Draw and use ray diagrams for the formation of a real image by a converging lens

3.2.3 Thin Lenses – Real Images with Converging Lenses 📚

What is a Converging Lens?

A converging (convex) lens is thicker in the middle than at the edges. It bends parallel rays of light toward a common point called the focal point (F). Think of it like a flashlight beam that comes together to illuminate a spot.

Ray Diagram Basics 🔍

To draw a ray diagram for a real image:

  1. Draw the lens and mark its centre (C) and focal points (F) on both sides.
  2. Place the object at a distance $u$ from the lens on the left side.
  3. Draw three rays from the top of the object:
    1. Parallel to the principal axis → refracts through the lens and passes through the far focal point.
    2. Through the centre of the lens → passes straight without bending.
    3. Through the near focal point → refracts parallel to the principal axis.
  4. Mark where the refracted rays intersect on the right side – that point is the top of the image.
  5. Extend the image downwards to complete the real inverted image.

Lens Formula & Sign Conventions 📐

The relationship between object distance ($u$), image distance ($v$), and focal length ($f$) is given by:

Formula Sign Convention
$$\frac{1}{f} = \frac{1}{v} - \frac{1}{u}$$
  • $u$ is negative if the object is on the left (incoming side).
  • $v$ is positive for real images on the right.
  • $f$ is positive for converging lenses.

Example Problem 🎯

Object distance: $u = -30\,\text{cm}$ (to the left of the lens). Focal length: $f = +10\,\text{cm}$ (converging lens).

Find the image distance $v$ and state whether the image is real or virtual.

  1. Insert values into the lens formula:
    $$\frac{1}{10} = \frac{1}{v} - \frac{1}{-30}$$
  2. Calculate:
    $$\frac{1}{10} = \frac{1}{v} + \frac{1}{30}$$
    $$\frac{1}{v} = \frac{1}{10} - \frac{1}{30} = \frac{3-1}{30} = \frac{2}{30} = \frac{1}{15}$$
    $$v = 15\,\text{cm}$$
  3. Since $v$ is positive, the image is on the right side of the lens and is a real inverted image.

Exam Tips & Quick Reference 📌

Remember the sign conventions:

  • Object distance $u$ is always negative.
  • Image distance $v$ is positive for real images.
  • Focal length $f$ is positive for converging lenses.

When drawing ray diagrams:

  1. Always start with the principal axis.
  2. Mark the focal points clearly.
  3. Use at least three rays for accuracy.
  4. Check that the image is inverted for real images.

📝 Practice: Try a problem where the object is beyond the focal point, then one inside the focal point, and note how the image changes.

Revision

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