Solved Examples: Using the Thin Lens Equation to Find Focal Length

📚 Quick Study Guide

🔍 The thin lens equation relates the object distance ($d_o$), the image distance ($d_i$), and the focal length ($f$) of a lens.

💡 The formula is: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$.

📝 Focal length ($f$) is positive for converging lenses and negative for diverging lenses.

📏 Object distance ($d_o$) is always positive.

🖼️ Image distance ($d_i$) is positive for real images and negative for virtual images.

➕ Magnification ($M$) is given by $M = -\frac{d_i}{d_o}$.

👓 A positive magnification indicates an upright image, while a negative magnification indicates an inverted image.

🧪 Practice Quiz

1. A lens forms a real image 20 cm from the lens when the object is placed 40 cm away. What is the focal length of the lens?
   1. 10 cm
   2. 13.3 cm
   3. 20 cm
   4. 60 cm
2. An object is placed 15 cm from a converging lens with a focal length of 10 cm. What is the image distance?
   1. 30 cm
   2. -30 cm
   3. 6 cm
   4. -6 cm
3. A diverging lens has a focal length of -20 cm. An object is placed 30 cm from the lens. What is the image distance?
   1. -12 cm
   2. 12 cm
   3. 50 cm
   4. -50 cm
4. What type of image is formed if the image distance is negative?
   1. Real
   2. Inverted
   3. Virtual
   4. Enlarged
5. A lens has a focal length of 25 cm. An object is placed 50 cm away. What is the magnification?
   1. -1
   2. 1
   3. -0.5
   4. 0.5
6. If an object is placed at the focal point of a converging lens, where is the image formed?
   1. At the lens
   2. At twice the focal length
   3. At infinity
   4. Between the lens and the focal point
7. A lens creates an upright image. What is the sign of the magnification?
   1. Positive
   2. Negative
   3. Zero
   4. Undefined