The power of a lens is given by the formula:

Power = (refractive index - 1) * (1 / radius of curvature)

Given that the power of the biconvex lens is 10 dioptre and the radius of curvature of each surface is 10 cm, we can use the formula to find the refractive index of the material of the lens.

Let's break down the problem into steps:

Step 1: Find the power of each surface of the lens
Since the lens is biconvex, both surfaces have the same power. Therefore, the power of each surface is 10/2 = 5 dioptre.

Step 2: Convert the power into meters
Since the power is given in dioptre, we need to convert it into meters by dividing it by 100. Therefore, the power of each surface is 5/100 = 0.05 m^-1.

Step 3: Find the refractive index
Using the formula for power, we can rearrange it to solve for the refractive index:

Power = (refractive index - 1) * (1 / radius of curvature)

0.05 = (refractive index - 1) * (1 / 0.1)

Simplifying this equation, we get:

0.05 = (refractive index - 1) * 10

0.05 = 10 * refractive index - 10

10 * refractive index = 10 + 0.05

10 * refractive index = 10.05

refractive index = 10.05 / 10

refractive index = 1.005

Step 4: Simplify the refractive index
To simplify the refractive index, we need to express it as a fraction. Since the refractive index represents the ratio of the speed of light in a vacuum to the speed of light in the material, it will always be greater than 1. In this case, the refractive index is 1.005, which can be written as 1005/1000.

Step 5: Simplify the fraction
To further simplify the fraction, we divide both the numerator and denominator by their common factor, which is 5. Therefore, the refractive index is:

refractive index = 1005/1000 = 201/200

Comparing this simplified fraction with the given options, we find that option A, 3/2, is the correct answer.