PhysicsRay opticsClass 10Class 12

Lens ray diagram: interactive simulation

Every ray that leaves the tip of the object and passes through a lens meets at one point — the image — or appears to come from it. Three rays are enough to find that point: one parallel to the axis, one through the optical centre and one through the focus.

Useful for: JEE Main, NEET, CBSE

Try this

Drag the object along the axis and see where the image moves, when it becomes virtual and when it disappears to infinity. All numbers use the Cartesian sign convention.

  1. 1

    Convex lens, f = 15 cm. Put the object at 30 cm (2F).

    What you should see

    The image forms at 30 cm on the other side: real, inverted, same size (m = −1).

  2. 2

    Move the object to 10 cm, inside the focal length.

    What you should see

    The image jumps to the same side as the object: virtual, erect, magnified 3 times — a magnifying glass.

  3. 3

    Place the object exactly at F (15 cm).

    What you should see

    The refracted rays come out parallel, so the image is at infinity.

  4. 4

    Switch to a concave lens and drag the object anywhere.

    What you should see

    The image is always virtual, erect and smaller, and stays between the lens and F.

Formulas behind it

Lens formula

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

Magnification

m=vu=hihom = \frac{v}{u} = \frac{h_i}{h_o}

Power

P=1f (m)=100f (cm) DP = \frac{1}{f\,(\text{m})} = \frac{100}{f\,(\text{cm})}\ \text{D}

Common mistakes

  • Using the mirror formula 1/v + 1/u = 1/f for a lens.
  • Putting u as positive. In the Cartesian convention the object distance on the left is negative.
  • Calculating power with f in centimetres without the factor of 100.
  • Drawing the parallel ray of a concave lens through the far focus instead of diverging from the near focus.
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FAQ

Why does a concave lens always form a virtual image?

It spreads every ray outwards, so the refracted rays never actually meet. Traced backwards, they appear to come from a point between the lens and its focus.

Where should the object be for a real, magnified image with a convex lens?

Between F and 2F. The image then forms beyond 2F, inverted and larger.

What does a negative magnification mean?

The image is inverted. Positive m means an erect image.

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