What is the lens formula and mirror formula?

The lens formula is 1/v − 1/u = 1/f and the mirror formula is 1/v + 1/u = 1/f, where u is object distance, v image distance and f focal length, all measured using the Cartesian sign convention.

What is the sign convention in ray optics?

Distances are measured from the pole/optical centre. Distances measured in the direction of incident light are positive; against it are negative. So a real object on the left has a negative object distance (u is negative). Heights above the axis are positive, below are negative.

When does a convex lens form a virtual image?

A convex lens forms a virtual, erect and magnified image only when the object is placed between the optical centre and the focus (object distance less than the focal length) — this is how a magnifying glass works.

What is magnification?

Magnification m = height of image ÷ height of object = v/u for lenses (and −v/u for mirrors). If |m| > 1 the image is enlarged, if |m| < 1 it is diminished; a negative m means the image is inverted.

Class 12 · CBSE / NCERT · Physics

Ray Optics — Class 12

Ray diagrams finally make sense when you can move the object yourself. Slide it past F and 2F and watch the image flip, grow and turn virtual — then solve any numerical with the lens & mirror solver.

Lens formula1/v − 1/u = 1/f. Power P = 1/f (in metres), unit dioptre (D).

Mirror formula1/v + 1/u = 1/f, with f = R/2 (R = radius of curvature).

MagnificationLens m = v/u; Mirror m = −v/u. Also m = h′/h.

Sign conventionMeasure from pole/centre. Along incident light = +, against = −. Real object on left ⇒ u is negative.

1. Convex Lens Ray Diagram Interactive

Move the object and change the focal length. Two rays are drawn for you — one parallel ray (bends through F) and one through the optical centre (straight). Where they meet is the image.

Object distance (u) 30 cm Focal length (f) 15 cm

Real, inverted image beyond 2F.

2. Lens & Mirror Solver Interactive

Pick a device, type the object distance and focal length, and get the image distance, magnification and nature — with the sign convention applied for you.

Device Object distance (cm, in front) Focal length magnitude (cm)

Image distance, v−60 cm

Magnification, m−2.0

3. Image formation by a convex lens (learn the 6 cases)

Object position	Image position	Nature	Size
At infinity	At F	Real, inverted	Point-sized
Beyond 2F	Between F and 2F	Real, inverted	Diminished
At 2F	At 2F	Real, inverted	Same size
Between F and 2F	Beyond 2F	Real, inverted	Magnified
At F	At infinity	Real, inverted	Highly magnified
Between F and lens	Same side as object	Virtual, erect	Magnified

Concave lens & convex mirror are the easy ones: they always give a virtual, erect, diminished image, wherever the object is.

4. Solved numericals

Q1. An object is placed 30 cm in front of a convex lens of focal length 20 cm. Find the image distance and magnification.

Given: u = −30 cm, f = +20 cm

1/v = 1/f + 1/u = 1/20 + 1/(−30) = 3/60 − 2/60 = 1/60

⇒ v = +60 cm (positive ⇒ real, on the other side)

m = v/u = 60/(−30) = −2 (inverted, 2× magnified)

Q2. A concave mirror of focal length 15 cm forms an image of an object placed 10 cm in front of it. Find the image position and nature.

Given: u = −10 cm, f = −15 cm

1/v = 1/f − 1/u = 1/(−15) − 1/(−10) = −2/30 + 3/30 = 1/30

⇒ v = +30 cm (positive ⇒ behind the mirror ⇒ virtual)

m = −v/u = −30/(−10) = +3 (erect, magnified) — this is the shaving/make-up mirror.

5. Sign-convention survival kit

Real object ⇒ u is always negative. Plug in u = −(object distance).
Convex lens & convex mirror: f positive. Concave lens & concave mirror: f negative.
Positive v: for a lens ⇒ real image (other side); for a mirror ⇒ virtual image (behind).
Negative m ⇒ inverted (and real). Positive m ⇒ erect (and virtual).
Power of a lens P = 1/f with f in metres; unit dioptre (D). Convex = +, concave = −.

Frequently asked questions

What is the lens maker's formula?

1/f = (n − 1)(1/R₁ − 1/R₂), where n is the refractive index of the lens material and R₁, R₂ are the radii of curvature of its two surfaces.

Why does a convex lens act as a magnifying glass?

When the object is closer than the focal length, the refracted rays diverge. Tracing them backward gives a virtual, erect and magnified image on the same side — which is exactly what a magnifying glass shows.

What is the difference between real and virtual images?

A real image is formed where light rays actually meet and can be caught on a screen (always inverted). A virtual image is where rays only appear to come from and cannot be caught on a screen (always erect).

What is the unit of power of a lens?

The dioptre (D). Power P = 1/f, where f is in metres. A lens of focal length 50 cm has a power of 1/0.5 = +2 D.