Light: Reflection & Refraction Essentials

This cheat sheet distills the fundamental principles governing how light interacts with mirrors and lenses, covering reflection, refraction, image formation, and key formulas.

Core Principles

Laws of Reflection: Angle of incidence equals angle of reflection (∠i = ∠r).
Laws of Reflection: Incident ray, reflected ray, and normal lie in the same plane.
Spherical Mirrors: Concave mirrors converge light; convex mirrors diverge light.
Concave Mirror Image (Object at infinity): At F, Real, Inverted, Highly diminished.
Concave Mirror Image (Object beyond C): Between C & F, Real, Inverted, Diminished.
Concave Mirror Image (Object at C): At C, Real, Inverted, Same size.
Concave Mirror Image (Object between C & F): Beyond C, Real, Inverted, Enlarged.
Concave Mirror Image (Object between F & P): Behind mirror, Virtual, Erect, Enlarged.
Convex Mirror Image: Always behind mirror, virtual, erect, and diminished.
Laws of Refraction: Incident ray, refracted ray, and normal lie in the same plane.
Snell's Law: Relates refractive index to angles of incidence and refraction.
Refractive Index: Denser medium bends light towards normal; rarer medium bends away.
Refraction through Glass Slab: Emergent ray parallel to incident ray, with lateral displacement.
Spherical Lenses: Convex lenses converge light; concave lenses diverge light.
Convex Lens Image (Object at infinity): At F, Real, Inverted, Highly diminished.
Convex Lens Image (Object beyond 2F): Between F & 2F, Real, Inverted, Diminished.
Convex Lens Image (Object at 2F): At 2F, Real, Inverted, Same size.
Convex Lens Image (Object between F & 2F): Beyond 2F, Real, Inverted, Enlarged.
Convex Lens Image (Object between F & O): Same side of lens, Virtual, Erect, Enlarged.
Concave Lens Image: Always virtual, erect, diminished, and formed on the same side as the object.
Sign Convention: Distances left of pole/optical center are negative; right are positive.
Sign Convention: Heights above principal axis are positive; below are negative.

Action Steps

1. Identify the optical component: mirror or lens.
2. Determine the type: concave/convex mirror or lens.
3. Apply the New Cartesian Sign Convention for all distances and heights.
4. Use the appropriate formula (mirror or lens) to calculate unknowns.
5. Calculate magnification to determine image size and nature (real/virtual, erect/inverted).
6. Interpret results based on sign conventions and image formation rules.

Formulas

$R = 2f$
$\frac{1}{f} = \frac{1}{v} + \frac{1}{u}$ (Mirror Formula)
$m = \frac{h_i}{h_o} = -\frac{v}{u}$ (Magnification - Mirror)
$n = \frac{\sin i}{\sin r}$ (Snell’s Law)
$n = \frac{\text{Speed of light in vacuum}}{\text{Speed of light in medium}}$ (Refractive Index)
$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$ (Lens Formula)
$m = \frac{h_i}{h_o} = \frac{v}{u}$ (Magnification - Lens)
$P = \frac{1}{f}$ (Power of a Lens)

Key Terms

Pole (P): Geometric center of a spherical mirror.
Centre of curvature (C): Center of the sphere from which the mirror or lens is a part.
Radius of curvature (R): Distance from the pole to the center of curvature (R = 2f).
Principal axis: Line passing through the pole/optical center and center of curvature.
Principal focus (F): Point where parallel rays converge or appear to diverge after reflection/refraction.
Focal length (f): Distance from the pole/optical center to the principal focus.
Refractive index (n): Ratio of the speed of light in vacuum to its speed in a specific medium.
Magnification (m): Ratio of image height to object height, indicating image size and orientation.
Dioptre (D): Unit of power of a lens, equal to the reciprocal of the focal length in meters.

Pro Tips

Always draw a simple ray diagram to visualize the image formation before calculations.
Remember: Real images are always inverted; virtual images are always erect.
Focal length (f) is positive for concave mirrors and convex lenses (converging).
Focal length (f) is negative for convex mirrors and concave lenses (diverging).
Magnification (m) > 0 indicates a virtual, erect image; m < 0 indicates a real, inverted image.

Pitfalls to Avoid

Confusing the mirror formula with the lens formula.
Incorrectly applying the New Cartesian Sign Convention.
Mixing up magnification formulas for mirrors versus lenses.
Forgetting that focal length is negative for diverging optical components (convex mirror, concave lens).
Misinterpreting the nature of the image (real/virtual, erect/inverted) from magnification sign.

Real World Examples

Convex mirrors provide a wider field of view, always forming a diminished, erect, virtual image.: Rear-view mirrors in vehicles
Concave mirrors produce an enlarged, erect, virtual image when the object is placed between F and P.: Shaving mirrors or dentist mirrors
Convex lenses are used to converge light rays before they reach the eye's natural lens.: Eyeglasses for farsightedness (hyperopia)
Concave lenses are used to diverge light rays before they reach the eye's natural lens.: Eyeglasses for nearsightedness (myopia)
Utilize total internal reflection, a phenomenon based on the laws of refraction and refractive index differences.: Optical fibers