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 problem, we need to determine what can be measured using a spherometer on a plano-convex lens. Let's go through the steps systematically.

### Step-by-Step Solution:

1. **Understand the Lens Shape**: A plano-convex lens has one flat surface (plano) and one outwardly curved surface (convex). The curvature of the lens is important for determining its optical properties.

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

3. **Measure the Radius of Curvature**: By placing the spherometer on the convex surface of the lens, we can measure the height (h) that the central screw rises above the level of the three legs. The radius of curvature (R) can then be calculated using the formula:
\[ R = \frac{(l^2)}{6h} + \frac{h}{2} \]
where \( l \) is the distance between the legs of the spherometer.

4. **Determine What Cannot Be Measured**: The focal length of the lens cannot be directly measured with a spherometer. The focal length is related to the radius of curvature and the refractive index of the material, which are not directly measurable with this instrument.

5. **Conclusion**: The only measurable quantity using the spherometer on the plano-convex lens is the radius of curvature of the curved surface.

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