Rucete ✏ AP Physics 2 In a Nutshell
5. Geometrical Optics
This chapter explains image formation by plane mirrors, curved mirrors, and lenses. It covers how real and virtual images are created by reflection and refraction, and discusses practical problem-solving strategies for geometrical optics.
Image Formation in Plane Mirrors
• Plane mirrors produce virtual images that are upright and the same size as the object.
• Image appears behind the mirror due to the brain tracing diverging reflected rays backward.
• Law of reflection applies: angle of incidence equals angle of reflection.
Image Formation in Curved Mirrors
Concave Mirrors
• Parallel rays converge to a real focal point after reflection.
• Image characteristics depend on object location:
– Beyond center of curvature (C): real, inverted, smaller.
– At C: real, inverted, same size.
– Between C and Focal point (F): real, inverted, larger.
– At F: no image formed (rays parallel).
– Between F and mirror: virtual, upright, enlarged.
• Spherical aberration can occur if curvature is large.
Convex Mirrors
• Always produce virtual, upright, smaller images.
• Used for wide field-of-view applications (e.g., stores, vehicles).
Algebraic Considerations for Mirrors
• Mirror equation: 1/F = 1/S₀ + 1/Sᵢ
F = focal length, S₀ = object distance, Sᵢ = image distance.
• Positive F: concave mirror; Negative F: convex mirror.
• Magnification (m): m = –Sᵢ/S₀ = hᵢ/h₀
• Negative magnification: inverted image; Positive magnification: upright image.
Image Formation in Lenses
Converging Lenses (Convex)
• Parallel rays refract and converge at a real focal point.
• Image characteristics depend on object location:
– Beyond 2F: real, inverted, smaller.
– At 2F: real, inverted, same size.
– Between F and 2F: real, inverted, larger.
– At F: no image formed (rays parallel).
– Inside F: virtual, upright, enlarged (like a magnifying glass).
Diverging Lenses (Concave)
• Parallel rays refract as if diverging from a virtual focal point.
• Always produce virtual, upright, smaller images.
• Used in eyeglasses for nearsightedness correction.
Algebraic Considerations for Lenses
• Lens equation (same form as mirror equation): 1/F = 1/S₀ + 1/Sᵢ
• Positive F: converging lens; Negative F: diverging lens.
• Sign conventions:
– Positive Sᵢ: real image (opposite side from object).
– Negative Sᵢ: virtual image (same side as object).
• Magnification (m): m = –Sᵢ/S₀ = hᵢ/h₀
• Positive m: upright image; Negative m: inverted image.
In a Nutshell
Geometrical optics uses reflection and refraction to explain image formation by mirrors and lenses. Curved surfaces create real or virtual images depending on object placement. Mathematical relationships for focal length, object distance, and image distance allow precise prediction of image characteristics, essential for understanding optical devices from telescopes to corrective lenses.