Subjects physics

Angle Refraction F5A6D2

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1. **State the problem:** Light is incident on crown glass at an angle of $45.0^\circ$. We need to find the angle of refraction inside the glass. 2. **Formula used:** Snell's Law states: $$n_1 \sin \theta_1 = n_2 \sin \theta_2$$ where $n_1$ and $n_2$ are the refractive indices of the first and second medium, and $\theta_1$ and $\theta_2$ are the angles of incidence and refraction respectively. 3. **Known values:** - Air refractive index $n_1 = 1.00$ - Crown glass refractive index $n_2 = 1.52$ - Angle of incidence $\theta_1 = 45.0^\circ$ 4. **Apply Snell's Law:** $$1.00 \times \sin 45.0^\circ = 1.52 \times \sin \theta_2$$ 5. **Calculate $\sin 45.0^\circ$:** $$\sin 45.0^\circ = \frac{\sqrt{2}}{2} \approx 0.7071$$ 6. **Substitute and solve for $\sin \theta_2$:** $$0.7071 = 1.52 \times \sin \theta_2$$ $$\sin \theta_2 = \frac{0.7071}{1.52}$$ $$\sin \theta_2 = \cancel{\frac{0.7071}{\cancel{1.52}}}0.4653$$ 7. **Find $\theta_2$ by taking inverse sine:** $$\theta_2 = \sin^{-1}(0.4653) \approx 27.8^\circ$$ **Final answer:** The angle of refraction inside the crown glass is approximately $27.8^\circ$.