Question

Which of the following is the lens maker's formula?

• A. \( \frac{1}{f} = \left( \frac{1}{v} - \frac{1}{u} \right) \)
• B. \( \frac{1}{f} = \left( \mu - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \)
• C. \( f = \mu \left( R_1 + R_2 \right) \)
• D. \( f = \left( \mu + 1 \right) \left( \frac{R_1 + R_2}{2} \right) \)

Hint:

The lens maker’s formula helps calculate the focal length based on the lens' curvature and refractive index. It’s essential for designing lenses in optical systems.

Answer 1

The Correct Option is B

Step 1: Understanding lens maker's formula.
The lens maker's formula allows us to calculate the focal length of a lens based on the radii of curvature of its surfaces and the refractive index of the material. Step 2: Formula derivation.
The lens maker's formula is: \[ \frac{1}{f} = \left( \mu - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \] where:
\(f\) is the focal length of the lens,
\(\mu\) is the refractive index of the lens material,
\(R_1\) and \(R_2\) are the radii of curvature of the two surfaces of the lens.
Step 3: Conclusion.
This formula is crucial for designing optical lenses, such as eyeglasses, cameras, and microscopes, as it helps determine the necessary curvature and material properties for achieving a specific focal length.