Optics and photoelectric effect: Identify the correct combined statements about threshold frequency and polarization at Brewster’s angle

Introduction / Context:
This question blends two cornerstone ideas in optics: the photoelectric effect (quantum threshold) and polarization by reflection (Brewster’s law). It checks whether you can correctly recall the definitions and key geometric property at the polarizing angle for a common medium like glass.

Given Data / Assumptions:

• Photoelectric emission requires photon energy ≥ work function, leading to a threshold frequency.
• For glass–air interface, the Brewster (polarizing) angle is near 57–58°.
• At Brewster’s angle, reflected and refracted rays are perpendicular.

Concept / Approach:
Photoelectric effect: photons with frequency f carry energy hf. If hf is less than the work function, no electrons are emitted—defining a minimum, the threshold frequency. Polarization: Brewster’s law states tan(θ_B) = n_2/n_1. For air-to-glass (n≈1.5), θ_B ≈ arctan(1.5) ≈ 56–57.5°. At θ_B, the reflected light is perfectly plane-polarized, and the reflected and refracted beams are at right angles.

Step-by-Step Solution:
Map threshold frequency: “minimum frequency for emission” → correct definition.Estimate θ_B for glass: arctan(1.5) ≈ 56–57.5°, so 57.5° is a standard rounded value.Recall geometric property at θ_B: reflected ⟂ refracted rays → orthogonal relationship.Therefore, all three statements hold simultaneously.

Verification / Alternative check:
Laboratory demonstrations show zero photoemission below threshold regardless of intensity. Glare reduction at the Brewster angle confirms polarization and orthogonality in reflection/refraction geometry.

Why Other Options Are Wrong:
Any single statement alone is incomplete; the combined option (all) is the most accurate.“None of the above” contradicts established theory and measurements.

Common Pitfalls:
Confusing intensity thresholds with frequency thresholds; and mixing up Brewster’s angle with critical angle for total internal reflection (a different phenomenon).

Final Answer:
All the above.