## Problem Restatement A flint glass plate (\( n = 1.66 \)) is **9.50 cm** thick and is covered with a layer of water (\( n = 1.33 \)) **17. cm** deep. **Question:** Calculate the **apparent thickness** of the plate as viewed from straight above the water (nearly normal incidence). --- ## Solution ### Step 1: Concept The **apparent thickness** \( t_a \) of an object viewed through a medium is given by: \[ t_{\text{apparent}} = \frac{t_{\text{real}}}{n_{\text{rel}}} \] where \( n_{\text{rel}} = \frac{n_{\text{plate}}}{n_{\text{medium above}}} \). Here, the plate is in water, so the observer sees the plate through water: \[ n_{\text{rel}} = \frac{n_{\text{glass}}}{n_{\text{water}}} \] ### Step 2: Plug in Values Given: - \( t_{\text{real}} = 9.50 \) cm - \( n_{\text{glass}} = 1.66 \) - \( n_{\text{water}} = 1.33 \) \[ t_{\text{apparent}} = \frac{t_{\text{real}} \cdot n_{\text{water}}}{n_{\text{glass}}} \] \[ t_{\text{apparent}} = \frac{9.50 \times 1.33}{1.66} \] \[ t_{\text{apparent}} = \frac{12.635}{1.66} \] \[ t_{\text{apparent}} \approx 7.62 \text{ cm} \] --- ## **Final Answer** \[ \boxed{7.62 \ \text{cm}} \] **The apparent thickness of the glass plate is approximately 7.62 cm.**