Ray diagram practice for lenses and mirrors

New lens and mirror problems on a grid that prints to scale. Draw the rays, type what you measure, see the drawn key.

Sign convention
How the rays are drawn and marked

Set

    Your answers save on this device as you type.

    How it works

    Each problem puts a lens or mirror on a squared grid, marks F and 2F (or F and C), and stands an object arrow on the axis. You draw the principal rays with a ruler, find where they meet, and measure the image. Type what you measured: it is marked against the exact answer from the lens or mirror formula, with a tolerance for drawing. The key draws all the rays to scale, so you can lay it over your own.

    Six levels

    1. Convex lens, object beyond 2F, at 2F, or between F and 2F.
    2. Convex lens as a magnifying glass (object inside F), and the concave lens.
    3. Concave mirror, every object position, including at F.
    4. Convex mirror.
    5. Lens and mirror formula numericals in your sign convention: find the image, find the object, work back from the magnification, and the power of a lens.
    6. A mix, with “where must the object be?” questions like the NCERT image tables, including an object at infinity.

    Curved mirrors and the lens formula are not on the AQA GCSE or Cambridge IGCSE syllabus; levels 1 and 2 cover their lens ray diagrams (IGCSE draws the convex lens only).

    An example from set RAYS26

    A convex lens of focal length 6 cm, an object 6 cm tall, 9 cm from the lens, at 1 square = 2 cm. On the grid that is f = 3 squares and the object 4.5 squares away, between F and 2F. The ray parallel to the axis and the ray through the centre cross 9 squares beyond the lens, 6 squares below the axis: the image is 18 cm away and 12 cm tall, real, inverted and enlarged. By the formula (New Cartesian), 1/v = 1/6 + 1/(−9) = 1/18, so v = +18 cm and m = v/u = −2. Open set RAYS26

    Questions

    How do you draw a ray diagram for a convex lens?

    Draw two rays from the top of the object. One goes parallel to the axis, then bends through the focus on the far side. One goes straight through the centre of the lens. Where they cross is the top of the image. A third ray, through the near focus and out parallel, checks your drawing.

    Which sign convention should I use?

    The one your course uses. CBSE and NCERT use the New Cartesian convention: distances to the left of the lens or mirror are negative, so u is negative. Edexcel A level uses real is positive, which also suits GCSE and IGCSE: there a virtual image distance typed without its minus sign still counts, with a note. AP Physics 2 uses so and si with real images positive. Each sheet prints its convention, and a sheet never mixes them.

    How accurate does my drawing need to be?

    A measured distance or height counts if it is within 3 mm on the paper (0.3 of a square, at the scale given) or within 5%, whichever is more. Magnification counts within 0.15 or 5% (0.2 for an object 1.5 squares tall). The key gives the exact value from the formula, so you can see how close your drawing came.

    Why is the image virtual when the object is inside F?

    Inside the focus, the rays leaving a convex lens or a concave mirror spread out and never meet. Extended backwards as dashed lines, they meet behind the object or behind the mirror. That point is a virtual image: upright, enlarged, and impossible to catch on a screen.

    What happens when the object is at F?

    The rays leave parallel to each other, so they never meet and no image is formed. Textbooks say the image is at infinity. Level 3 sometimes puts the object at F of a concave mirror.

    Why does a convex mirror always give a small upright image?

    A convex mirror spreads light out, so the reflected rays only seem to come from points behind it, between the pole and F. For any real object the image is virtual, upright and smaller than the object. That is why it is used as a rear-view mirror.

    How do I print the grids to scale?

    Print at 100% or Actual size, not Fit to page. Every grid square is then 1 cm, and the problem says what one square stands for. Check one square with a ruler before you start. Letter and A4 both work, and no problem is split across pages.

    How do I use this with a class?

    Share with class sends a link to the same problems. To stop copying, print a class set: each student gets a different set, and the keys follow, labelled by copy number.

    Checked 26 October 2026: NCERT Science class 10, chapter 9 Light: Reflection and Refraction (PDF), Tables 9.1, 9.2, 9.4 and 9.5 and sections 9.2.3, 9.2.4, 9.3.6 and 9.3.7; AQA GCSE Physics 8463 specification (PDF), 4.6.2.5 Lenses; Cambridge IGCSE Physics 0625 syllabus 2026 to 2028 (PDF), 3.2.3 Thin lenses; Pearson Edexcel A level Physics specification (PDF), items 80 and 81; AP Physics 2 Course and Exam Description (PDF), topics 13.2 and 13.4; OpenStax College Physics 2e, 25.6 and 25.7.