import tkinter as tk from tkinter import ttk import math class OpticsSim: def __init__(self, root): self.root = root self.root.title("八年级物理｜光的反射 & 三棱镜色散") self.root.geometry("1000x720") self.W = 860 self.H = 540 self.canvas = tk.Canvas(root, width=self.W, height=self.H, bg="#000000") self.canvas.pack(pady=4) # 模式 self.mode = tk.StringVar(value="reflect") # reflect / prism self.show_normal = tk.BooleanVar(value=True) self.is_specular = tk.BooleanVar(value=True) # 反射参数 self.theta_i_var = tk.DoubleVar(value=40.0) # 入射角 i self.mirror_alpha_var = tk.DoubleVar(value=0.0) # 镜面转角 α # 三棱镜色散色表 self.rainbow = [ ("red", 1.510), ("orange", 1.515), ("yellow", 1.518), ("green", 1.522), ("cyan", 1.526), ("blue", 1.530), ("#4B0082", 1.535), ("violet", 1.540) ] # 控制面板 ctrl = ttk.Frame(root) ctrl.pack() ttk.Radiobutton(ctrl, text="光的反射", variable=self.mode, value="reflect", command=self.draw).grid(row=0, column=0, padx=4) ttk.Radiobutton(ctrl, text="三棱镜色散", variable=self.mode, value="prism", command=self.draw).grid(row=0, column=1, padx=4) ttk.Checkbutton(ctrl, text="显示法线", variable=self.show_normal, command=self.draw).grid(row=0, column=2, padx=4) ttk.Checkbutton(ctrl, text="镜面反射(关闭=漫反射)", variable=self.is_specular, command=self.draw).grid(row=0, column=3, padx=4) ttk.Label(ctrl, text="入射角 i：").grid(row=1, column=0, padx=3) ttk.Scale(ctrl, from_=0, to=80, variable=self.theta_i_var, orient=tk.HORIZONTAL, length=160, command=lambda x:self.draw()).grid(row=1, column=1) ttk.Label(ctrl, text="镜面转角 α：").grid(row=1, column=2, padx=3) ttk.Scale(ctrl, from_=-30, to=30, variable=self.mirror_alpha_var, orient=tk.HORIZONTAL, length=160, command=lambda x:self.draw()).grid(row=1, column=3) ttk.Button(ctrl, text="潜望镜演示", command=self.draw_periscope).grid(row=1, column=4, padx=6) self.info_label = ttk.Label(root, text="i = 40.0° , r = 40.0° , α = 0.0°｜镜转α → 反射光线转 2α", font=("Arial",11)) self.info_label.pack() self.draw() def deg2rad(self, d): return d * math.pi / 180 def rad2deg(self, r): return r * 180 / math.pi def snell(self, th1, n1, n2): s = (n1/n2)*math.sin(th1) if abs(s)>1: return None return math.asin(s) def draw_reflect(self): cx, cy = self.W//2, self.H//2 i_deg = self.theta_i_var.get() alpha_deg = self.mirror_alpha_var.get() i_rad = self.deg2rad(i_deg) alpha_rad = self.deg2rad(alpha_deg) # 镜面 L = 320 mx1 = cx - L*math.cos(alpha_rad) my1 = cy - L*math.sin(alpha_rad) mx2 = cx + L*math.cos(alpha_rad) my2 = cy + L*math.sin(alpha_rad) self.canvas.create_line(mx1, my1, mx2, my2, fill="#dddddd", width=4) # 法线：垂直镜面 normal_ang = alpha_rad + math.pi/2 if self.show_normal.get(): nl = 220 nx1 = cx - nl*math.cos(normal_ang) ny1 = cy - nl*math.sin(normal_ang) nx2 = cx + nl*math.cos(normal_ang) ny2 = cy + nl*math.sin(normal_ang) self.canvas.create_line(nx1, ny1, nx2, ny2, fill="#44aaff", dash=(4,4), width=2) # 入射光方向（相对于法线） in_ang = normal_ang - i_rad in_len = 240 sinx = cx - in_len*math.cos(in_ang) siny = cy - in_len*math.sin(in_ang) self.canvas.create_line(sinx, siny, cx, cy, fill="#ff3333", width=3) if self.is_specular.get(): # 镜面反射：r = i out_ang = normal_ang + i_rad out_len = 240 soutx = cx + out_len*math.cos(out_ang) souty = cy + out_len*math.sin(out_ang) self.canvas.create_line(cx, cy, soutx, souty, fill="#33ff33", width=3) else: # 漫反射：多条随机散开 import random for _ in range(12): dr = self.deg2rad(random.uniform(-35, 35)) out_ang = normal_ang + i_rad + dr out_len = 160 ox = cx + out_len*math.cos(out_ang) oy = cy + out_len*math.sin(out_ang) self.canvas.create_line(cx, cy, ox, oy, fill="#88ff88", width=2) self.info_label.config(text=f"入射角 i={i_deg:.1f}° , 反射角 r={i_deg:.1f}° , 镜面转角 α={alpha_deg:.1f}°｜镜转 α，反射光线转动 2α") def draw_prism(self): self.info_label.config(text="三棱镜色散：白光分解七色光，红光偏折最小，紫光最大") cx, cy = self.W//2, self.H//2 side = 180 pts = [] for idx in range(3): ang = self.deg2rad(30 + idx*120) x = cx + side*math.cos(ang) y = cy + side*math.sin(ang) pts.append((x,y)) self.canvas.create_polygon(pts, fill="#223344", outline="#88aacc", width=2) theta_in_deg = self.theta_i_var.get() theta_in = self.deg2rad(theta_in_deg) in_len = 260 sx = cx - in_len*math.cos(theta_in) sy = cy - in_len*math.sin(theta_in) self.canvas.create_line(sx, sy, cx, cy, fill="white", width=3) out_len = 360 for color, n in self.rainbow: tr = self.snell(theta_in, 1.0, n) if tr is None: continue dev = theta_in - tr out_ang = theta_in + dev * 1.35 ox = cx + out_len * math.cos(out_ang) oy = cy + out_len * math.sin(out_ang) self.canvas.create_line(cx, cy, ox, oy, fill=color, width=2) def draw_periscope(self): self.canvas.delete("all") self.info_label.config(text="潜望镜：光线两次镜面反射，方向不变") # 两个平面镜，45° L = 160 # 上镜面 x1, y1 = 220, 120 x2, y2 = 280, 180 self.canvas.create_line(x1,y1,x2,y2, fill="#dddddd", width=3) # 下镜面 x3, y3 = 220, 360 x4, y4 = 280, 420 self.canvas.create_line(x3,y3,x4,y4, fill="#dddddd", width=3) # 光路 self.canvas.create_line(120, 150, 250, 150, fill="#ff3333", width=3) self.canvas.create_line(250, 150, 250, 390, fill="#33ff33", width=3) self.canvas.create_line(250, 390, 380, 390, fill="#ffff33", width=3) def draw(self, *args): self.canvas.delete("all") m = self.mode.get() if m == "reflect": self.draw_reflect() elif m == "prism": self.draw_prism() if __name__ == "__main__": root = tk.Tk() app = OpticsSim(root) root.mainloop()