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An electromagnetic wave from an under water source with perpendicular polarization is incident on a water-air interface at angle 20o with normal to surface. For water assume εr = 81, μr = 1. The critical angle θc is
- a)83.62o
- b)6.38o
- c)42.6o
- d)None of the above
Correct answer is option 'B'. Can you explain this answer?
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Explanation:
When an electromagnetic wave passes from one medium to another, it undergoes reflection, transmission, and refraction. The angle of incidence, angle of reflection, angle of transmission, and critical angle are important parameters that determine how the wave behaves at the interface.
Given:
- Angle of incidence (θi) = 20°
- Refractive index of water (nw) = 1.33
- Refractive index of air (na) = 1
Calculation:
1. Angle of refraction (θr):
The angle of refraction can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.
Snell's Law: nw * sin(θi) = na * sin(θr)
Substituting the given values:
1.33 * sin(20°) = 1 * sin(θr)
sin(θr) = 1.33 * sin(20°) / 1
sin(θr) = 0.4438
θr ≈ 26.32°
2. Critical angle (θc):
The critical angle is the angle of incidence for which the angle of refraction becomes 90°. It can be calculated using the formula:
θc = sin^(-1)(na / nw)
Substituting the given values:
θc = sin^(-1)(1 / 1.33)
θc ≈ 48.75°
Answer:
The critical angle (θc) is approximately 48.75°, which is not among the given options. Therefore, the correct answer is option 'B' - None of the above.
When an electromagnetic wave passes from one medium to another, it undergoes reflection, transmission, and refraction. The angle of incidence, angle of reflection, angle of transmission, and critical angle are important parameters that determine how the wave behaves at the interface.
Given:
- Angle of incidence (θi) = 20°
- Refractive index of water (nw) = 1.33
- Refractive index of air (na) = 1
Calculation:
1. Angle of refraction (θr):
The angle of refraction can be calculated using Snell's law, which states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is equal to the ratio of the refractive indices of the two media.
Snell's Law: nw * sin(θi) = na * sin(θr)
Substituting the given values:
1.33 * sin(20°) = 1 * sin(θr)
sin(θr) = 1.33 * sin(20°) / 1
sin(θr) = 0.4438
θr ≈ 26.32°
2. Critical angle (θc):
The critical angle is the angle of incidence for which the angle of refraction becomes 90°. It can be calculated using the formula:
θc = sin^(-1)(na / nw)
Substituting the given values:
θc = sin^(-1)(1 / 1.33)
θc ≈ 48.75°
Answer:
The critical angle (θc) is approximately 48.75°, which is not among the given options. Therefore, the correct answer is option 'B' - None of the above.
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An electromagnetic wave from an under water source with perpendicular polarization is incident on a water-air interface at angle 20o with normal to surface. For water assume εr=81, μr=1. The critical angle θcisa)83.62ob)6.38oc)42.6od)None of the aboveCorrect answer is option 'B'. Can you explain this answer?
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