Polarisation: Brewster's law and Malus's law: Class 12 practice
Reflected light is completely polarised at Brewster's angle, where tan θ_B = n. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Trigonometry
The idea behind polarisation: brewster's law and malus's law
Reflected light is completely polarised at Brewster's angle, where tan θ_B = n. Through two polarisers at angle θ, transmitted intensity I = I₀cos²θ (Malus's law); unpolarised light is halved by the first polariser.
Step-by-step method
- For Brewster: θ_B = tan⁻¹ n.
- For Malus: I = I₀ cos²θ.
- Halve unpolarised light at the first polariser.
Worked example 1 (Basic)
Find Brewster's angle for glass of refractive index 1.33.
- θ_B = tan⁻¹(1.33)
- Answer: 53.06°
Worked example 2 (Standard)
Polarised light of intensity 17 W/m² passes a polariser at 45° to its plane. Find the transmitted intensity.
- I = 17 cos²45°
- Answer: 8.5 W/m²
Worked example 3 (Challenge)
Unpolarised light (84 W/m²) passes two polarisers with axes at 60°. Find the final intensity.
- After first: 42
- After second: 42 cos²60°
- Answer: 10.5 W/m²
Common mistakes and misconceptions
- Using cos θ instead of cos²θ
- Forgetting the first halving
Practice questions
- (Basic) Find Brewster's angle for glass of refractive index 1.6.
- (Basic) Find Brewster's angle for glass of refractive index 1.5.
- (Standard) Polarised light of intensity 49 W/m² passes a polariser at 60° to its plane. Find the transmitted intensity.
- (Standard) Polarised light of intensity 86 W/m² passes a polariser at 53° to its plane. Find the transmitted intensity.
- (Challenge) Unpolarised light (17 W/m²) passes two polarisers with axes at 37°. Find the final intensity.
- (Challenge) Unpolarised light (80 W/m²) passes two polarisers with axes at 30°. Find the final intensity.
Answer key with full working
- Q1: θ_B = tan⁻¹(1.6) → Answer: 57.99°
- Q2: θ_B = tan⁻¹(1.5) → Answer: 56.31°
- Q3: I = 49 cos²60° → Answer: 12.25 W/m²
- Q4: I = 86 cos²53° → Answer: 31.15 W/m²
- Q5: After first: 8.5 → After second: 8.5 cos²37° → Answer: 5.42 W/m²
- Q6: After first: 40 → After second: 40 cos²30° → Answer: 30 W/m²
Syllabus note
This skill is listed under "Wave Optics" for Class 12 in the NCERT/CBSE books. ICSE, IGCSE, IB and state boards may teach it in a different chapter or year.
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.
Related practice and notes
Frequently asked questions
Which chapter is polarisation: brewster's law and malus's law in?
"Wave Optics", Class 12 Physics (NCERT/CBSE). Other boards may place it differently.
How were the answers checked?
Answers on this page are generated and automatically re-checked by a second, independent calculation. They have not been reviewed by a teacher — if you spot a problem, tell us on WhatsApp.