Mirror Formula Table
Interactive calculator and formulas for Concave and Convex mirrors.
Equations
Mirror Equation
Relates focal length (f), image distance (v), and object distance (u). Valid for ALL spherical mirrors.
1/f = 1/v + 1/uMagnification
Ratio of image height to object height. Negative m means Inverted.
m = -v / u = h_i / h_oRadius of Curvature
The radius of the sphere the mirror was cut from.
R = 2fFocal Length (Concave)
Focus is in FRONT of the mirror.
f is Negative (-)Focal Length (Convex)
Focus is BEHIND the mirror.
f is Positive (+)Object Distance (u)
Object is always placed in front (Left) of the mirror.
u is Always Negative (-)Real Image (v)
Formed in front of the mirror (can be caught on screen).
v is Negative (-)Concave
• Used in Headlights, Shaving Mirrors.
• Can form Real OR Virtual images.
• f is Negative.
Convex
• Used in Rear-view mirrors (Wide View).
• ALWAYS Virtual & Diminished.
• f is Positive.
Mirror Solver
The Magic of Reflection
Mirrors don't just show your face; they can magnify, shrink, and flip reality. It all depends on the curve. Let's master the math behind the magic.
The "Spoon" Analogy
Concave (Eating Side)
The "Cave" that holds the soup.
- If close: Face looks Big & Upright.
- If far: Face looks Small & Upside Down.
Convex (Back Side)
The "Bulge" that pushes out.
- Always makes you look Small & Funny.
- You can see the whole room behind you (Wide View).
Cheat Sheet: The Sign Convention
This is where 90% of students lose marks. Follow these rules strictly!
| Variable | Sign Rule | Meaning |
|---|---|---|
| u | ALWAYS (-) | Object is placed on the Left. |
| f | Concave: (-)Convex: (+) | Focus is Real (Front) vs Virtual (Behind). |
| v | Real: (-)Virtual: (+) | Front of mirror vs Behind mirror. |
| m | Inverted: (-)Upright: (+) | Upside down vs Right side up. |
The "Infinity" Rule
If you put an object exactly at the Focal Point ($u = f$), the reflected rays become parallel. They never meet. The image forms at **Infinity** (essentially, it disappears/blurs into nothingness).
Frequently Asked Questions
What is the Mirror Formula?
The Mirror Formula is $1/f = 1/v + 1/u$. It connects the Focal Length ($f$), Image Distance ($v$), and Object Distance ($u$). It works for both Concave and Convex mirrors.
How do I remember Concave vs Convex?
Concave has a "Cave". It goes IN. (Like the spoon side you eat with). Convex bulges OUT. (Like the back of the spoon).
Why is Object Distance ($u$) always negative?
By standard Cartesian sign convention, light travels Left → Right. We place the object on the Left. Measuring from the Pole (center) to the Left is moving AGAINST the light direction, so it is negative.
What does Negative Magnification ($m$) mean?
A negative $m$ means the image is Inverted (Upside down). And crucially, all Real images are inverted, so negative $m$ also means it's a Real Image.
Can a Convex mirror form a Real image?
For a real object? Never. A convex mirror always diverges light rays, so they only appear to meet behind the mirror. The image is always Virtual, Upright, and Diminished.
What is the Focal Length sign for Concave mirrors?
Negative (-). The focus point is in front of the mirror (the "Real" side).
Why do dentists use Concave mirrors?
When you place an object (like a tooth) very close to a concave mirror (inside the focal point, $u < f$), it creates a Magnified, Upright, Virtual image. This helps dentists see details clearly.
What are the main uses of Convex mirrors?
They are used as Rear-view mirrors in cars and security mirrors in shops. Why? Because they imply give a wide field of view and the image is always upright (though smaller).
How do I convert Radius (R) to Focal Length (f)?
Simple! $f = R / 2$. The focal point is exactly halfway between the Center of Curvature and the Pole.
What happens if the object is at the Center of Curvature ($C$)?
For a concave mirror, the image forms exactly at $C$ as well. It is Real, Inverted, and the Same Size as the object ($m = -1$).