Section 6.7: Problem-Solving Strategies
In optics, approaching problems methodically improves accuracy and understanding. Key strategies include:
- Draw accurate diagrams showing object, image, principal axis, and focal points.
- Identify the type of mirror or lens (concave, convex, plane, converging, diverging).
- Write down known quantities and relevant formulas (mirror/lens formula, magnification, diffraction equations).
- Use the sign conventions consistently (real vs virtual images, upright vs inverted, distances).
- Check units and convert if necessary (cm → m, nm → m).
- Estimate expected results to verify reasonableness.
- Label all rays in ray diagrams clearly (incident, reflected/refracted, focal ray).
Example: Lens Problem Strategy
An object is placed 20 cm from a converging lens of focal length 10 cm. Outline the steps to find the image position and magnification.
- Identify type of lens: converging (positive focal length).
- Write known: u = 20 cm, f = 10 cm.
- Apply lens formula: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \).
- Solve for v: \( \frac{1}{v} = \frac{1}{10} + \frac{1}{20} = \frac{3}{20} \) → \( v \approx 6.67\,\text{cm} \).
- Calculate magnification: \( m = \frac{v}{u} = \frac{6.67}{20} \approx 0.33 \) (image is real, inverted, reduced).
Practice Problems
- Outline steps to solve for image formed by a concave mirror with an object beyond the center of curvature.
- Explain how to determine whether an image is real or virtual using the sign convention.
- Draw a labeled ray diagram for a converging lens with an object at 1.5f.
- Describe a systematic approach to calculate fringe spacing in double-slit interference.
- Explain the method to find the first minimum in single-slit diffraction problems.