Waves: Exploring Reflection, Refraction, and Diffraction in A-Level Science
What Are Waves?
Waves transfer energy without transporting matter, classified as transverse or longitudinal.
Key Wave Behaviors
Reflection
Reflection occurs when waves bounce off a surface.
Law of Reflection:
θi=θr\theta_i = \theta_rθi=θr
Where:
- θi\theta_iθi: Angle of incidence.
- θr\theta_rθr: Angle of reflection.
Refraction
Refraction occurs when waves change direction as they pass from one medium to another, due to a change in speed.
Snell’s Law:
n1sinθ1=n2sinθ2n_1 \sin\theta_1 = n_2 \sin\theta_2n1sinθ1=n2sinθ2
Where:
- n1,n2n_1, n_2n1,n2: Refractive indices.
- θ1,θ2\theta_1, \theta_2θ1,θ2: Angles of incidence and refraction.
Diffraction
Diffraction occurs when waves bend around obstacles or pass through small openings.
Key Factor: Wavelength and obstacle size determine the extent of diffraction.
Applications of Wave Behavior
Optics
Reflection and refraction are fundamental in lens design and microscopy.
Telecommunications
Refraction and diffraction are used in signal transmission.
Structural Engineering
Diffraction patterns help analyze material stress and flaws.
Example Problem
Light enters glass (n=1.5n = 1.5n=1.5) from air at 30∘30^\circ30∘. Find the angle of refraction.
- Formula:
sinθ2=n1sinθ1n2\sin\theta_2 = \frac{n_1 \sin\theta_1}{n_2}sinθ2=n2n1sinθ1
- Substitute Values:
sinθ2=1⋅sin30∘1.5=0.51.5=0.333\sin\theta_2 = \frac{1 \cdot \sin 30^\circ}{1.5} = \frac{0.5}{1.5} = 0.333sinθ2=1.51⋅sin30∘=1.50.5=0.333
- Result:
θ2=sin−1(0.333)≈19.47∘\theta_2 = \sin^{-1}(0.333) \approx 19.47^\circθ2=sin−1(0.333)≈19.47∘
Common Mistakes in Wave Behavior Problems
- Mixing up angles of incidence and refraction.
- Forgetting to use consistent units.
- Neglecting wave properties like wavelength in diffraction.
Practice Questions
- A wave reflects off a surface at 45∘45^\circ45∘. Calculate the angle of reflection.
- Explain how refraction applies to fiber optics.
- Describe one application of diffraction in telecommunications.