Optics: Lenses and Mirrors Summary

Images from Lenses and Mirrors

Ray Diagrams

  • Simplify diagrams by focusing on rays from the top and bottom of the object, especially the top when the base is on the optical axis.

  • Represent objects as arrows with a height equivalent to the object's height.

Rules for Drawing Ray Diagrams

  • Optical Axis: A horizontal line through the center of the lens/mirror.

  • Lenses/Mirrors: Drawn vertically with light incident on the planar, convex, or concave surface.

  • Object: Typically on the left-hand side (LHS) of the lens, represented by an arrow.

  • Focus: Focal point represented by F.

Lenses

  • Lenses form images by refraction.

  • Convex Lenses: Converging lenses.

  • Concave Lenses: Diverging lenses.

  • Focal point (F) is where rays converge (convex) or appear to diverge from (concave).

  • Focal length (f) is the distance from the lens to the focal point; lenses have two focal points.

  • Optical power P = \frac{1}{f}, measured in diopters (D), indicates how strongly a lens bends light.

Rays for Convex Lenses (do > f):

  • Ray parallel to the optical axis refracts through the focus on the other side.

  • Ray through the focus on the LHS refracts and exits parallel to the optical axis.

  • Ray through the center of the lens does not refract.

Real and Virtual Images

  • Real Image: Light rays pass through the image point; can be projected onto a screen.

  • Virtual Image: Light rays do not pass through the image point; cannot be projected.

  • Concave lenses and convex mirrors typically produce virtual images.

Sign Convention for Lenses

  1. Light travels from left to right.

  2. Object distance (do) is positive.

  3. Real image distance (di) is positive.

  4. Virtual image distance is negative.

  5. Converging lens: f is positive.

  6. Diverging lens: f is negative.

  7. Heights are measured from the head to the tail of the arrow.

Thin Lens Equation

  • \frac{1}{do} + \frac{1}{di} = \frac{1}{f} (Relates object/image distances to focal length).

Magnification

  • m = \frac{hi}{ho} = -\frac{di}{do}

  • $|m| < 1$: Image is smaller.

  • $|m| > 1$: Image is larger.

  • Negative m: Inverted image.

  • Positive m: Upright image.

Mirrors

  • Types: Planar (flat), Spherical (concave, convex).

Flat Mirrors

  • Images are always virtual.

  • Image is as far behind the mirror as the object is in front.

Spherical Mirrors

  • Concave: Positive focal length.

  • Convex: Negative focal length.

  • Radius of curvature (R), focal length f = \frac{R}{2}

Sign Convention for Mirrors

  1. Light travels from left to right.

  2. Object distance is positive.

  3. Real image distance is positive.

  4. Virtual image distance is negative.

  5. Concave mirror: f and R are positive.

  6. Convex mirror: f and R are negative.

  7. Heights are measured from head to tail.

  • Real/virtual image definitions and the magnification equation apply to mirrors.

Mirror Equation

  • \frac{1}{do} + \frac{1}{di} = \frac{1}{f}

Rays for Mirrors (Concave, do > f):

  • Ray parallel to optical axis reflects through the focus.

  • Ray through focus reflects parallel to the optical axis.

  • Ray to the center of the mirror reflects at an equal angle.