Optics Cheatsheet

Cheat Codes & Shortcuts

• Reflection: Angle of incidence = Angle of reflection (\( \theta_i = \theta_r \)).
• Snell’s Law: \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \).
• Refractive Index: \( n = \frac{c}{v} \), where \( c \) is speed of light in vacuum, \( v \) in medium.
• Lens Formula: \( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \), where \( f \) is focal length, \( u \) object distance, \( v \) image distance.
• Magnification: \( m = \frac{h_i}{h_o} = -\frac{v}{u} \).
• Critical Angle: \( \theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right) \), for \( n_1 > n_2 \).
• Power of a Lens: \( P = \frac{1}{f} \) (in meters, \( P \) in diopters).
• Thin Lens Maker’s Formula: \( \frac{1}{f} = (n - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \).
• Wave Equation: \( v = f \lambda \), where \( v \) is wave speed, \( f \) frequency, \( \lambda \) wavelength.
• Interference: Constructive if path difference = \( m \lambda \); Destructive if \( m + \frac{1}{2} \lambda \).

Quick Reference Table

Type	Concept	Formula/Description
Reflection	Law of Reflection	\( \theta_i = \theta_r \)
Refraction	Snell’s Law	\( n_1 \sin \theta_1 = n_2 \sin \theta_2 \)
Lens	Lens Formula	\( \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \)
Magnification	Magnification Formula	\( m = -\frac{v}{u} \)
Critical Angle	Total Internal Reflection	\( \theta_c = \sin^{-1} \left( \frac{n_2}{n_1} \right) \)
Interference	Path Difference	Constructive: \( m \lambda \), Destructive: \( (m + \frac{1}{2}) \lambda \)

Advice

Optics Quick Tips

• Reflection: Use \( \theta_i = \theta_r \) for plane mirrors; image is virtual, same size.
• Refraction: Apply Snell’s Law \( n_1 \sin \theta_1 = n_2 \sin \theta_2 \) for bending of light.
• Lenses: Converging lenses have positive focal length; diverging lenses have negative.
• Interference: Check path difference for constructive or destructive interference.
• Sign Convention: For lenses, object distance \( u \) is positive if on the incident side.

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