(a) (i) Frequency and Wavelength in Refraction
Step 1 (Governing Principle): [0.5 Mark]
The frequency ($f$) of a light wave is determined by the source of the light and remains an intrinsic property of the wave. When light travels from one medium to another, the boundary conditions of the electromagnetic field require the frequency to remain constant to maintain phase continuity at the interface.
Step 2 (Reasoning for Wavelength Change): [0.5 Mark]
The speed of light ($v$) in a medium is given by the relation $v = f \lambda$. Since the speed of light changes when it enters a medium of different refractive index ($n = c/v$), and the frequency ($f$) remains constant, the wavelength ($\lambda$) must change to satisfy the equation:
$$\lambda' = \frac{v}{f} = \frac{c}{n \cdot f} = \frac{\lambda}{n}$$Thus, the wavelength changes inversely proportional to the refractive index of the medium.
(b) (ii) Identification and Uses of Electromagnetic Radiation
Step 1 (Formula / Governing Law): [0.5 Mark]
Given frequency $f = 1.0 \times 10^{11} \text{ Hz}$. The electromagnetic spectrum is categorized by frequency ranges. We identify the radiation based on the provided frequency value.
Step 2 (Step-by-Step Working): [0.5 Mark]
The frequency range $10^{11} \text{ Hz}$ to $10^{12} \text{ Hz}$ falls within the Microwave region of the electromagnetic spectrum.
Step 3 (Final Concluded Answer): [1.0 Mark]
Identification: Microwaves.
Two Uses:
- Used in microwave ovens for cooking food.
- Used in RADAR systems for aircraft navigation and remote sensing.
💡 EL10 Concept Insight: Think of frequency like the steady beat of a drum—the drummer (the light source) doesn't change their rhythm just because the sound travels through air or water. However, because the light "slows down" in denser materials, the waves get squashed together, which is why the wavelength shrinks!