Section 6.3: Lenses
Lenses are optical devices that converge or diverge light rays to form images. There are two main types:
- Convex Lens: Converging lens; forms real or virtual images depending on object position.
- Concave Lens: Diverging lens; forms virtual, upright, and reduced images.
The lens formula relates object distance (\(u\)), image distance (\(v\)), and focal length (\(f\)): \[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \] Magnification: \( m = \frac{v}{u} \)
Example: Image Formation by a Convex Lens
An object is placed 30 cm from a convex lens of focal length 10 cm. Find the image distance and magnification.
Using the lens formula: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) \( \frac{1}{10} = \frac{1}{v} - \frac{1}{30} \) → \( \frac{1}{v} = \frac{1}{10} + \frac{1}{30} = \frac{4}{30} \) → \( v = 7.5\,\text{cm} \) Magnification: \( m = \frac{v}{u} = \frac{7.5}{30} = 0.25 \) (image is real, inverted, and reduced)
Practice Problems
- A concave lens has a focal length of 15 cm. An object is placed 20 cm from it. Find the image distance and magnification.
- An object is at 25 cm from a convex lens of focal length 10 cm. Determine the nature and position of the image.
- Draw ray diagrams for a convex lens when the object is beyond 2f, at 2f, and between f and 2f.
- Explain why concave lenses always produce virtual images.
- A convex lens forms an image 30 cm from the lens. The object is 20 cm away. Find the focal length.