Lens & Mirror Ray Diagram
Drag the object and watch the construction rays, the image and every number change live — for concave and convex mirrors and lenses, with full New Cartesian sign-convention working.
The mirror formula is 1/v + 1/u = 1/f and the lens formula is 1/v − 1/u = 1/f, with magnification m = −v/u for a mirror and m = v/u for a lens. In the New Cartesian convention u is negative. An object 30 cm from a concave mirror of f = −15 cm gives v = −30 cm: real, inverted, same size.
Set up the experiment
Everything on the right updates as you type or drag.
The image
Step-by-step with signs
New Cartesian sign convention — exactly the way it is written in the exam.
All object positions Learn by heart
The row that matches your diagram is highlighted.
| Object position | Image position | Size | Nature |
|---|
Where this is used
How to read this diagram
1. The object is the upright blue arrow on the left. Light always travels from it towards the mirror or lens — left to right.
2. Each coloured ray is one of the standard construction rays. Where two of them cross, the tip of the image sits.
3. Dashed lines are not real light. They are construction lines, or the backward extensions of the rays that your eye follows to a virtual image.
4. The red arrow is the image. Solid = real (can be caught on a screen). Dashed = virtual (only seen by looking into the mirror or lens).
Ray diagrams that are actually correct
Every ray here is constructed from the rules in your textbook, and every number comes from the mirror or lens formula with proper signs — so the picture and the calculation always agree.
Pick the device
Concave mirror, convex mirror, convex (converging) lens or concave (diverging) lens.
Set f, u and h
Slide the focal length, then drag the object or type the exact distance and height.
Follow the rays
Turn each construction ray on or off and see which pair of rays fixes the image.
Check the signs
Read the signed substitution, then compare your answer with the positions table.
New Cartesian sign convention
- The pole (P) of the mirror or the optical centre (O) of the lens is the origin.
- The object is always placed on the left, so incident light travels left → right.
- Distances measured in the direction of the incident light are +, against it are −. So u is always negative.
- Heights above the principal axis are +, below it are −.
- Concave mirror and convex lens: f is negative / positive respectively. Convex mirror and concave lens: the opposite.
The two formulas
Mirror: 1/v + 1/u = 1/f · m = −v/u
Lens: 1/v − 1/u = 1/f · m = v/u
In both, m = h′/h. A negative m means an inverted (and therefore real) image; a positive m means erect and virtual. For mirrors the radius of curvature R = 2f.
The construction rays
- A ray parallel to the principal axis passes through F after reflection/refraction (or appears to come from F).
- A ray through (or towards) F comes back parallel to the axis.
- For a mirror, a ray through C strikes along the normal and returns along the same path.
- For a lens, a ray through the optical centre goes straight on without bending.
Any two of these are enough to fix the image — the third is your check.
Power of a lens
P = 1 / f (in metres) dioptre (D)
A convex lens of focal length 25 cm has P = 1/0.25 = +4 D; a concave lens of 20 cm has P = −5 D. Converging lenses have positive power, diverging lenses negative. When thin lenses are placed in contact, P = P1 + P2.
Lens & Mirror Ray Diagram — your questions
What is the New Cartesian sign convention?
The pole of the mirror, or the optical centre of the lens, is the origin. The object is always placed on the left so light travels left to right. Distances measured along the incident light are positive and those against it negative, which makes u always negative. Heights above the principal axis are positive, below it negative. Concave mirrors and concave lenses have negative f; convex mirrors and convex lenses have positive f.
What is the mirror formula and how do I use it?
The mirror formula is 1/v + 1/u = 1/f. Write down the signs first, then substitute. An object 30 cm in front of a concave mirror of focal length 15 cm gives u = −30 and f = −15, so 1/v = 1/f − 1/u = −1/15 + 1/30 = −1/30, giving v = −30 cm. The image is 30 cm in front of the mirror, real and inverted, with m = −v/u = −1.
What is the lens formula and how is it different from the mirror formula?
The lens formula is 1/v − 1/u = 1/f, with a minus sign where the mirror formula has a plus, because light passes through a lens instead of coming back. Magnification is m = v/u for a lens but m = −v/u for a mirror. In both cases m = h′/h, a negative m means a real inverted image, and for mirrors R = 2f.
What are the image positions for a concave mirror?
Object at infinity: image at F, point-sized, real and inverted. Beyond C: between F and C, diminished, real, inverted. At C: at C, same size, real, inverted. Between C and F: beyond C, magnified, real, inverted. At F: at infinity, highly magnified, real, inverted. Between F and the pole: behind the mirror, magnified, virtual and erect.
How do you draw a ray diagram for a concave mirror?
Use any two of these rays. A ray parallel to the principal axis reflects through F. A ray passing through F reflects back parallel to the axis. A ray through the centre of curvature C strikes along the normal and returns along the same path. Where two reflected rays cross is the tip of the image; the third ray is your check.
What kind of image does a convex mirror always form?
A convex mirror always forms a virtual, erect and diminished image between its pole and focus, whatever the object distance. Because the image is always small and upright, the mirror shows a wide field of view, which is why convex mirrors are used as rear-view mirrors on vehicles and as security mirrors in shops.
What is the power of a lens and how is it calculated?
Power is the reciprocal of the focal length in metres, P = 1/f, measured in dioptres (D). A convex lens of focal length 25 cm has P = 1 ÷ 0.25 = +4 D, while a concave lens of 20 cm has P = −5 D. Converging lenses have positive power, diverging lenses negative, and thin lenses in contact add: P = P₁ + P₂.