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import math import tkinter as tk from tkinter import ttk, colorchooser class RefractionVisualizer(tk.Tk): def __init__(self): super().__init__() self.title("光的折射控制器 | 斯涅尔定律可视化") self.geometry("800x600") # 初始化参数 self.incident_angle = 30 # 入射角（度） self.n1 = 1.0 # 介质1折射率 self.n2 = 1.33 # 介质2折射率 self.light_color = "#ff0000" # 光线颜色 self.has_total_reflection = False self.refract_angle = 0 self.init_ui() self.calculate_refraction() self.draw_refraction() def init_ui(self): # 标题区域 title_frame = ttk.Frame(self) title_frame.pack(pady=10) ttk.Label(title_frame, text="光的折射控制器", font=("微软雅黑", 20, "bold")).pack() ttk.Label(title_frame, text="斯涅尔定律：n₁·sinθ₁ = n₂·sinθ₂", font=("微软雅黑", 16)).pack() # 画布区域 self.canvas = tk.Canvas(self, width=780, height=400, bg="#fafbfc", bd=1, relief="solid") self.canvas.pack(pady=10) # 控制区域 control_frame = ttk.Frame(self) control_frame.pack(pady=10, fill="x", padx=20) # 左侧控制（入射角、介质1折射率） left_frame = ttk.Frame(control_frame) left_frame.pack(side="left", fill="x", expand=True, padx=10) # 入射角 ttk.Label(left_frame, text=f"入射角 θ₁：{self.incident_angle}°", font=("微软雅黑", 12)).pack(anchor="w") self.angle_slider = ttk.Scale(left_frame, from_=0, to=89, orient="horizontal", command=self.update_angle) self.angle_slider.set(self.incident_angle) self.angle_slider.pack(fill="x", pady=5) # 介质1折射率 ttk.Label(left_frame, text=f"介质1 折射率 n₁：{self.n1:.2f}", font=("微软雅黑", 12)).pack(anchor="w") self.n1_slider = ttk.Scale(left_frame, from_=1.0, to=2.0, orient="horizontal", command=self.update_n1) self.n1_slider.set(self.n1) self.n1_slider.pack(fill="x", pady=5) # 右侧控制（介质2折射率、颜色选择） right_frame = ttk.Frame(control_frame) right_frame.pack(side="right", fill="x", expand=True, padx=10) # 介质2折射率 ttk.Label(right_frame, text=f"介质2 折射率 n₂：{self.n2:.2f}", font=("微软雅黑", 12)).pack(anchor="w") self.n2_slider = ttk.Scale(right_frame, from_=1.0, to=2.0, orient="horizontal", command=self.update_n2) self.n2_slider.set(self.n2) self.n2_slider.pack(fill="x", pady=5) # 颜色选择 self.color_label = ttk.Label(right_frame, text=f"当前颜色：{self.light_color}", font=("微软雅黑", 12)) self.color_label.pack(anchor="w") self.color_btn = ttk.Button(right_frame, text="选择光线颜色", command=self.choose_color) self.color_btn.pack(fill="x", pady=5) def update_angle(self, value): self.incident_angle = int(float(value)) self.angle_slider.master.winfo_children()[0].config(text=f"入射角 θ₁：{self.incident_angle}°") self.calculate_refraction() self.draw_refraction() def update_n1(self, value): self.n1 = round(float(value), 2) self.n1_slider.master.winfo_children()[2].config(text=f"介质1 折射率 n₁：{self.n1:.2f}") self.calculate_refraction() self.draw_refraction() def update_n2(self, value): self.n2 = round(float(value), 2) self.n2_slider.master.winfo_children()[0].config(text=f"介质2 折射率 n₂：{self.n2:.2f}") self.calculate_refraction() self.draw_refraction() def choose_color(self): color = colorchooser.askcolor(initialcolor=self.light_color)[1] if color: self.light_color = color self.color_label.config(text=f"当前颜色：{self.light_color}") self.draw_refraction() def calculate_refraction(self): theta1_rad = math.radians(self.incident_angle) sin_theta2 = (self.n1 * math.sin(theta1_rad)) / self.n2 if abs(sin_theta2) > 1: self.has_total_reflection = True self.refract_angle = self.incident_angle else: self.has_total_reflection = False theta2_rad = math.asin(sin_theta2) self.refract_angle = round(math.degrees(theta2_rad), 1) def draw_arrow(self, start_x, start_y, end_x, end_y): # 绘制光线 self.canvas.create_line(start_x, start_y, end_x, end_y, fill=self.light_color, width=2) # 计算箭头 dx = end_x - start_x dy = end_y - start_y angle = math.atan2(dy, dx) arrow_len = 10 arrow_angle = math.pi / 6 # 箭头两点 p1_x = end_x - arrow_len * math.cos(angle - arrow_angle) p1_y = end_y - arrow_len * math.sin(angle - arrow_angle) p2_x = end_x - arrow_len * math.cos(angle + arrow_angle) p2_y = end_y - arrow_len * math.sin(angle + arrow_angle) self.canvas.create_polygon(end_x, end_y, p1_x, p1_y, p2_x, p2_y, fill=self.light_color) def draw_angle_arc(self, center_x, center_y, radius, start_angle, end_angle, label): # 绘制圆弧 start_x = center_x + radius * math.cos(start_angle) start_y = center_y + radius * math.sin(start_angle) end_x = center_x + radius * math.cos(end_angle) end_y = center_y + radius * math.sin(end_angle) self.canvas.create_arc( center_x - radius, center_y - radius, center_x + radius, center_y + radius, start=math.degrees(start_angle), extent=math.degrees(end_angle - start_angle), outline="#2c3e50", width=1, style="arc" ) # 标注文字 mid_angle = (start_angle + end_angle) / 2 label_x = center_x + (radius + 15) * math.cos(mid_angle) label_y = center_y + (radius + 15) * math.sin(mid_angle) self.canvas.create_text(label_x, label_y, text=label, fill="#2c3e50", font=("微软雅黑", 10)) def draw_refraction(self): # 清空画布 self.canvas.delete("all") w = 780 h = 400 center_x = w / 2 interface_y = h / 2 ray_length = 180 # 1. 绘制介质分界面 self.canvas.create_line(0, interface_y, w, interface_y, fill="#2c3e50", width=2) # 标注介质 self.canvas.create_text(20, interface_y - 20, text=f"介质1 (n₁ = {self.n1:.2f})", fill="#2c3e50", font=("微软雅黑", 12)) self.canvas.create_text(20, interface_y + 40, text=f"介质2 (n₂ = {self.n2:.2f})", fill="#2c3e50", font=("微软雅黑", 12)) # 2. 绘制法线（虚线） self.canvas.create_line(center_x, 0, center_x, h, fill="#7f8c8d", width=1, dash=(5, 5)) # 3. 计算光线坐标 theta1_rad = math.radians(self.incident_angle) theta2_rad = math.radians(self.refract_angle) # 入射光线 incident_start_x = center_x - ray_length * math.sin(theta1_rad) incident_start_y = interface_y - ray_length * math.cos(theta1_rad) self.draw_arrow(incident_start_x, incident_start_y, center_x, interface_y) # 4. 折射/反射光线 if self.has_total_reflection: # 全反射 reflect_end_x = center_x + ray_length * math.sin(theta2_rad) reflect_end_y = interface_y - ray_length * math.cos(theta2_rad) self.draw_arrow(center_x, interface_y, reflect_end_x, reflect_end_y) self.canvas.create_text(center_x + 50, interface_y - 80, text="全反射", fill="#e74c3c", font=("微软雅黑", 12)) else: # 折射 refract_end_x = center_x + ray_length * math.sin(theta2_rad) refract_end_y = interface_y + ray_length * math.cos(theta2_rad) self.draw_arrow(center_x, interface_y, refract_end_x, refract_end_y) # 5. 标注角度 self.draw_angle_arc(center_x, interface_y, 30, -math.pi/2, -math.pi/2 + theta1_rad, f"θ₁ = {self.incident_angle}°") self.draw_angle_arc(center_x, interface_y, 50, math.pi/2 - theta2_rad, math.pi/2, f"θ₂ = {self.refract_angle:.1f}°") if __name__ == "__main__": app = RefractionVisualizer() app.mainloop()
