Lenses are optical devices that bend light to form images. They're crucial in many everyday tools, from eyeglasses to cameras. Understanding how lenses work helps us grasp the principles of optics and image formation.
Ray tracing is a key technique for predicting image characteristics with lenses. By following specific rules and tracing key light rays, we can determine an image's position, size, and orientation. This method reveals how object distance affects image formation.
Image Formation by Lenses
Rules for thin lens ray tracing
- Ray tracing determines position, size, and orientation of image formed by thin lens
- Thin lens has thickness negligible compared to diameter
- Three key rays used in ray tracing:
- Parallel ray refracts through lens and passes through focal point on other side
- Central ray passes through center of lens and continues straight without changing direction
- Focal ray passes through focal point on object side and refracts parallel to optical axis on other side
- Image forms at point where three key rays intersect after passing through lens
Image formation through ray tracing
- To find image formed by thin lens using ray tracing:
- Draw optical axis, lens, and object
- Draw three key rays from top of object:
- Parallel ray drawn parallel to optical axis from top of object, then through lens and focal point on image side
- Central ray drawn from top of object through center of lens, continuing straight
- Focal ray drawn from top of object through focal point on object side, then refracted parallel to optical axis on image side
- Point where three rays intersect on image side is top of image
- Draw line from this point perpendicular to optical axis to determine image's position and size
- Image characteristics depend on object's distance from lens:
- Object beyond 2F (twice focal length) produces real, inverted, smaller image
- Object between F and 2F produces real, inverted, larger image
- Object at 2F produces real, inverted, same size image
- Object between lens and F produces virtual, upright, larger image
- Magnification of the image is determined by the ratio of image size to object size
Lens power from focal length
- Lens power (P) is reciprocal of focal length (f) in meters
- $P = \frac{1}{f}$
- Unit of power is diopter (D), reciprocal of meter (m⁻¹)
- Shorter focal length has higher power and stronger converging or diverging effect (magnifying glass)
- Longer focal length has lower power and weaker converging or diverging effect (telescope)
- Converging (positive) lenses have positive power
- Converging lens with 0.25 m focal length has power of $P = \frac{1}{0.25} = +4$ D
- Diverging (negative) lenses have negative power
- Diverging lens with -0.5 m focal length has power of $P = \frac{1}{-0.5} = -2$ D
Lens Characteristics and Image Formation
- Refraction is the bending of light as it passes through a lens, governed by the lens equation
- Index of refraction determines how much light bends when entering or exiting a lens
- Aberration can occur in lenses, causing distortions in the image
- Chromatic dispersion results in different colors of light being refracted at slightly different angles