Optics Formula Table
Interactive formulas for Light, Lenses, Mirrors, and Refraction.
Snell's Law
Relates refractive indices and angles at a boundary.
n₁sin(θ₁) = n₂sin(θ₂)Refractive Index
Ratio of light speed in vacuum (c) to medium (v).
n = c / vCritical Angle
Angle for Total Internal Reflection (n₁ > n₂).
sin(θc) = n₂ / n₁Apparent Depth
Objects underwater appear shallower than they are.
d' = d (n₂ / n₁)Mirror Equation
Relates object (u), image (v), and focal length (f).
1/f = 1/v + 1/uMagnification
Ratio of image height to object height.
m = -v / uFocal Length (Radius)
Focal length is half the radius of curvature.
f = R / 2Lens Formula
Thin lens equation (note the minus sign for lenses in some conventions, but standard Cartesian is 1/v - 1/u = 1/f).
1/f = 1/v - 1/uLens Maker's Formula
Design lenses by curvature and material.
1/f = (n-1)(1/R₁ - 1/R₂)Power of Lens
Reciprocal of focal length in METERS.
P = 1 / fSimple Microscope
Magnification with image at near point (D=25cm).
M = 1 + (D/f)Compound Microscope
Total mag is Objective × Eyepiece mag.
M ≈ -(L/f₀)(D/fₑ)Telescope
Ratio of focal lengths.
M = -f₀ / fₑSnell's Law Solver
Lens Solver
See the Light
Geometric optics isn't just formulas; it's geometry in action. Let's visualize how light bends, bounces, and tricks our eyes using simple analogies.
Analogy: The "Muddy" Refraction
Why does light bend when it enters glass/water? Imagine a **Car driving on Pavement**. It drives fast and straight. Now, imagine it hits a patch of **Mud** at an angle.
- 🚗The Right Wheel hits the mud first and slows down.
- 💨The Left Wheel is still on pavement, moving fast.
- ↩️The car Pivots (Bends) towards the mud!
Light acts the same. Glass is the "mud" → light slows down → light bends.
Visual Cheat Sheet: Mirrors & Lenses
Converging Systems
• Brings light rays Together to a point.
• Can start fires with sunlight.
• Creates Real (inverted) OR Virtual (magnified) images.
Diverging Systems
• Spreads light rays Apart.
• Makes things look smaller (wide view).
• ALWAYS creates Virtual, Upright, Diminished images.
Real World Magic
Rainbows
Raindrops act as tiny prisms. Sunlight enters → Refracts → Reflects off the back → Refracts out. Total internal reflection + Dispersion!
Mirages
Hot air near the ground ($\downarrow n$) bends light from the sky UP into your eyes. Your brain thinks the blue sky is on the ground (Water!).
Sparkle
Diamond has $n=2.4$. Light gets trapped inside by TIR, bouncing around before exiting the top facet with brilliance.
Exam Tip: Sign Convention
Use the **CARTESIAN** method (Like math graphs).
Frequently Asked Questions
Why does a pencil look bent in water?
This is Refraction. Light travels slower in water than in air. When light rays coming from the pencil leave the water, they speed up and bend. Your brain assumes light travels in a straight line, so it "sees" the pencil part in a higher position than it actually is.
How do I remember if a lens is Convex or Concave?
Convex bulges OUT (like a belly). It brings light together (Converges). Concave caves IN (like a cave). It spreads light out (Diverges).
What is the "Critical Angle"?
Imagine throwing a stone at a lake. If you throw it steeply, it goes in. If you throw it shallowly (glancing angle), it skips off the surface. Light acts the same! If light from underwater hits the surface at a shallow angle (the Critical Angle), it reflects back down instead of escaping. This is Total Internal Reflection.
Why is the sky blue but sunsets are red?
This is Rayleigh Scattering. Blue light waves are tiny and scatter easily off air molecules, filling the sky with blue. At sunset, sunlight travels through much thick,er atmosphere. The blue is scattered away completely, leaving only the longer Red/Orange waves to reach your eyes.
How do Fiber Optic cables keep light inside?
They use a core of glass with a high refractive index surrounded by a cladding with a lower index. The light hits the boundary at an angle shallower than the critical angle, so it reflects 100% perfectly (Total Internal Reflection) and zig-zags down the cable for miles.
What does "20/20 Vision" mean?
It means you can see clearly at 20 feet what a "normal" person sees at 20 feet. If you have 20/40 vision, you must be 20 feet away to see what a normal person sees from 40 feet away (you are nearsighted).
Why do diamonds sparkle?
Diamonds have a very high Refractive Index ($n=2.42$). This means light slows down massively and bends sharply. It also has a small Critical Angle ($24^\circ$), so light gets trapped inside, bouncing around many times before exiting, creating a glittering effect.
What is a Real vs. Virtual image?
Real Image: Light rays actually meet. Can be projected on a screen (Movie theater). Virtual Image: Light rays only appear to meet. Cannot be caught on a screen (Your face in a mirror).
Does light always travel in straight lines?
In a vacuum or uniform medium, yes. But gravity can bend light (General Relativity) and lenses/medium changes bend it (Refraction).
Why use a parabolic mirror instead of spherical?
Spherical mirrors suffer from "Spherical Aberration"—light hitting the edges doesn't focus at the exact same point as light hitting the center, causing blur. Parabolic mirrors focus ALL parallel rays to a single perfect point (used in telescopes and car headlights).