The focal length of a thin lens is -20.0 cm. A screen is placed 160 cm from the lens. What is

step 1 You're giving a diagram, similar to what's drawn here in this problem, and you have to find how

The focal length of a thin lens is -20.0 cm. A screen is...

The focal length of a thin lens is $-20.0 \mathrm{~cm}$. A screen is placed $160 \mathrm{~cm}$ from the lens. What is the $y$ -coordinate of the point where the light ray shown hits the screen? The incident ray is parallel to the central axis and is $1.0 \mathrm{~cm}$ from that axis.

Key Concepts

Thin Lens Optics

This concept deals with the approximation where a lens is considered to have negligible thickness compared to the other distances in the problem. Using the thin lens approximation simplifies the analysis of image formation and ray tracing because it assumes that the refraction occurs at a single plane, allowing us to use geometric methods to determine the paths of light rays through the lens.

Focal Length Sign Convention

Focal length is a fundamental concept in lens optics, and its sign indicates the type of lens and the behavior of light rays. A positive focal length corresponds to a converging lens that brings parallel rays to a focus, while a negative focal length indicates a diverging lens, where parallel rays appear to diverge from a virtual focal point. Understanding the sign convention is crucial for correctly applying ray diagrams and mathematical relationships.

Ray Tracing for Diverging Lenses

In the context of diverging lenses, ray tracing involves drawing the path of light rays and using the focal point for a diverging lens (located on the same side as the incoming light) to determine the direction of the rays after refraction. When a ray comes in parallel to the principal axis, it refracts as if it were coming from the virtual focal point. Mastery of this concept allows one to calculate where the refracted ray will intersect a screen or another plane.

Geometric Relationships and Similar Triangles

Geometric constructions, especially by using similar triangles, are an essential tool in optics problems. Once the direction of a ray is established using the focal point, similar triangles help link the distances along the principal axis with the vertical distances (heights) of the rays. This method is particularly useful in calculating the precise location where a ray, after refraction, will meet a screen or an image plane.

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