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Difficulty: EasyRefraction of Light, Total Internal Reflection, and Prisms

A light ray traveling inside a transparent glass prism of refractive index 1.501.50 strikes the boundary with air. What is the sine of the critical angle (sin⁡C\sin C) for total internal reflection to occur at this boundary?

  1. 0.670.67Answer
  2. B
    1.501.50
  3. C
    0.500.50
  4. D
    0.870.87

Answer

The sine of the critical angle (sin⁡C\sin C) for total internal reflection at the glass-air boundary is 0.670.67.
For light moving from a medium with refractive index nn into air, total internal reflection occurs when the angle of incidence exceeds the critical angle CC. The critical angle satisfies sin⁡C=1n\sin C = \frac{1}{n}. Substituting n=1.50n = 1.50 gives sin⁡C=11.50=0.67\sin C = \frac{1}{1.50} = 0.67.

Step-by-Step Solution

1
Identify the relationship between the refractive index (nn) and the critical angle (CC) when light travels from a medium to air.
sin⁡C=1n\sin C = \frac{1}{n}
By Snell's law, at the critical angle of incidence, the angle of refraction in air is 90∘90^\circ (so sin⁡90∘=1\sin 90^\circ = 1).
2
Substitute the given refractive index (n=1.50n = 1.50) into the formula.
sin⁡C=11.50=23≈0.67\sin C = \frac{1}{1.50} = \frac{2}{3} \approx 0.67
Dividing 11 by 1.501.50 yields 0.666...0.666..., which rounds to 0.670.67.

Key Concept

Critical Angle and Total Internal Reflection
Estimated Time:45s
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Topics

Refraction of Light, Total Internal Reflection, and Prisms

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