The two faces of a thin lens have radii r1=+10.0 cm and r2=-25.0 cm, respectively. The lens is

step 1 So in this question, we are given a lens whose radiuses are given to us R1 is equal to 10 centim

The two faces of a thin lens have radii r1=+10.0 cm and...

The two faces of a thin lens have radii $r_{1}=+10.0 \mathrm{~cm}$ and $r_{2}=-25.0 \mathrm{~cm}$, respectively. The lens is made of glass of index $1.740 .$ Calculate $(a)$ the focal length and $(b)$ the power of the lens.

Key Concepts

Lensmaker's Formula

Lensmaker's formula relates the focal length of a lens to the refractive index of its material and the radii of curvature of its two surfaces. This formula is critical for understanding how the shape and material properties of a lens determine its ability to converge or diverge light, and it is fundamental in the design and analysis of optical systems.

Focal Length

The focal length of a lens is the distance from the lens at which parallel incident rays converge to a point (for a converging lens) or appear to diverge from (for a diverging lens). It is a key parameter in lens design and in determining the magnification of an optical system.

Optical Power

Optical power is a measure of the ability of a lens to bend light and is defined as the inverse of its focal length (in meters). It is expressed in diopters and is important in various applications such as corrective eyewear, photography, and microscopy, as it quantifies the lens's converging or diverging strength.

Sign Conventions in Optics

The sign conventions used in optics, particularly for the radii of curvature of lens surfaces and the focal length, are essential for correctly applying formulas like the lensmaker's formula. These conventions determine whether a surface is convex or concave and whether a lens is converging or diverging, allowing for consistent analysis and calculation in optical system design.

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