Ray Optics — Complete Formula

Reflection of Light

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Laws of Reflection	[i = r]	[i] = angle of incidence, [r] = angle of reflection	—	Basic law ⭐
Plane Mirror	[d_i = -d_o]	[d_i] = image distance, [d_o] = object distance	m	Image formed behind mirror

💡 Memory Hint:
Angle in = Angle out

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Mirror Formula	[\dfrac{1}{f} = \dfrac{1}{v} + \dfrac{1}{u}]	[f] = focal length, [v] = image distance, [u] = object distance	m	Most important ⭐
Magnification	[m = \dfrac{h_i}{h_o} = -\dfrac{v}{u}]	[h_i] = image height, [h_o] = object height	—	Sign matters ⚠️
Focal Length	[f = \dfrac{R}{2}]	[R] = radius of curvature	m	Standard relation ⭐

💡 Memory Hint:
Use sign convention carefully ⚠️

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Snell’s Law	[n_1 \sin i = n_2 \sin r]	[n_1, n_2] = refractive indices	—	Basic law ⭐
Refractive Index	[n = \dfrac{c}{v}]	[c] = speed of light, [v] = speed in medium	—	Optical density ⭐

💡 Memory Hint:
Denser medium → slower light

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Critical Angle	[\sin C = \dfrac{1}{n}]	[C] = critical angle	—	For denser → rarer ⭐
Condition	[i > C]	—	—	TIR occurs ⚠️

💡 Memory Hint:
Only from denser to rarer medium

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Formula	[\dfrac{n_2}{v} – \dfrac{n_1}{u} = \dfrac{n_2 – n_1}{R}]	[n_1, n_2] = refractive indices, [R] = radius	m	Important ⭐

💡 Memory Hint:
Extension of mirror formula

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Lens Formula	[\dfrac{1}{f} = \dfrac{1}{v} – \dfrac{1}{u}]	[f] = focal length, [v] = image distance, [u] = object distance	m	Very important ⭐
Magnification	[m = \dfrac{h_i}{h_o} = \dfrac{v}{u}]	[h_i] = image height, [h_o] = object height	—	No negative sign ⚠️
Power of Lens	[P = \dfrac{1}{f}]	[P] = power (in diopters), [f] in meters	D	Used in optics ⭐

💡 Memory Hint:
Convex → positive [f], Concave → negative [f]

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Equivalent Focal Length	[\dfrac{1}{f} = \dfrac{1}{f_1} + \dfrac{1}{f_2}]	[f_1, f_2] = focal lengths	m	In contact ⭐
Power Addition	[P = P_1 + P_2]	—	D	Simple addition ⭐

💡 Memory Hint:
Lenses in contact → powers add

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Lens Maker	[\dfrac{1}{f} = (n – 1)\left(\dfrac{1}{R_1} – \dfrac{1}{R_2}\right)]	[n] = refractive index, [R_1, R_2] = radii	m	For thin lens ⭐

💡 Memory Hint:
Shape + material → focal length

Concept	Formula	Symbols Meaning	SI Units	Key Notes / Tricks
Angle Relation	[A = r_1 + r_2]	[A] = prism angle	rad	Geometry relation
Deviation	[\delta = i + e – A]	[\delta] = deviation	rad	Path bending ⭐
Minimum Deviation	[n = \dfrac{\sin\left(\dfrac{A + \delta_m}{2}\right)}{\sin\left(\dfrac{A}{2}\right)}]	[\delta_m] = min deviation	—	Important ⭐

💡 Memory Hint:
Minimum deviation → symmetrical path

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Magnification	[m = 1 + \dfrac{D}{f}]	[D] = least distance of distinct vision (~25 cm), [f] = focal length	—	Magnifies small objects ⭐

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Magnification	[m = \dfrac{L}{f_o} \cdot \dfrac{D}{f_e}]	[L] = tube length, [f_o, f_e] = focal lengths	—	Very high magnification ⭐

Concept	Formula	Symbols Meaning	SI Units	Key Notes
Magnification	[m = \dfrac{f_o}{f_e}]	[f_o] = objective focal length, [f_e] = eyepiece focal length	—	For distant objects ⭐

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