Numerical answer · +4 / −1
Light goes from vacuum to a medium with refractive index 1.5. If incidence angle is such that sin θ₁ = 0.9, then 10 sin θ₂ equals:
Answer and solution
Answer 6
Solution
Physics sir · 3 steps
Light enters a denser medium, so it bends towards the normal: divide the sine by 1.5.
- Apply Snell's law. At the boundary, n sin θ stays the same on both sides. Vacuum has n₁ = 1 and the medium has n₂ = 1.5.
n₁ sin θ₁ = n₂ sin θ₂
- Put in numbers. 1 × 0.9 = 1.5 × sin θ₂, so sin θ₂ = 0.9/1.5 = 0.6. It is smaller than 0.9, as it should be: the ray bends towards the normal.
- So. 10 sin θ₂ = 10 × 0.6 = 6.
The common slip: 13.5. Multiplying 0.9 by 1.5 instead of dividing gives sin θ₂ = 1.35, which is impossible for a sine, so 10 sin θ₂ comes out as 13.5.
The idea to keep. Going into a denser medium, the sine of the angle shrinks by the ratio of refractive indices. If your sine comes out bigger than 1, you have flipped the ratio.
Answer from the NTA final answer key. Solution by PrepWiser.