Refractive index and speed of light: Class 10 practice
Refractive index n = c/v (speed in vacuum ÷ speed in the medium). Read the method, follow the three worked examples, then try the six questions.
What you should know first
- Scientific notation
The idea behind refractive index and speed of light
Refractive index n = c/v (speed in vacuum ÷ speed in the medium). Relative index n₂₁ = n₂/n₁ = v₁/v₂. Light slows down and bends towards the normal entering a denser medium.
Step-by-step method
- Use c = 3 × 10⁸ m/s.
- n = c/v or v = c/n.
- Relative index = ratio of the two absolute indices.
Worked example 1 (Basic)
Find the speed of light in a medium of refractive index 1.5.
- v = c/n = 3 × 10⁸/1.5
- = 2.000e+8 m/s
- Answer: 2.000e+8 m/s
Worked example 2 (Standard)
Light travels at 2.000e+8 m/s in a medium. Find its refractive index.
- n = c/v
- = 1.5
- Answer: 1.5
Worked example 3 (Challenge)
Find the refractive index of a medium with n = 1.5 relative to one with n = 2.42.
- n₂₁ = 1.5/2.42
- = 0.62
- Answer: 0.62
Common mistakes and misconceptions
- Inverting the ratio
- Thinking n can be less than 1 for real materials
Practice questions
- (Basic) Find the speed of light in a medium of refractive index 1.44.
- (Basic) Find the speed of light in a medium of refractive index 1.65.
- (Standard) Light travels at 1.818e+8 m/s in a medium. Find its refractive index.
- (Standard) Light travels at 2.256e+8 m/s in a medium. Find its refractive index.
- (Challenge) Find the refractive index of a medium with n = 2.42 relative to one with n = 1.5.
- (Challenge) Find the refractive index of a medium with n = 2.42 relative to one with n = 1.44.
Answer key with full working
- Q1: v = c/n = 3 × 10⁸/1.44 → = 2.083e+8 m/s → Answer: 2.083e+8 m/s
- Q2: v = c/n = 3 × 10⁸/1.65 → = 1.818e+8 m/s → Answer: 1.818e+8 m/s
- Q3: n = c/v → = 1.65 → Answer: 1.65
- Q4: n = c/v → = 1.33 → Answer: 1.33
- Q5: n₂₁ = 2.42/1.5 → = 1.613 → Answer: 1.613
- Q6: n₂₁ = 2.42/1.44 → = 1.681 → Answer: 1.681
Syllabus note
This skill is listed under "Light Reflection and Refraction" for Class 10 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
- Light Reflection and Refraction chapter notes (Class 10)
- Mirror formula and magnification
- Power of a lens and lens combinations
- Snell's law
- Ohm's law and resistors in series and parallel
- Electric power and energy consumption
- Lens formula and magnification
- Resistivity and resistance of a wire
- All Class 10 practice
Frequently asked questions
Which chapter is refractive index and speed of light in?
"Light Reflection and Refraction", Class 10 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.