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:
- Draw the lens and mark its centre (C) and focal points (F) on both sides.
- Place the object at a distance \$u\$ from the lens on the left side.
- Draw three rays from the top of the object:
- Parallel to the principal axis → refracts through the lens and passes through the far focal point.
- Through the centre of the lens → passes straight without bending.
- Through the near focal point → refracts parallel to the principal axis.
- Mark where the refracted rays intersect on the right side – that point is the top of the image.
- 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.
- Insert values into the lens formula:
\$\frac{1}{10} = \frac{1}{v} - \frac{1}{-30}\$
- 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}\$
- 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:
- Always start with the principal axis.
- Mark the focal points clearly.
- Use at least three rays for accuracy.
- 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.