讲解一下这道题---**Extracted Content:**
**Question 13:**
(10 分) 如图所示, 平静湖面岸边的垂钓者的眼睛恰好位于岸边P点正上方 h₁ = 1.8m 的高度处, 浮标 Q 离 P 点的距离 s₁ = 2.4m, 鱼饵灯 M 在浮标正前方 s₂ = 3.6m 处的水下 h₂ = 4.8m 深度处, 垂钓者发现鱼饵灯恰好被浮标挡住。 求:
① 水的折射率;
② 若鱼饵灯缓慢竖直上浮, 当它离水面多深时, 鱼饵灯发出的光恰好无法从水面 PQ 间射出。 (结果可用根号表示)
**Diagram Description:**
* **Type:** Physics diagram illustrating light refraction/total internal reflection at a water surface.
* **Elements:**
* A horizontal line represents the water surface.
* Point P is on the shore (presumably the edge of the water surface).
* An observer's eye is located vertically above P at a height h₁ = 1.8m.
* A float (浮标) Q is on the water surface, s₁ = 2.4m away from P.
* A light source (鱼饵灯) M is underwater, vertically below a point 3.6m away from P along the direction PQ, at a depth h₂ = 4.8m. The diagram shows M at a horizontal distance s₂ = 3.6m from the vertical line through P.
* A dashed line connects the eye, Q, and M, representing the path of light from M to the eye, being blocked by Q. This suggests the light from M to the eye passes just over Q.
* Angles of incidence and refraction are indicated (i and r).
* Right angles are shown at P on the shore and at the point directly above M on the water surface.
* Distances are labeled: h₁ = 1.8 (observer height), s₁ = 2.4 (distance PQ), s₂ = 3.6 (horizontal distance from P to the vertical line through M), h₂ = 4.8 (depth of M).
* A triangle is formed by the eye, Q, and the point on the water surface directly above M.
* Another triangle is formed by M, the point on the water surface directly above M, and Q.
**Mathematical Expressions/Notes:**
* Some handwritten calculations are visible, including:
* sin(r) = 2.4 / sqrt(2.4^2 + 1.8^2) = 2.4 / sqrt(5.76 + 3.24) = 2.4 / sqrt(9) = 2.4 / 3 = 0.8 = 4/5
* sin(i) = 3.6 / sqrt(3.6^2 + 4.8^2) = 3.6 / sqrt(12.96 + 23.04) = 3.6 / sqrt(36) = 3.6 / 6 = 0.6 = 3/5
* n = sin(r) / sin(i) = (4/5) / (3/5) = 4/3
* sin(C) = 1/n (where C is the critical angle)
* sin(C) = 3/4
* Calculation related to the second part, likely involving critical angle and depth, resulting in X = 3.6 / tan(C).
* Calculation using tan(C) derived from sin(C) = 3/4. Using a right triangle with opposite side 3 and hypotenuse 4, the adjacent side is sqrt(4^2 - 3^2) = sqrt(16-9) = sqrt(7). So tan(C) = 3/sqrt(7).
* X = 3.6 / (3/sqrt(7)) = 3.6 * sqrt(7) / 3 = 1.2 * sqrt(7).
* The value 3.6/sqrt(7) and 3.6 are visible, likely intermediate steps.
* Final calculated value 1.2*sqrt(7) is written.
**Other Text:**
* "用为" (used as) - incomplete phrase at the top.