A LADY IS GETTING MARRIED IN 2DAYS TIME.HER HUSBAND BUYS HER A DIAMOND RING.ON THE DAY OF HER WEDDING HER HUSBAND PLACES THE RING ON HER FINGER.THE RING REFRACTS AT AN ANGLE OF 23.24 DEGREES.CALCULATE THE ANGLE OF INCIDENCE IF THE REFRACTIVE INDEX OF A RING IS 2.42
sineAngle*1=2.42*sin23.24
calculate angle of incidence.
To calculate the angle of incidence, we'll use Snell's Law, which relates the angle of incidence (θ₁), the angle of refraction (θ₂), and the refractive indexes of the media involved:
n₁ * sin(θ₁) = n₂ * sin(θ₂)
In this case, the refractive index of the ring is given as 2.42, and the angle of refraction is given as 23.24 degrees.
We need to find the angle of incidence (θ₁) when the ring refracts at an angle of 23.24 degrees.
Rearranging Snell's Law, we have:
sin(θ₁) = (n₂ / n₁) * sin(θ₂)
Substituting the given values, we get:
sin(θ₁) = (2.42 / 1) * sin(23.24)
Now, we can solve for θ₁ by taking the inverse sine of both sides:
θ₁ = arcsin((2.42 / 1) * sin(23.24))
Using a calculator, we can evaluate this expression:
θ₁ ≈ arcsin(1.019 * 0.395)
θ₁ ≈ arcsin(0.402)
θ₁ ≈ 23.9 degrees
Therefore, the angle of incidence is approximately 23.9 degrees.