A wavefront travels from air to the medium "Q". It makes an angle of 45˚ with the boundary in air and makes an angle of 30˚ with the boundary in medium "Q". What is the refractive index of medium Q?
Correct answer: B. sin(45) / sin(30).
- A. sin(30) / sin(45).
- B. sin(45) / sin(30).
- C. sin(60) / sin(45).
- D. sin(45) / sin(60).
Explanation
To calculate the refractive index of medium Q, we can use Snell's law, which relates the angles of incidence and refraction to the refractive indices of the two media involved.Snell's law states: n1 * sin(theta1) = n2 * sin(theta2)Where:n1 = refractive index of the first medium (in this case, air)theta1 = angle of incidence in the first mediumn2 = refractive index of the second medium (in this case, medium Q)theta2 = angle of refraction in the second mediumGiven:Angle of incidence in air (theta1) = 45˚Angle of refraction in medium Q (theta2) = 30˚Let's denote the refractive index of medium Q as n2.Applying Snell's law:n1 * sin(theta1) = n2 * sin(theta2)Substituting the known values:1 * sin(45˚) = n2 * sin(30˚)Simplifying:sin(45˚) = n2 * sin(30˚)Using trigonometric values:1/√2 = n2 * (1/2)Rearranging and solving for n2:n2 = (1/√2) / (1/2)n2 = 2/√2n2 = √2Therefore, the refractive index of medium Q is equal to √2.
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