Light is incident on an air glass boundary at an angle of incidence of 400. If the refractive index of the glass is 1.7, determine the angle of refraction

Physics

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Step-by-step solution

3 steps
  1. State Snell's Law.

    Snell's Law describes the relationship between the angles of incidence and refraction when light passes between two different media.

    n1sin⁡(θ1)=n2sin⁡(θ2)n_1 \sin(\theta_1) = n_2 \sin(\theta_2)

    where:
    n1n_1 is the refractive index of the first medium (air)
    θ1\theta_1 is the angle of incidence
    n2n_2 is the refractive index of the second medium (glass)
    θ2\theta_2 is the angle of refraction

  2. Identify the given values.

    Refractive index of air, n1=1n_1 = 1 (approximately)
    Angle of incidence, θ1=40°\theta_1 = 40°
    Refractive index of glass, n2=1.7n_2 = 1.7
    Angle of refraction, θ2=?\theta_2 = ?

  3. Substitute the values into Snell's Law and solve for θ2\theta_2.

    1×sin⁡(40°)=1.7×sin⁡(θ2)1 \times \sin(40°) = 1.7 \times \sin(\theta_2)

    Calculate sin⁡(40°)\sin(40°):

    sin⁡(40°)≈0.6428\sin(40°) \approx 0.6428 1×0.6428=1.7×sin⁡(θ2)1 \times 0.6428 = 1.7 \times \sin(\theta_2) 0.6428=1.7×sin⁡(θ2)0.6428 = 1.7 \times \sin(\theta_2)

    Divide by 1.7:

    sin⁡(θ2)=0.64281.7\sin(\theta_2) = \frac{0.6428}{1.7} sin⁡(θ2)≈0.3781\sin(\theta_2) \approx 0.3781

    To find θ2\theta_2, take the inverse sine (arcsin):

    θ2=arcsin⁡(0.3781)\theta_2 = \arcsin(0.3781) θ2≈22.22°\theta_2 \approx 22.22°

    The angle of refraction is approximately 22.22°.

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