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

Question

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

Accepted Answer

1. **Function of Spherometer:** A spherometer is a precision instrument primarily designed to measure the radius of curvature ($R$) of spherical surfaces, such as lenses and mirrors.
2. **Measurement Principle:** It measures the small height or 'sagitta' ($h$) of the curved surface relative to a plane defined by its three legs. Using the distance between the legs ($l$) and the measured sagitta, the radius of curvature is calculated using the formula: $R = \frac{l^2}{6h} + rac{h}{2}$.
3. **Why other options are incorrect:** 
   - **Focal Length ($f$):** Requires knowledge of both the radius of curvature ($R$) and the refractive index ($\mu$) using the Lens Maker's Formula. Since the material (and thus $\mu$) is unknown, $f$ cannot be measured directly with just a spherometer.
   - **Refractive Index ($\mu$):** Cannot be determined without knowing the focal length.
   - **Aperture:** This is the diameter of the lens, which is typically measured with a ruler or vernier calipers, not a spherometer.

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