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 $27.8^\circ$.
Angle Refraction F5A6D2
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