6. Conclusion:
Based on the given information, the focal length of the convex lens with a radius of curvature of 40 cm for each surface and a refractive index of 1.5 is undefined or infinite, which is represented by option A.