Fundamental Optics Formulas to Know for AP Physics 2 (2025)

Understanding fundamental optics formulas is key in AP Physics 2. These formulas explain how light interacts with different media, lenses, and mirrors, helping us predict image formation, magnification, and wave behavior. Mastering these concepts is essential for grasping advanced optics.

1. Snell's Law: n₁ sin θ₁ = n₂ sin θ₂

   • Describes the relationship between the angles of incidence and refraction when light passes between two media.
   • n₁ and n₂ are the indices of refraction for the two media.
   • θ₁ is the angle of incidence, and θ₂ is the angle of refraction.

2. Index of Refraction: n = c / v

   • Defines how much light slows down in a medium compared to its speed in a vacuum (c).
   • v is the speed of light in the medium.
   • Higher index values indicate greater light bending.

3. Thin Lens Equation: 1/f = 1/do + 1/di

   • Relates the focal length (f) of a lens to the object distance (do) and the image distance (di).
   • Useful for determining where an image will form based on the position of the object.
   • Applies to both converging and diverging lenses.

4. Lens Magnification: M = -di/do = hi/ho

   • Describes the ratio of the height of the image (hi) to the height of the object (ho).
   • Negative sign indicates image orientation (inverted or upright).
   • Magnification greater than 1 indicates an enlarged image.

5. Mirror Equation: 1/f = 1/do + 1/di

   • Similar to the thin lens equation, but specifically for spherical mirrors.
   • Helps determine the location and size of the image formed by a mirror.
   • Applies to both concave and convex mirrors.

6. Mirror Magnification: M = -di/do = hi/ho

   • Indicates how much larger or smaller the image is compared to the object.
   • The sign of M indicates whether the image is real (inverted) or virtual (upright).
   • Useful for understanding image characteristics in mirrors.

7. Critical Angle: sin θc = n₂/n₁ (where n₂ < n₁)

   • Defines the angle of incidence above which total internal reflection occurs.
   • Only applicable when light travels from a denser medium to a less dense medium.
   • Important for understanding fiber optics and optical devices.

8. Brewster's Angle: tan θB = n₂/n₁

   • The angle at which light with a particular polarization is perfectly transmitted through a transparent dielectric surface.
   • Useful in applications involving polarized light, such as photography and optics.
   • Helps minimize glare and reflections.

9. Wave Equation: v = fλ

   • Relates the speed of a wave (v) to its frequency (f) and wavelength (λ).
   • Fundamental for understanding wave behavior in different media.
   • Applies to all types of waves, including light waves.

10. Diffraction Grating Equation: d sin θ = mλ

• Describes the condition for constructive interference in light passing through a grating.
• d is the distance between grating lines, m is the order of the maximum.
• Essential for analyzing spectra and understanding wave properties.