Overview
This lecture explains how to use ray diagrams to determine the properties and locations of images formed by spherical mirrors and lenses.
Ray Diagrams for Concave Mirrors
- The principal axis is a horizontal reference line for ray diagrams.
- The focal point (F) is where parallel rays converge after reflecting off the mirror.
- Focal length is the distance from the mirror to the focal point.
- Placing the object outside the focal point results in a real, inverted, and enlarged image.
- The image distance (di) is positive for real images (on the same side as the object).
- Magnification (M) is negative for inverted images; |M| > 1 means the image is larger than the object.
Concave Mirror: Object Inside Focal Point
- Placing the object between the mirror and focal point produces an upright, enlarged, and virtual image.
- Virtual images have negative image distance (di), as they appear on the opposite side of the mirror.
- Virtual images are formed where rays appear, but do not actually converge.
Ray Diagrams for Convex Mirrors
- Convex mirrors always produce virtual, upright, and reduced images.
- The focal length of a convex mirror is negative.
- Image distance (di) is always negative, indicating a virtual image.
- Rays appear to converge behind the mirror.
Mirror and Lens Equations
- Mirror (or thin lens) equation: 1/f = 1/do + 1/di
- Magnification (M) = hi/ho = -di/do, where hi = image height and ho = object height.
- Power of a lens: P = 1/f (f in meters), measured in diopters (m⁻¹).
Lenses: Convergent and Divergent
- Convergent lenses have positive focal length; divergent lenses have negative focal length.
- Divergent lenses always produce virtual, upright, and reduced images.
- Convergent lenses can produce real or virtual images, depending on object location.
- For convergent lenses, beyond focal point yields real, inverted, and possibly enlarged images.
Key Terms & Definitions
- Principal Axis — reference horizontal line in ray diagrams.
- Focal Point (F) — point where parallel rays meet after reflection/refraction.
- Focal Length (f) — distance from mirror/lens to focal point.
- Image Distance (di) — distance from mirror/lens to image.
- Magnification (M) — ratio of image height to object height.
- Virtual Image — appears to form where rays seem to converge, not actually.
- Real Image — formed where rays actually converge.
- Power of Lens (P) — inverse of focal length in meters; unit is diopter.
Action Items / Next Steps
- Practice drawing ray diagrams for different mirror and lens setups.
- Memorize the mirror/lens equations and when image distances are considered positive or negative.
- Convert focal lengths to meters before calculating power.