Optics - Formula Sheet

Essential Mathematical Formulas

This reference sheet contains the mathematical formulas required to analyze wave propagation, light refraction, spherical lens characteristics, and vision correction systems.

1. Light Wave Equation

c = \(\nu\) * \(\lambda\)

• c: Velocity of light in vacuum (approximately 3 x 10^8 ms^-1)
• \(\nu\): Frequency of the light wave (in Hertz, Hz)
• \(\lambda\): Wavelength of the light wave (in meters, m)

2. Refractive Index of a Medium

\(\mu\) = c / v

• \(\mu\): Absolute refractive index of the medium (dimensionless)
• c: Speed of light in vacuum
• v: Speed of light in the specific medium

3. Snell's Law of Refraction

sin i / sin r = \(\mu_2\) / \(\mu_1\)

• i: Angle of incidence
• r: Angle of refraction
• \(\mu_1\): Refractive index of the incident medium
• \(\mu_2\): Refractive index of the refracting medium

4. Rayleigh's Scattering Law

S is proportional to 1 / \(\lambda^4\)

• S: Amount or intensity of scattered light
• \(\lambda\): Wavelength of the incident light wave

5. Lens Formula

1 / f = 1 / v - 1 / u

• f: Focal length of the lens
• v: Distance of the image from the optical center
• u: Distance of the object from the optical center

6. Linear Magnification

m = h' / h = v / u

• m: Magnification of the lens
• h': Height of the formed image
• h: Height of the object
• v: Distance of the image
• u: Distance of the object

7. Lens Maker's Formula

1 / f = (\(\mu\) - 1) * (1 / R1 - 1 / R2)

• f: Focal length of the constructed lens
• \(\mu\): Refractive index of the lens material
• R1, R2: Radii of curvature of the first and second spherical refracting surfaces respectively

8. Power of a Lens

P = 1 / f

• P: Lens power measured in Diopters (D)
• f: Focal length of the lens, which must be expressed in meters (m)

9. Myopia Correction Focal Length

For correction to infinity: f = -x

For correction between finite distances: f = (x * y) / (x - y)

• f: Required focal length of the corrective concave lens
• x: Distance of the defective eye's far-point
• y: Distance of the desired far-point to be seen

10. Hypermetropia Correction Focal Length

f = (d * D) / (d - D)

• f: Required focal length of the corrective convex lens
• d: Distance of the defective eye's near-point
• D: Least distance of distinct vision for a normal eye (typically 25 cm or 0.25 m)