Useful Formulas

A quick reference to the optical formulas behind microscopy and microspectroscopy — the relationships that govern resolution, magnification and the quantitative spectral measurements CRAIC instruments perform. For spectral unit conversions (nanometers, microns and wavenumbers), see Units for Microspectroscopy.

Resolution and numerical aperture

• Numerical aperture: NA = n · sin θ — n is the refractive index of the medium between objective and sample; θ is the half-angle of the light cone the objective accepts.
• Abbe diffraction limit (lateral resolution): d = λ / (2 · NA)
• Rayleigh criterion: d = 0.61 · λ / NA
• Depth of field (approx.): DOF ≈ λ · n / NA²

Magnification

• Total magnification: M_total = M_objective × M_eyepiece (or × the camera projection factor)

Spectroscopy

• Transmittance: T = I / I₀
• Absorbance (optical density): A = −log₁₀(T)
• Beer–Lambert law: A = ε · c · l — absorbance is proportional to molar absorptivity ε, concentration c and path length l.
• Reflectance: R = I_reflected / I_reference

Please send suggestions for additional formulas to webmaster@craictechnologies.com.