1️⃣ Sign Convention for Spherical Lenses
When working with spherical lenses, we use a standard sign convention where:
- All distances are measured from the optical center of the lens.
- Distances measured towards the right (along the incident light’s direction) are positive (+).
- Distances measured towards the left (against the incident light’s direction) are negative (-).
- The focal length (f) is positive for convex lenses and negative for concave lenses.
- Object height (h) is always positive, while image height (h′) is positive for erect images and negative for inverted images.
2️⃣ Lens Formula
Lenses follow a mathematical relationship between the object distance (u), image distance (v), and focal length (f): 1/v−1/u=1/f
This equation applies to both convex and concave lenses. The correct sign must be used for each value to ensure accurate results.
3️⃣ Magnification of a Lens
Magnification (m) describes how much larger or smaller an image is compared to the object: m=h′/h
- If m is positive, the image is erect and virtual.
- If m is negative, the image is inverted and real.
- If |m| > 1, the image is enlarged; if |m| < 1, the image is diminished.
4️⃣ Example Problems
Example 1: Concave Lens
A concave lens has a focal length of 15 cm. An object is placed such that its image forms 10 cm away from the lens. Find the object distance and magnification.
Example 2: Convex Lens
A convex lens with a focal length of 10 cm has a 2 cm tall object placed 15 cm from the lens. Find the position, nature, and size of the image.
5️⃣ Power of a Lens
The power (P) of a lens is a measure of how strongly it bends light. It is given by: P=1fP = \frac{1}{f}
where f is in meters (m), and P is measured in diopters (D).
- A convex (converging) lens has positive power.
- A concave (diverging) lens has negative power.
Example:
- A convex lens with f = 0.5 m → Power = +2 D
- A concave lens with f = -0.4 m → Power = -2.5 D
Key Points
✅ Use the correct sign convention for all distances.
✅ Convex lenses have positive focal lengths, while concave lenses have negative focal lengths.
✅ Magnification (m) determines whether the image is real/inverted or virtual/erect.
✅ The power of a lens helps determine its ability to converge or diverge light.
