A plano convex lens of unknown material and unknown focal length is given. With the help of a spherometer we can measure the

Options

A. focal length of lens
B. radius of curvature of curved surface
C. aperture of lens
D. refractive index of material

Answer

To solve the question, we need to determine what can be measured using a spherometer when dealing with a plano-convex lens of unknown material and focal length.

### Step-by-Step Solution:

1. **Understanding the Spherometer**:
A spherometer is an instrument used to measure the curvature of a surface. It typically consists of a central screw and three legs that form a triangle. When placed on a curved surface, the height of the central screw can be adjusted to touch the surface, allowing for the measurement of the curvature.

2. **Identifying the Lens Type**:
A plano-convex lens has one flat (plano) surface and one outwardly curved (convex) surface. The curvature of the convex surface is what we are interested in measuring.

3. **Using the Spherometer**:
- Place the plano-convex lens on a flat surface.
- Position the spherometer on the lens such that the three legs are on the flat surface of the lens.
- Adjust the central screw until it just touches the curved surface of the lens.

4. **Calculating the Radius of Curvature**:
The spherometer can be used to measure the height (h) that the central screw is raised above the plane formed by the three legs. This height, along with the distance between the legs (L), can be used to calculate the radius of curvature (R) of the curved surface using the formula:
\[ R = \frac{L^2}{6h} + \frac{h}{2} \]
This formula derives from the geometry of the spherometer and the properties of the curvature.

5. **Conclusion**:
From the above steps, we conclude that the primary measurement that can be made using a spherometer with a plano-convex lens is the **radius of curvature** of the curved surface of the lens.

### Final Answer:
With the help of a spherometer, we can measure the **radius of curvature** of the curved surface of the plano-convex lens.