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一分钟带你get凸透镜成像规律~（BV1ut8MzwE1j）

MMRRlly
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@miorbaw7
此快照首次捕获于
2025/12/02 23:52
3 个月前
此快照最后确认于
2025/12/02 23:52
3 个月前
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原视频地址
源代码：
PYTHON
from manim import *
import math

import numpy as np
from scipy.optimize import fsolve

class Project(Scene):
    def construct(self):
        
        self.wait(1)
        
        xOy = NumberPlane(
            axis_config={
                "stroke_color": BLUE
            }
        )
        self.play(Write(xOy)) # 坐标纸
        self.wait(1)
        
        
        mirrowup = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(0, 3),
            color=WHITE,
            buff=0
        )
        mirrowdown = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(0, -3),
            color=WHITE,
            buff=0
        )
        self.play(FadeIn(mirrowup),FadeIn(mirrowdown)) # 凸透镜
        self.wait(1)
        
        
        custom_dotted_line = self.create_custom_dashed_line(
            start=LEFT * 7.35,
            end=RIGHT * 7.35,
            dash_length=0.2,
            dot_distance=0.3,
            color=YELLOW,
            stroke_width=3
        )

        self.play(FadeIn(custom_dotted_line)) # 主光轴
        self.wait(1)
        
        
        text1 = Text("F", font = "Consolas", font_size=36).move_to([-2, -0.25, 0])
        text2 = Text("F", font = "Consolas", font_size=36).move_to([2, 0.25, 0])
        text3 = Text("2F", font = "Consolas", font_size=36).move_to([-4, -0.25, 0])
        text4 = Text("2F", font = "Consolas", font_size=36).move_to([4, 0.25, 0])
        self.play(FadeIn(text1),FadeIn(text2),FadeIn(text3),FadeIn(text4)) # 焦距
        self.wait(1)
        
        # >2F

        obj = Arrow(
            start=xOy.c2p(-6, 0),
            end=xOy.c2p(-6, 2),
            color=RED,
            buff=0
        )
        self.play(FadeIn(obj))
        self.wait(1)
        
        line1 = Line(
            start=xOy.c2p(-6, 2),
            end=xOy.c2p(0, 0),
            stroke_width=3, 
            color=GRAY
        )
        light1 = Arrow(
            start=xOy.c2p(-6, 2),
            end=xOy.c2p(-3, 1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line2 = Line(
            start=xOy.c2p(-6, 2),
            end=xOy.c2p(0, 2),
            stroke_width=3, 
            color=GRAY
        )
        light2 = Arrow(
            start=xOy.c2p(-6, 2),
            end=xOy.c2p(-3, 2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line3 = Line(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(3, -1),
            stroke_width=3, 
            color=GRAY
        )
        light3 = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(1.5, -0.5),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line4 = Line(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(3, -1),
            stroke_width=3, 
            color=GRAY
        )
        light4 = Arrow(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(1.5, 0.5),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        self.play(Create(line1), GrowArrow(light1), Create(line2), GrowArrow(light2))
        self.wait(0.5)
        self.play(Create(line3), GrowArrow(light3), Create(line4), GrowArrow(light4))
        self.wait(1)
        pic = Arrow(
            start=xOy.c2p(3, 0),
            end=xOy.c2p(3, -1),
            color=RED,
            buff=0
        )
        self.play(FadeIn(pic))
        self.wait(3)
        
        self.play(
            FadeOut(line1),
            FadeOut(light1),
            FadeOut(line2),
            FadeOut(light2),
            FadeOut(line3),
            FadeOut(light3),
            FadeOut(line4),
            FadeOut(light4),
            FadeOut(pic),
        )
        self.wait(1)
        
        # 2F

        self.play(obj.animate.move_to(xOy.c2p(-4, 1)))
        self.wait(1)
        
        line1 = Line(
            start=xOy.c2p(-4, 2),
            end=xOy.c2p(0, 0),
            stroke_width=3, 
            color=GRAY
        )
        light1 = Arrow(
            start=xOy.c2p(-4, 2),
            end=xOy.c2p(-2, 1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line2 = Line(
            start=xOy.c2p(-4, 2),
            end=xOy.c2p(0, 2),
            stroke_width=3, 
            color=GRAY
        )
        light2 = Arrow(
            start=xOy.c2p(-4, 2),
            end=xOy.c2p(-2, 2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line3 = Line(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(4, -2),
            stroke_width=3, 
            color=GRAY
        )
        light3 = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(2, -1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line4 = Line(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(4, -2),
            stroke_width=3, 
            color=GRAY
        )
        light4 = Arrow(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(2, 0),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        self.play(Create(line1), GrowArrow(light1), Create(line2), GrowArrow(light2))
        self.wait(0.5)
        self.play(Create(line3), GrowArrow(light3), Create(line4), GrowArrow(light4))
        self.wait(1)
        pic = Arrow(
            start=xOy.c2p(4, 0),
            end=xOy.c2p(4, -2),
            color=RED,
            buff=0
        )
        self.play(FadeIn(pic))
        self.wait(3)
        
        self.play(
            FadeOut(line1),
            FadeOut(light1),
            FadeOut(line2),
            FadeOut(light2),
            FadeOut(line3),
            FadeOut(light3),
            FadeOut(line4),
            FadeOut(light4),
            FadeOut(pic),
        )
        
        # <2F >F

        self.play(obj.animate.move_to(xOy.c2p(-3, 1)))
        self.wait(1)
        
        line1 = Line(
            start=xOy.c2p(-3, 2),
            end=xOy.c2p(0, 0),
            stroke_width=3, 
            color=GRAY
        )
        light1 = Arrow(
            start=xOy.c2p(-3, 2),
            end=xOy.c2p(-1.5, 1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line2 = Line(
            start=xOy.c2p(-3, 2),
            end=xOy.c2p(0, 2),
            stroke_width=3, 
            color=GRAY
        )
        light2 = Arrow(
            start=xOy.c2p(-3, 2),
            end=xOy.c2p(-1.5, 2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line3 = Line(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(6, -4),
            stroke_width=3, 
            color=GRAY
        )
        light3 = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(3, -2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line4 = Line(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(6, -4),
            stroke_width=3, 
            color=GRAY
        )
        light4 = Arrow(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(3, -1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        self.play(Create(line1), GrowArrow(light1), Create(line2), GrowArrow(light2))
        self.wait(0.5)
        self.play(Create(line3), GrowArrow(light3), Create(line4), GrowArrow(light4))
        self.wait(1)
        pic = Arrow(
            start=xOy.c2p(6, 0),
            end=xOy.c2p(6, -4),
            color=RED,
            buff=0
        )
        self.play(FadeIn(pic))
        self.wait(3)
        
        self.play(
            FadeOut(line1),
            FadeOut(light1),
            FadeOut(line2),
            FadeOut(light2),
            FadeOut(line3),
            FadeOut(light3),
            FadeOut(line4),
            FadeOut(light4),
            FadeOut(pic),
        )
        
        # F

        self.play(obj.animate.move_to(xOy.c2p(-2, 1)))
        self.wait(1)
        
        line1 = Line(
            start=xOy.c2p(-2, 2),
            end=xOy.c2p(0, 0),
            stroke_width=3, 
            color=GRAY
        )
        light1 = Arrow(
            start=xOy.c2p(-2, 2),
            end=xOy.c2p(-1, 1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line2 = Line(
            start=xOy.c2p(-2, 2),
            end=xOy.c2p(0, 2),
            stroke_width=3, 
            color=GRAY
        )
        light2 = Arrow(
            start=xOy.c2p(-2, 2),
            end=xOy.c2p(-1, 2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line3 = Line(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(4, -4),
            stroke_width=3, 
            color=GRAY
        )
        light3 = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(2, -2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line4 = Line(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(6, -4),
            stroke_width=3, 
            color=GRAY
        )
        light4 = Arrow(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(3, -1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        self.play(Create(line1), GrowArrow(light1), Create(line2), GrowArrow(light2))
        self.wait(0.5)
        self.play(Create(line3), GrowArrow(light3), Create(line4), GrowArrow(light4))
        self.wait(3)
        
        self.play(
            FadeOut(line1),
            FadeOut(light1),
            FadeOut(line2),
            FadeOut(light2),
            FadeOut(line3),
            FadeOut(light3),
            FadeOut(line4),
            FadeOut(light4),
        )
        
        # <F

        self.play(obj.animate.move_to(xOy.c2p(-1, 1)))
        self.wait(1)
        
        line1 = Line(
            start=xOy.c2p(-1, 2),
            end=xOy.c2p(0, 0),
            stroke_width=3, 
            color=GRAY
        )
        light1 = Arrow(
            start=xOy.c2p(-1, 2),
            end=xOy.c2p(-0.5, 1),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line2 = Line(
            start=xOy.c2p(-1, 2),
            end=xOy.c2p(0, 2),
            stroke_width=3, 
            color=GRAY
        )
        light2 = Arrow(
            start=xOy.c2p(-1, 2),
            end=xOy.c2p(-0.5, 2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line3 = Line(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(2, -4),
            stroke_width=3, 
            color=GRAY
        )
        light3 = Arrow(
            start=xOy.c2p(0, 0),
            end=xOy.c2p(1, -2),
            stroke_width=3, 
            color=GRAY,
            buff=0
        )
        line4 = Line(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(6, -4),
            stroke_width=3, 
            color=GRAY
        )
        light4 = Arrow(
            start=xOy.c2p(0, 2),
            end=xOy.c2p(3, -1),
            stroke_width=3, 
            color=GRAY,
            buff=0,
        )
        self.play(Create(line1), GrowArrow(light1), Create(line2), GrowArrow(light2))
        self.wait(0.5)
        self.play(Create(line3), GrowArrow(light3), Create(line4), GrowArrow(light4))
        self.wait(1)
        f3 = DashedVMobject(
            Line(
                start=xOy.c2p(-1, 2),
                end=xOy.c2p(-2, 4),
                color=GRAY
            ),
            num_dashes=10,
            dashed_ratio=0.5
        )
        f4 = DashedVMobject(
            Line(
                start=xOy.c2p(0, 2),
                end=xOy.c2p(-2, 4),
                color=GRAY
            ),
            num_dashes=10,
            dashed_ratio=0.5
        )
        self.play(Create(f3), Create(f4))
        pic = DashedVMobject(
            Arrow(
                start=xOy.c2p(-2, 0),
                end=xOy.c2p(-2, 4),
                color=RED,
                buff=0
            ),
            num_dashes=10,
            dashed_ratio=0.5
        )
        self.play(FadeIn(pic))
        self.wait(3)
        
        self.play(
            FadeOut(line1),
            FadeOut(light1),
            FadeOut(line2),
            FadeOut(light2),
            FadeOut(line3),
            FadeOut(light3),
            FadeOut(line4),
            FadeOut(light4),
            FadeOut(pic),
            FadeOut(f3),
            FadeOut(f4),
            FadeOut(xOy),
            FadeOut(custom_dotted_line),
            FadeOut(mirrowup),
            FadeOut(mirrowdown),
            FadeOut(text1),
            FadeOut(text2),
            FadeOut(text3),
            FadeOut(text4),
            FadeOut(obj)
        )
        
        self.wait(1)
        
        text = Text("谢谢观看", color=WHITE)
        
        self.play(FadeIn(text))
        self.wait(2)
        self.play(FadeOut(text))
        self.wait(1)

    def create_custom_dashed_line(self, start, end, dash_length, dot_distance, color, stroke_width):
        direction = (end - start)
        length = np.linalg.norm(direction)
        unit_vector = direction / length if length > 0 else direction

        total_segments = int((length) // (dash_length + dot_distance))
        vgroup = VGroup()

        current_point = start.copy()

        for _ in range(total_segments):
            dash_end = current_point + unit_vector * dash_length
            dash = Line(current_point, dash_end, color=color, stroke_width=stroke_width)
            vgroup.add(dash)
            current_point = dash_end

            dot_point = current_point + unit_vector * (dot_distance / 2)
            dot = Dot(point=dot_point, radius=0.04, color=color)
            vgroup.add(dot)
            current_point = dot_point + unit_vector * (dot_distance / 2)

        return vgroup

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