Which formula is used to calculate the focal length of a lens?

Which formula is used to calculate the focal length of a lens?

• A. 1/f = (n - 1) * (1/R1 + 1/R2)
• B. 1/f = (n - 1) * (1/R1 - 1/R2)
• C. f = (n * R1 * R2)/(R1 + R2)
• D. f = n * R1 * R2

Answer: (B)

The formula that is used to calculate the focal length of a lens in terms of its refractive index and the radii of curvature of its surfaces is presented correctly. The equation is based on the lensmaker's equation, which is fundamental in understanding how the geometry and material of a lens impact its focusing ability. In the formula, \( f \) represents the focal length of the lens, \( n \) is the refractive index relative to air (or vacuum), and \( R1 \) and \( R2 \) are the radii of curvature of the lens surfaces. The first surface of the lens has a radius \( R1 \), and the second surface has a radius \( R2 \). The convention usually assumes that \( R1 \) is positive if the first surface is convex and negative if it is concave, while \( R2 \) is typically negative for a convex surface as viewed from the lens's perspective. The formula appropriately combines these factors to yield a focal length that reflects how strongly the lens converges or diverges light. This particular structure ensures that the correct sign conventions are applied, thus leading to an accurate calculation of the focal length. Understanding this formula is essential for students studying optics,

The formula that is used to calculate the focal length of a lens in terms of its refractive index and the radii of curvature of its surfaces is presented correctly. The equation is based on the lensmaker's equation, which is fundamental in understanding how the geometry and material of a lens impact its focusing ability.

In the formula, ( f ) represents the focal length of the lens, ( n ) is the refractive index relative to air (or vacuum), and ( R1 ) and ( R2 ) are the radii of curvature of the lens surfaces. The first surface of the lens has a radius ( R1 ), and the second surface has a radius ( R2 ). The convention usually assumes that ( R1 ) is positive if the first surface is convex and negative if it is concave, while ( R2 ) is typically negative for a convex surface as viewed from the lens's perspective.

The formula appropriately combines these factors to yield a focal length that reflects how strongly the lens converges or diverges light. This particular structure ensures that the correct sign conventions are applied, thus leading to an accurate calculation of the focal length.

Understanding this formula is essential for students studying optics,