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Zorluk: OrtaWave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

A ray of light traveling inside a transparent medium strikes the boundary with air. If the critical angle for total internal reflection at this boundary is 30∘30^\circ, what is the refractive index of the medium?

  1. 2.002.00Cevap
  2. B
    0.500.50
  3. C
    0.870.87
  4. D
    1.151.15

Cevap

The refractive index of the medium is 2.002.00.
For light traveling from a medium into air, the critical angle CC is related to the refractive index nn by n=1sin⁡Cn = \frac{1}{\sin C}. Substituting C=30∘C = 30^\circ gives n=1sin⁡30∘=10.5=2.00n = \frac{1}{\sin 30^\circ} = \frac{1}{0.5} = 2.00.

Adım Adım Çözüm

1
Identify the relationship between critical angle CC and refractive index nn
The formula for light passing into air is n=1sin⁡Cn = \frac{1}{\sin C}.
Total internal reflection occurs when light travels from a denser medium to a less dense medium (air, nair=1n_{air} = 1) at an angle greater than the critical angle.
2
Substitute the given critical angle C=30∘C = 30^\circ into the formula
sin⁡30∘=0.5\sin 30^\circ = 0.5, so n=10.5=2.00n = \frac{1}{0.5} = 2.00.
Taking the reciprocal of sin⁡30∘\sin 30^\circ gives the correct refractive index.

Anahtar Kavram

Critical Angle and Refractive Index
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Konular

Wave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

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