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A ray of light travels from air to glass. i) Determine the angle of incidence. ii) Calculate the angle of refraction if the refractive index of glass is 1.5. iii) Can total internal reflection occur f

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3 parts
i

43∘43^\circ

ii

27.05∘27.05^\circ

iii

No\text{No}

Step-by-step solution

5 steps

7) Figure 8 shows a ray of light ray traveling from air to glass.

Part i· 1 step

Determine the angle of incidence

The angle of incidence is the angle between the incident ray and the normal. From Figure 8, this angle is directly given.

  1. Identify the angle of incidence from the diagram.

    The angle between the incident ray and the normal is 43∘43^\circ.
    The angle of incidence is 43∘\boxed{43^\circ}.

Part ii

27.05∘27.05^\circ

Calculate the angle of refraction, if the refractive index of glass is 1.5

We use Snell's Law: n1sin⁡θ1=n2sin⁡θ2n_1 \sin \theta_1 = n_2 \sin \theta_2.
Given:
Refractive index of air (n1n_1) ≈1\approx 1
Angle of incidence (θ1\theta_1) =43∘= 43^\circ (from part i)
Refractive index of glass (n2n_2) =1.5= 1.5

  1. Substitute the values into Snell's Law.

    1⋅sin⁡(43∘)=1.5⋅sin⁡θ21 \cdot \sin(43^\circ) = 1.5 \cdot \sin \theta_2

  2. Solve for sin⁡θ2\sin \theta_2.

    sin⁡θ2=sin⁡(43∘)1.5\sin \theta_2 = \frac{\sin(43^\circ)}{1.5} sin⁡θ2≈0.681991.5\sin \theta_2 \approx \frac{0.68199}{1.5} sin⁡θ2≈0.45466\sin \theta_2 \approx 0.45466

  3. Calculate θ2\theta_2.

    θ2=arcsin⁡(0.45466)\theta_2 = \arcsin(0.45466) θ2≈27.05∘\theta_2 \approx 27.05^\circ

    The angle of refraction is 27.05∘\boxed{27.05^\circ}.

Part iii

No\text{No}

Can total internal reflection occur for light traveling from air to glass?

Total internal reflection (TIR) occurs when light travels from an optically denser medium to an optically rarer medium, and the angle of incidence exceeds the critical angle.

  1. Analyze the conditions for total internal reflection.

    In this scenario, light is traveling from air (optically rarer medium, n≈1n \approx 1) to glass (optically denser medium, n=1.5n = 1.5). For total internal reflection to occur, the light must travel from the denser medium to the rarer medium. Since the light is traveling from air to glass, total internal reflection cannot occur.
    The answer is No\boxed{\text{No}}.

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