Critical angle and total internal reflection: Class 12 practice
Total internal reflection happens when light goes from a denser to a rarer medium at an angle greater than the critical angle C, where sin C = n_rarer/n_denser (= 1/n for air).. Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Inverse sine
The idea behind critical angle and total internal reflection
Total internal reflection happens when light goes from a denser to a rarer medium at an angle greater than the critical angle C, where sin C = n_rarer/n_denser (= 1/n for air).
Step-by-step method
- Check light goes dense → rare.
- sin C = 1/n (or n₂/n₁).
- Compare the incidence angle with C.
Worked example 1 (Basic)
Find the critical angle for a medium of refractive index 1.6 (to air).
- sin C = 1/1.6 = 0.625
- C = 38.68°
- Answer: 38.68°
Worked example 2 (Standard)
Light in a medium of n = 1.5 meets the surface with air at 50°. Is it totally internally reflected?
- C = 41.81°
- 50° > C → TIR
- Answer: Yes, total internal reflection
Worked example 3 (Challenge)
Find the critical angle for light going from a medium of n = 2.42 into water (n = 1.33).
- sin C = 1.33/2.42
- C = 33.34°
- Answer: 33.34°
Common mistakes and misconceptions
- Applying TIR from rare to dense
- Using n instead of 1/n
Practice questions
- (Basic) Find the critical angle for a medium of refractive index 1.5 (to air).
- (Basic) Find the critical angle for a medium of refractive index 1.33 (to air).
- (Standard) Light in a medium of n = 1.33 meets the surface with air at 41°. Is it totally internally reflected?
- (Standard) Light in a medium of n = 2.42 meets the surface with air at 32°. Is it totally internally reflected?
- (Challenge) Find the critical angle for light going from a medium of n = 1.5 into water (n = 1.33).
- (Challenge) Find the critical angle for light going from a medium of n = 1.6 into water (n = 1.33).
Answer key with full working
- Q1: sin C = 1/1.5 = 0.667 → C = 41.81° → Answer: 41.81°
- Q2: sin C = 1/1.33 = 0.752 → C = 48.75° → Answer: 48.75°
- Q3: C = 48.75° → 41° < C → refracts out → Answer: No, it refracts into air
- Q4: C = 24.41° → 32° > C → TIR → Answer: Yes, total internal reflection
- Q5: sin C = 1.33/1.5 → C = 62.46° → Answer: 62.46°
- Q6: sin C = 1.33/1.6 → C = 56.23° → Answer: 56.23°
Syllabus note
This skill is listed under "Ray 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 critical angle and total internal reflection in?
"Ray 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.