Lens Formula Table
Interactive calculator for Thin Lenses (Convex & Concave).
Equations
Lens Equation
Relates focal length (f), image distance (v), and object distance (u). Note the MINUS sign.
1/f = 1/v - 1/uMagnification
Ratio of image size to object size. Note: NO minus sign (unlike mirrors).
m = v / u = h_i / h_oPower of Lens
Ability to bend light. Short focal length = High Power.
P = 1 / f (in meters)Focal Length (Convex)
Converging lens. Focus is Real.
f is Positive (+)Focal Length (Concave)
Diverging lens. Focus is Virtual.
f is Negative (-)Object Distance (u)
Object is distinctively placed on the Left.
u is Always Negative (-)Real Image (v)
Formed on the Right side (opposite to object).
v is Positive (+)Convex
• Corrects Long-sightedness.
• Can form Real OR Virtual images.
• f is Positive.
Concave
• Corrects Near-sightedness.
• ALWAYS Virtual & Diminished.
• f is Negative.
Lens Solver
Lenses: Shaping Vision
From the glasses we wear to the cameras in our phones, lenses control where light lands. Let's explore how curvature changes reality.
The "Doctor's Prescription"
Myopia (Near-Sighted)
You can see near, but far is blurry.
- Eye is "Too Strong" (Light focuses too early).
- Needs a Diverging lens to push focus back.
Long-Sightedness
You can see far, but reading is blurry.
- Eye is "Too Weak" (Light focuses too late).
- Needs a Converging lens to pull focus forward.
Cheat Sheet: The Lens Rules
| Concept | Convex Lens (+) | Concave Lens (-) |
|---|---|---|
| Action | Converges Light (Focuses) | Diverges Light (Spreads) |
| Focal Length | Positive (+) | Negative (-) |
| Image Type | Can be Real or Virtual | ALWAYS Virtual |
| Example | Magnifying Glass, Telescope | Peephole, Flashlight Beam |
Power Up!
To find Power, you MUST divide 100 by the focal length in CENTIMETERS.
Frequently Asked Questions
What is the Lens Formula?
The Lens Formula is $1/f = 1/v - 1/u$. Note the Minus sign between $v$ and $u$. This is the key difference from the Mirror Formula.
How do I calculate Lens Power?
Power ($P$) is the reciprocal of Focal Length ($f$). Formula: $P = 1/f$. Crucial: $f$ MUST be in Meters. The unit of Power is Diopters ($D$).
My glasses prescription is -2.0D. What does it mean?
A negative power means you have a Concave Lens. This corrects Myopia (Near-sightedness). Your focal length is $f = 1/-2 = -0.5$ meters (-50cm).
What lens corrects Long-sightedness?
Long-sightedness (Hypermetropia) means your eye focuses light behind the retina. You need a Convex Lens (Converging) to bring the focus forward onto the retina. The power will be Positive (+).
Why does a Convex lens magnify things?
When you place an object inside the focal length ($u < f$) of a convex lens, it creates a Virtual, Erect, and Magnified image. This is how a simple magnifying glass works.
Can a Concave lens form a Real image?
No. For a real object, a concave lens always diverges light rays. They appear to come from a virtual point. The image is always Virtual, Upright, and Diminished.
What is the difference between Real and Virtual images in lenses?
Real Image: Formed on the opposite side of the lens (where light goes). Can be screen-projected. Virtual Image: Formed on the SAME side as the object. Cannot be screen-projected.
Why is underwater vision blurry?
Your eye's cornea is a lens that bends light because air ($n=1$) and cornea ($n=1.37$) have different indices. Water ($n=1.33$) is too similar to the cornea, so light hardly bends at all, and your eye cannot focus. Goggles restore the air-cornea interface.
How do cameras focus?
Cameras move the lens back and forth (changing $v$) to ensure the image forms exactly on the sensor film. In contrast, your eye changes the shape of the lens (changing $f$) to focus.
What is "Diopter"?
A Diopter ($D$) is the unit of optical power. $1 D = 1 m^{-1}$. A lens of 1 Diopter has a focal length of 1 Meter. A lens of 10 Diopters has a focal length of 0.1 Meters (10cm).