The focal length of a plano-convex lens is equal to its radius of curvature. The value of the refractive index of its material is-

The relationship between the focal length (f), radius of curvature (R), and the refractive index (n) of a plano-convex lens can be described using the lens maker's formula. For a plano-convex lens, the formula is given by:

Lens Maker's Formula

The formula is:

f = (n - 1) * (R / 2)

Given Conditions

In this case, we know that the focal length (f) is equal to the radius of curvature (R). Therefore, we can set:

f = R

Substituting Values

Now, substituting this into the lens maker's formula:

R = (n - 1) * (R / 2)

Solving for the Refractive Index

To find the refractive index (n), we can rearrange the equation:

• Multiply both sides by 2: 2R = (n - 1) * R
• Divide both sides by R (assuming R is not zero): 2 = n - 1
• Add 1 to both sides: n = 3

Final Result

The refractive index of the material of the plano-convex lens is 3.