AP Physics 2 questions on Combinations of Lenses and Optical Instruments

📚 Quick Study Guide

• 🔍 Thin Lens Equation: $\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$, where $f$ is the focal length, $d_o$ is the object distance, and $d_i$ is the image distance.
• ✨ Magnification: $M = -\frac{d_i}{d_o} = \frac{h_i}{h_o}$, where $h_i$ is the image height and $h_o$ is the object height. A negative $M$ indicates an inverted image.
• 👓 Lensmaker's Equation: $\frac{1}{f} = (n-1)(\frac{1}{R_1} - \frac{1}{R_2})$, where $n$ is the refractive index of the lens material, $R_1$ is the radius of curvature of the first surface, and $R_2$ is the radius of curvature of the second surface.
• 💡 Combinations of Lenses: The total magnification is the product of the individual magnifications: $M_{total} = M_1 \cdot M_2 \cdot M_3 \dots$. The image formed by the first lens acts as the object for the second lens.
• 🔬 Optical Instruments: Understand the principles of microscopes and telescopes, including objective and eyepiece lenses, and how they work together to produce magnified images.
• 🌈 Sign Conventions: Focal length ($f$) is positive for converging lenses and negative for diverging lenses. Object distance ($d_o$) is always positive if the object is on the same side as the incoming light. Image distance ($d_i$) is positive for real images and negative for virtual images.

🧪 Practice Quiz

1. Question 1: A converging lens with a focal length of 10 cm is placed 30 cm from an object. What is the image distance?
   1. A) 5 cm
   2. B) 15 cm
   3. C) 20 cm
   4. D) 30 cm
2. Question 2: An object is placed 5 cm in front of a diverging lens with a focal length of -10 cm. What is the magnification?
   1. A) -2
   2. B) 2
   3. C) 1/3
   4. D) -1/3
3. Question 3: Two converging lenses, each with a focal length of 20 cm, are placed 60 cm apart. An object is placed 30 cm in front of the first lens. Where is the final image formed relative to the second lens?
   1. A) 15 cm
   2. B) 20 cm
   3. C) 30 cm
   4. D) 60 cm
4. Question 4: A microscope has an objective lens with a magnification of 50x and an eyepiece with a magnification of 10x. What is the total magnification of the microscope?
   1. A) 5x
   2. B) 40x
   3. C) 60x
   4. D) 500x
5. Question 5: What type of image is formed by a single diverging lens when the object is real?
   1. A) Real and inverted
   2. B) Real and upright
   3. C) Virtual and inverted
   4. D) Virtual and upright
6. Question 6: A telescope has an objective lens with a long focal length and an eyepiece with a short focal length. What is the purpose of this arrangement?
   1. A) To decrease magnification
   2. B) To increase magnification
   3. C) To form a real image
   4. D) To reduce aberrations
7. Question 7: If the radius of curvature of both sides of a lens are equal and the refractive index of the lens is 1.5, what is the focal length of the lens in terms of the radius of curvature R?
   1. A) R/2
   2. B) R
   3. C) 2R
   4. D) 4R