Every diagram on this page was built the same way a real image forms — by actually solving the mirror or lens formula for a specific object position first, then drawing the rays to converge exactly where that calculation says they should. Not illustrative sketches redrawn from memory, but geometry that matches the numbers.
How to use this page: For the ray diagrams, try predicting the image type (real/virtual, magnified/diminished) before reading the caption. For the numericals, attempt each on paper before revealing the solution. Every calculation and every diagram's geometry was independently verified before publishing.
Quick formula reference used throughout:
| What it finds | Formula |
|---|---|
| Mirror formula | 1/v + 1/u = 1/f |
| Lens formula | 1/v − 1/u = 1/f |
| Magnification | m = −v/u (mirror) or m = v/u (lens) |
| Power of a lens | P = 1/f (f in metres, P in dioptres) |
| Refractive index | n = c/v = sin i / sin r |
Ray Diagrams · Concave Mirror
All four diagrams use the same concave mirror (F at 10 units, C at 20 units) — only the object's position changes.
Object Beyond C
Real · Inverted · Diminished
Object At C
Real · Inverted · Same Size
Object Between C and F
Real · Inverted · Magnified
Object Between F and Pole
Virtual · Erect · Magnified
Ray Diagrams · Convex Mirror & Convex Lens
Convex Mirror — Any Object Position
Virtual · Erect · Diminished
Convex Lens — Beyond 2F
Real · Diminished
Convex Lens — At 2F
Real · Same Size
Convex Lens — Between F and 2F
Real · Magnified
Convex Lens — Between O and F
Virtual · Erect · Magnified
Complete Reference — All Cases Including the "At F" Position
| Object Position | Concave Mirror Image | Convex Lens Image |
|---|---|---|
| Beyond C / 2F | Real, inverted, diminished (between F,C) | Real, inverted, diminished (between F,2F) |
| At C / 2F | Real, inverted, same size, at C | Real, inverted, same size, at 2F |
| Between C/2F and F | Real, inverted, magnified, beyond C | Real, inverted, magnified, beyond 2F |
| At F | Image at infinity, highly magnified | Image at infinity, highly magnified |
| Between F and pole/centre | Virtual, erect, magnified, behind mirror | Virtual, erect, magnified, same side as object |
| Convex mirror / Concave lens | Always virtual, erect, diminished — regardless of object position | |
Numericals
Mirror Formula
A concave mirror has a focal length of 15 cm. An object is placed 20 cm in front of it. Find the image distance.
Reveal Solution
Apply sign convention
f = −15 cm, u = −20 cm
Mirror Formula — Find f
An object placed 30 cm from a mirror forms a real image 10 cm from the mirror. Find the focal length.
Reveal Solution
Both real, so both negative
u = −30 cm, v = −10 cm
Magnification
An object at 20 cm from a mirror forms an image at 40 cm. Find the magnification and describe the image.
Reveal Solution
Lens Formula
A convex lens of focal length 20 cm forms an image of an object placed 30 cm from it. Find the image distance.
Reveal Solution
f = +20 cm, u = −30 cm
Power of a Lens
A convex lens has a focal length of 25 cm. Find its power.
Reveal Solution
Convert to metres: f = 0.25 m
Power of a Concave Lens
A concave lens has a focal length of −40 cm. Find its power.
Reveal Solution
Focal Length from Power
A lens has a power of +4 D. Find its focal length in cm.
Reveal Solution
Refractive Index
Light travels at 2×10⁸ m/s in a certain medium. Find its refractive index. (Speed of light in vacuum = 3×10⁸ m/s)
Reveal Solution
Snell's Law
Light travelling from air into glass (refractive index 1.5) has an angle of incidence of 30°. Find the angle of refraction.
Reveal Solution
Combination of Lenses
Two lenses of focal length +20 cm and −10 cm are placed in contact. Find the combined power.
Reveal Solution
Powers of lenses in contact simply add.
Important Conceptual Questions
Why does a convex mirror always form a virtual image, regardless of object distance?
A convex mirror curves away from the object, so reflected rays always diverge rather than converge — they never actually cross in front of the mirror. The image is formed only where these diverging rays appear to meet when extended backward behind the mirror, which is by definition a virtual image.
What is the difference between the focal length of a concave mirror and a convex mirror in terms of sign convention?
By the Cartesian sign convention, distances measured in the direction of incident light are positive, and against it are negative. A concave mirror's focus lies in front of it (same side as the object), so its focal length is taken as negative. A convex mirror's focus lies behind it, so its focal length is taken as positive.
Why does light bend when passing from one medium to another?
Light bends because its speed changes when it enters a medium of different optical density — this change in speed at the boundary between two media causes the direction of travel to change, provided the light isn't hitting the boundary exactly perpendicular. This bending is what we call refraction.
What is the power of a lens, and why is it measured in dioptres?
Power measures how strongly a lens converges or diverges light, and is defined as the reciprocal of the focal length in metres. It's measured in dioptres (D) specifically because using metres for focal length gives power values that are convenient, practical numbers for real lenses — such as those used in spectacles — rather than the very large or small numbers that would result from other length units.
Why is the image formed by a plane mirror always virtual, erect, and the same size as the object?
A plane mirror has zero curvature, meaning it doesn't converge or diverge reflected rays at all — every ray simply reflects at an equal angle without bending toward or away from any focus. This means the image always forms exactly as far behind the mirror as the object is in front, at the same size and orientation, and can only be located by extending the reflected rays backward — making it inherently virtual.
A student wants to obtain a real, magnified image using a concave mirror. Where should the object be placed?
The object should be placed between the centre of curvature (C) and the focus (F). In this range, the image forms beyond C, is real, inverted, and larger than the object. Placing it exactly at F would send the image to infinity, and placing it closer than F would switch to a virtual, erect image instead.
Ray Diagrams and Numericals Test Different Skills — Track Them Separately
A student who can solve the mirror formula correctly might still struggle to sketch the right ray diagram for the same scenario, or vice versa. These are genuinely separate skills, and a single chapter score won't tell you which one needs more work.
What a Genelis weak area map looks like after working through Light practice
Next session: identifying image type from object position (30%) — not more formula drilling. Genelis tracks diagram and numerical skills separately, since strength in one doesn't guarantee strength in the other.
Genelis is an AI-powered personalized learning platform built on Adaptive Personalized Intelligence. The Genelis learning system tracks your accuracy across numericals, conceptual questions, and diagram-based reasoning separately for Light, so gaps in visual understanding don't hide behind a strong numerical score. Every wrong answer is logged to your wrong-question notebook for reattempt.
Learn smarter. Practice deeper. Improve continuously.
Genelis combines Adaptive Personalized Intelligence, AI-generated notes, targeted practice, mock tests, analytics, and personalised revision to help students improve every study session.
Questions Students Commonly Ask
Quick answers to the most common questions related to this guide.
What are the different image cases for a concave mirror?
A concave mirror produces five distinct cases depending on object position: beyond the centre of curvature C (real, inverted, diminished image between C and F), at C (real, inverted, same size, at C), between C and F (real, inverted, magnified, beyond C), at F (image forms at infinity, highly magnified), and between F and the pole (virtual, erect, magnified image formed behind the mirror). A convex mirror, by contrast, always produces a virtual, erect, diminished image regardless of object position.
What are the different image cases for a convex lens?
A convex lens produces five cases depending on object position: beyond 2F (real, inverted, diminished image between F and 2F on the other side), at 2F (real, inverted, same size, at 2F on the other side), between F and 2F (real, inverted, magnified image beyond 2F), at F (image at infinity), and between the optical centre and F (virtual, erect, magnified image on the same side as the object). A concave lens always produces a virtual, erect, diminished image between the optical centre and F, regardless of object position.
Why do ray diagrams use two specific rays instead of just one?
A single ray only shows one path light could take — it doesn't pin down where the image actually forms. Using two rays with known, predictable behaviour (one parallel to the principal axis that passes through the focus after reflection or refraction, and one passing through the centre of curvature for a mirror or the optical centre for a lens that continues undeviated) means their intersection point uniquely determines the image location. A third ray through the focus, emerging parallel to the axis, is often added only to double-check the construction.
How can I tell from a ray diagram whether an image is real or virtual?
If the actual reflected or refracted rays physically converge and cross at a point, the image is real and can be captured on a screen at that location — this is drawn with solid lines all the way to the intersection. If the rays instead diverge after reflection or refraction, no real crossing point exists; the image is virtual, formed only where the rays appear to come from when extended backward, which is drawn using dashed lines behind the mirror or on the object's side of the lens.