Ray diagrams for convex and concave lenses — all cases with characteristics

Question

What image is formed for different object positions in convex and concave lenses? Summarise all cases with image characteristics.

Solution — Step by Step

Three standard rays for lenses

Parallel ray: Passes through (or appears to come from) the focus after refraction
Central ray: Passes through the optical centre undeviated
Focal ray: Ray through F emerges parallel to the principal axis

For a convex lens, parallel rays converge to the focus on the other side. For a concave lens, parallel rays diverge as if from the focus on the same side.

Convex lens — 5 object positions

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

A convex lens behaves exactly like a concave mirror in terms of image characteristics. When the object is between F and the lens, it acts as a magnifying glass — the image is virtual, erect, and magnified.

Concave lens — always one case

Like a convex mirror, a concave lens always produces:

Image on the same side as the object (between O and F)
Virtual and erect
Diminished

This is true for all object positions. The image is always closer to the lens than the object and smaller.

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Why This Works

The thin lens formula:

$\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$

Sign convention: For a convex lens, $f > 0$ . For a concave lens, $f < 0$ . Object distance $u$ is always negative (object on the left).

Magnification: $m = \frac{v}{u}$

Note: the lens formula has a minus sign ( $1/v - 1/u$ ), unlike the mirror formula ( $1/v + 1/u$ ). Students who mix these up will get every answer wrong.

Alternative Method

A parallel between mirrors and lenses helps with memorisation:

Concave mirror	Convex lens	Both produce
Converging	Converging	Real images (mostly), virtual only when object is between F and surface

Convex mirror	Concave lens	Both produce
Diverging	Diverging	Always virtual, erect, diminished

Once you master one from each pair, you automatically know the other.

💡 Expert Tip

For Class 10 CBSE boards, lens ray diagrams carry 3-5 marks. Practice drawing at least the convex lens cases for object at 2F, between F and 2F, and between F and O. These three cover the most common exam questions.

Common Mistake

⚠️ Common Mistake

The formula difference between mirrors and lenses trips up many students. Mirror formula: $\frac{1}{v} + \frac{1}{u} = \frac{1}{f}$ . Lens formula: $\frac{1}{v} - \frac{1}{u} = \frac{1}{f}$ . Using the wrong formula is one of the most common errors in optics. Also, magnification for mirrors is $m = -v/u$ but for lenses it is $m = v/u$ (no negative sign). Double-check which formula you are using before substituting values.

Question

Solution — Step by Step

Why This Works

Alternative Method

Common Mistake

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