[{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-001","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":1,"stem":"A light ray strikes a mirror with an angle of incidence $i = 30^{\\circ}$. By the law of reflection, what is the angle of reflection?","stemZh":"一束光以入射角 $i=30^{\\circ}$ 射到镜面，根据反射定律，反射角是多少？","options":[{"id":"A","text":"$60^{\\circ}$"},{"id":"B","text":"$90^{\\circ}$"},{"id":"C","text":"$30^{\\circ}$"},{"id":"D","text":"$0^{\\circ}$"}],"answer":"C","explanation":"The law of reflection states the angle of reflection equals the angle of incidence: i' $= i = 30^{\\circ}$.","explanationZh":"反射定律：反射角等于入射角，即 $i'=i=30^{\\circ}。$","tags":["basic","reflection-refraction","reflection"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-002","images":[{"src":"/physics/diagrams/refraction-ray.svg","alt":"Ray of light entering glass from air, bending toward the $normal; n_air \\sin i = n_glass \\sin$ r.","altZh":"光从空气进入玻璃，向法线偏折；满足 n_空气 \\sin i = n_玻璃 \\sin r。"}],"moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":1,"stem":"Light in air $(n_1 = 1.0)$ enters glass $(n_2 = 1.5)$ at an angle of incidence $i = 30^{\\circ}$. Find the angle of refraction r.","stemZh":"$光从空气（n_1=1.0）射入玻璃（n_2=1.5），入射角 i=30^{\\circ}，求折射角$ r。","options":[{"id":"A","text":"$30^{\\circ}$"},{"id":"B","text":"$45^{\\circ}$"},{"id":"C","text":"$15^{\\circ}$"},{"id":"D","text":"$20^{\\circ}$"}],"answer":"D","explanation":"Snell's $law: n_1\\sin i = n_2\\sin r \\Rightarrow \\sin r = \\dfrac{1.0}{1.5}\\sin 30^{\\circ} = 0.333$, so $r \\approx 19.5^{\\circ} \\approx 20^{\\circ}$.","explanationZh":"$折射定律：n_1\\sin i=n_2\\sin r\\Rightarrow\\sin r=\\dfrac{1.0}{1.5}\\sin30^{\\circ}=0.333，故 r\\approx19.5^{\\circ}\\approx20^{\\circ}。$","tags":["basic","reflection-refraction","snell"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-003","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":1,"stem":"The speed of light in a medium is $v = 2.0 \\times 10^{8}\\ \\mathrm{m/s} (c = 3.0 \\times 10^{8}\\ \\mathrm{m/s})$. What is the refractive index n?","stemZh":"光在介质中的速度 $v=2.0\\times10^{8}\\ \\mathrm{m/s}（c=3.0\\times10^{8}\\ \\mathrm{m/s}），折射率 n$ 为多少？","options":[{"id":"A","text":"1.5"},{"id":"B","text":"0.67"},{"id":"C","text":"2.0"},{"id":"D","text":"1.0"}],"answer":"A","explanation":"Refractive index $n = \\dfrac{c}{v} = \\dfrac{3.0 \\times 10^{8}}{2.0 \\times 10^{8}} = 1.5$.","explanationZh":"折射率 $n=\\dfrac{c}{v}=\\dfrac{3.0\\times10^{8}}{2.0\\times10^{8}}=1.5。$","tags":["basic","reflection-refraction","refractive-index"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-004","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":2,"stem":"Glass has refractive index $n = 1.5$. What is the speed of light inside it?","stemZh":"玻璃折射率 $n=1.5，光在其中的传播速度是多少？$","options":[{"id":"A","text":"$4.5 \\times 10^{8}\\ \\mathrm{m/s}$"},{"id":"B","text":"$2.0 \\times 10^{8}\\ \\mathrm{m/s}$"},{"id":"C","text":"$1.5 \\times 10^{8}\\ \\mathrm{m/s}$"},{"id":"D","text":"$3.0 \\times 10^{8}\\ \\mathrm{m/s}$"}],"answer":"B","explanation":"$v = \\dfrac{c}{n} = \\dfrac{3.0 \\times 10^{8}}{1.5} = 2.0 \\times 10^{8}\\ \\mathrm{m/s}$.","explanationZh":"$v=\\dfrac{c}{n}=\\dfrac{3.0\\times10^{8}}{1.5}=2.0\\times10^{8}\\ \\mathrm{m/s}。$","tags":["basic","reflection-refraction","speed-in-medium"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-005","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":2,"stem":"Light goes from water $(n_1 = 1.33)$ into air $(n_2 = 1.0)$ at $i = 30^{\\circ}$. Find the angle of refraction r.","stemZh":"$光从水（n_1=1.33）射入空气（n_2=1.0），入射角 i=30^{\\circ}，求折射角$ r。","options":[{"id":"A","text":"$22^{\\circ}$"},{"id":"B","text":"$30^{\\circ}$"},{"id":"C","text":"$42^{\\circ}$"},{"id":"D","text":"$48^{\\circ}$"}],"answer":"C","explanation":"$\\sin r = \\dfrac{n_1}{n_2}\\sin i = \\dfrac{1.33}{1.0}\\sin 30^{\\circ} = 0.665$, so $r \\approx 41.7^{\\circ} \\approx 42^{\\circ}$.","explanationZh":"$\\sin r=\\dfrac{n_1}{n_2}\\sin i=\\dfrac{1.33}{1.0}\\sin30^{\\circ}=0.665，故 r\\approx41.7^{\\circ}\\approx42^{\\circ}。$","tags":["basic","reflection-refraction","snell"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-006","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":3,"stem":"Light in air $(n_1 = 1.0)$ enters glass $(n_2 = 1.5)$ at $i = 60^{\\circ}$. Find r.","stemZh":"$光从空气（n_1=1.0）射入玻璃（n_2=1.5），入射角 i=60^{\\circ}，求$ r。","options":[{"id":"A","text":"$60^{\\circ}$"},{"id":"B","text":"$40^{\\circ}$"},{"id":"C","text":"$30^{\\circ}$"},{"id":"D","text":"$35^{\\circ}$"}],"answer":"D","explanation":"$\\sin r = \\dfrac{1.0}{1.5}\\sin 60^{\\circ} = 0.6667 \\times 0.8660 = 0.577$, so $r \\approx 35.3^{\\circ} \\approx 35^{\\circ}$.","explanationZh":"$\\sin r=\\dfrac{1.0}{1.5}\\sin60^{\\circ}=0.6667\\times0.8660=0.577，故 r\\approx35.3^{\\circ}\\approx35^{\\circ}。$","tags":["applied","reflection-refraction","snell"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-007","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":3,"stem":"Light takes $t = 2.0 \\times 10^{-11}\\ \\mathrm{s}$ to cross a slab of thickness $d = 3.0 \\times 10^{-3}\\ \\mathrm{m}$. What is the refractive index $(c = 3.0 \\times 10^{8}\\ \\mathrm{m/s})$?","stemZh":"光穿过厚度 $d=3.0\\times10^{-3}\\ \\mathrm{m}$ 的平板耗时 $t=2.0\\times10^{-11}\\ \\mathrm{s}，折射率是多少（c=3.0\\times10^{8}\\ \\mathrm{m/s}）？$","options":[{"id":"A","text":"2.0"},{"id":"B","text":"1.0"},{"id":"C","text":"1.5"},{"id":"D","text":"0.5"}],"answer":"A","explanation":"$v = \\dfrac{d}{t} = \\dfrac{3.0 \\times 10^{-3}}{2.0 \\times 10^{-11}} = 1.5 \\times 10^{8}\\ \\mathrm{m/s}$, so $n = \\dfrac{c}{v} = \\dfrac{3.0 \\times 10^{8}}{1.5 \\times 10^{8}} = 2.0$.","explanationZh":"$v=\\dfrac{d}{t}=\\dfrac{3.0\\times10^{-3}}{2.0\\times10^{-11}}=1.5\\times10^{8}\\ \\mathrm{m/s}，故 n=\\dfrac{c}{v}=\\dfrac{3.0\\times10^{8}}{1.5\\times10^{8}}=2.0。$","tags":["applied","reflection-refraction","refractive-index","speed"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-008","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":3,"stem":"A ray strikes a mirror at an angle of incidence of $40^{\\circ}$. What is the angle between the incident ray and the reflected ray?","stemZh":"光线以入射角 $40^{\\circ}$ 射到镜面，入射光线与反射光线之间的夹角是多少？","options":[{"id":"A","text":"$40^{\\circ}$"},{"id":"B","text":"$80^{\\circ}$"},{"id":"C","text":"$50^{\\circ}$"},{"id":"D","text":"$140^{\\circ}$"}],"answer":"B","explanation":"Both rays make $40^{\\circ}$ with the normal, on opposite sides, so the angle between them is $40^{\\circ} + 40^{\\circ} = 80^{\\circ}$.","explanationZh":"两光线分别在法线两侧与法线成 $40^{\\circ}，故二者夹角为 40^{\\circ}+40^{\\circ}=80^{\\circ}。$","tags":["applied","reflection-refraction","reflection","angle-between"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-009","images":[{"src":"/physics/diagrams/refraction-ray.svg","alt":"Ray leaving glass into air, bending away from the $normal; n_glass \\sin i = n_air \\sin$ r.","altZh":"光从玻璃射向空气，偏离法线；满足 n_玻璃 \\sin i = n_空气 \\sin r。"}],"moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":3,"stem":"Light in glass $(n_1 = 1.5)$ strikes a glass–air boundary at $i = 37^{\\circ} (the\\text{ critical angle for glass is about }42^{\\circ})$. Find r in air $(n_2 = 1.0)$.","stemZh":"$光在玻璃（n_1=1.5）中以 i=37^{\\circ}$ 射向玻璃–空气界面（玻璃临界角约 $42^{\\circ}），求在空气中的折射角 r（n_2=1.0）。$","options":[{"id":"A","text":"$37^{\\circ}$"},{"id":"B","text":"$45^{\\circ}$"},{"id":"C","text":"$64^{\\circ}$"},{"id":"D","text":"$90^{\\circ}$"}],"answer":"C","explanation":"$\\sin r = \\dfrac{1.5}{1.0}\\sin 37^{\\circ} \\approx 1.5 \\times 0.60 = 0.90$, so $r \\approx 64^{\\circ} (since 37^{\\circ} < 42^{\\circ},\\text{ refraction }occurs)$.","explanationZh":"$\\sin r=\\dfrac{1.5}{1.0}\\sin37^{\\circ}\\approx1.5\\times0.60=0.90，故 r\\approx64^{\\circ}（因 37^{\\circ}<42^{\\circ}，发生折射）。$","tags":["applied","reflection-refraction","snell"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-010","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":3,"stem":"Monochromatic light of wavelength $\\lambda_0 = 600\\ \\mathrm{nm}$ in air enters glass with $n = 1.5$. What is its wavelength in the glass?","stemZh":"真空中波长 $\\lambda_0=600\\ \\mathrm{nm}$ 的单色光进入折射率 $n=1.5$ 的玻璃，在玻璃中的波长是多少？","options":[{"id":"A","text":"$900\\ \\mathrm{nm}$"},{"id":"B","text":"$600\\ \\mathrm{nm}$"},{"id":"C","text":"$300\\ \\mathrm{nm}$"},{"id":"D","text":"$400\\ \\mathrm{nm}$"}],"answer":"D","explanation":"Frequency is unchanged; wavelength shortens by the refractive $index: \\lambda = \\dfrac{\\lambda_0}{n} = \\dfrac{600}{1.5} = 400\\ \\mathrm{nm}$.","explanationZh":"$频率不变，波长按折射率缩短：\\lambda=\\dfrac{\\lambda_0}{n}=\\dfrac{600}{1.5}=400\\ \\mathrm{nm}。$","tags":["applied","reflection-refraction","wavelength","medium"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-011","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":4,"stem":"A student writes Snell's law as $n_1\\sin i = n_2\\sin r and$, for light going from air into glass, uses $n_1 = 1.5, n_2 = 1.0$. What is the error?","stemZh":"某学生把折射定律写成 $n_1\\sin i=n_2\\sin r，并用于空气→玻璃时取 n_1=1.5、n_2=1.0，错在哪里？$","options":[{"id":"A","text":"They swapped $n_1$ and $n_2$; air is the incident medium so $n_1 = 1.0$, glass is $n_2 = 1.5$"},{"id":"B","text":"They used the wrong formula"},{"id":"C","text":"Angles must be measured from the surface, not the normal"},{"id":"D","text":"There is nothing wrong"}],"optionsZh":[{"id":"A","text":"他们把 $n_1 与 n_2$ 颠倒了；空气是入射介质，应 $n_1=1.0、玻璃 n_2=1.5$"},{"id":"B","text":"公式用错了"},{"id":"C","text":"角度应从界面而非法线起算"},{"id":"D","text":"没有问题"}],"answer":"A","explanation":"In Snell's law $n_1$ is the refractive index of the incident medium. $Air→glass$ means $n_1 = 1.0 (air), n_2 = 1.5 (glass)$. Swapping them gives the wrong angle.","explanationZh":"折射定律中 $n_1 是入射介质的折射率。空气→玻璃应 n_1=1.0（空气）、n_2=1.5（玻璃）。颠倒两者会得到错误角度。$","tags":["trap","reflection-refraction","snell","n-order"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-012","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":4,"stem":"A ray meets a mirror making an angle of $60^{\\circ}$ with the mirror surface. What is the angle of reflection (measured from the normal)?","stemZh":"光线与镜面成 $60^{\\circ}$ 夹角入射，反射角（相对于法线）是多少？","options":[{"id":"A","text":"$60^{\\circ}$"},{"id":"B","text":"$30^{\\circ}$"},{"id":"C","text":"$120^{\\circ}$"},{"id":"D","text":"$90^{\\circ}$"}],"answer":"B","explanation":"The angle with the surface is $60^{\\circ}$, so the angle of incidence from the normal is $90^{\\circ} - 60^{\\circ} = 30^{\\circ}$. Reflection equals $incidence: 30^{\\circ}$ from the normal.","explanationZh":"与镜面夹角为 $60^{\\circ}，故相对法线的入射角为 90^{\\circ}-60^{\\circ}=30^{\\circ}。反射角等于入射角：相对法线 30^{\\circ}。$","tags":["trap","reflection-refraction","reflection","surface-vs-normal"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-013","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":4,"stem":"Light travels from air $(n = 1.0)$ into water $(n = 1.33)$. How does the refracted ray behave relative to the normal?","stemZh":"$光从空气（n=1.0）进入水（n=1.33），折射光线相对法线如何偏折？$","options":[{"id":"A","text":"Away from the normal"},{"id":"B","text":"It does not refract"},{"id":"C","text":"Toward the normal"},{"id":"D","text":"Back along the incident ray"}],"optionsZh":[{"id":"A","text":"偏离法线"},{"id":"B","text":"不发生折射"},{"id":"C","text":"偏向法线"},{"id":"D","text":"沿原入射光线返回"}],"answer":"C","explanation":"Entering a denser $(higher-n) medium$, the ray slows and bends toward the normal, so the angle of refraction is smaller than the angle of incidence.","explanationZh":"进入折射率更大的介质时，光速变慢，光线偏向法线，折射角小于入射角。","tags":["trap","reflection-refraction","bending","denser"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-014","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":5,"stem":"A ray enters a glass block $(n = 1.5) normally$, hitting the surface at $i = 0^{\\circ} (along\\text{ the }normal)$. What happens to its direction?","stemZh":"$光线垂直射入玻璃块（n=1.5），即沿法线以 i=0^{\\circ}$ 入射，其方向如何变化？","options":[{"id":"A","text":"It bends toward the normal"},{"id":"B","text":"$30^{\\circ}$"},{"id":"C","text":"It reflects back"},{"id":"D","text":"$0^{\\circ} —$ no bending"}],"answer":"D","explanation":"Normal incidence means $i = 0^{\\circ}$, so $\\sin r = \\dfrac{n_1}{n_2}\\sin 0^{\\circ} = 0$ and $r = 0^{\\circ}$. The ray passes straight through without bending (it does slow down, but direction is unchanged).","explanationZh":"正入射即 $i=0^{\\circ}，故 \\sin r=\\dfrac{n_1}{n_2}\\sin0^{\\circ}=0，r=0^{\\circ}。光线直线穿过不偏折（速度会变慢，但方向不变）。$","tags":["trap","reflection-refraction","normal-incidence","no-bend"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-reflection-refraction-015","moduleId":"optics","unitId":"geometric-optics","topicId":"reflection-refraction","difficulty":5,"stem":"Light in water $(n_1 = 1.33)$ strikes a water–air boundary at $i = 30^{\\circ} (water's\\text{ critical angle is about }49^{\\circ})$. Find r in air $(n_2 = 1.0)$.","stemZh":"$光在水（n_1=1.33）中以 i=30^{\\circ}$ 射向水–空气界面（水的临界角约 $49^{\\circ}），求在空气中的 r（n_2=1.0）。$","options":[{"id":"A","text":"$42^{\\circ}$"},{"id":"B","text":"$48^{\\circ}$"},{"id":"C","text":"Total internal reflection"},{"id":"D","text":"$30^{\\circ}$"}],"answer":"A","explanation":"$\\sin r = \\dfrac{1.33}{1.0}\\sin 30^{\\circ} = 0.665$, so $r \\approx 41.7^{\\circ} \\approx 42^{\\circ}$. Since $i = 30^{\\circ} < 49^{\\circ}$, refraction occurs — total internal reflection does NOT apply here.","explanationZh":"$\\sin r=\\dfrac{1.33}{1.0}\\sin30^{\\circ}=0.665，故 r\\approx41.7^{\\circ}\\approx42^{\\circ}。因 i=30^{\\circ}<49^{\\circ}$ 发生折射，此处不适用全反射。","tags":["trap","reflection-refraction","snell","no-tir-here"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-001","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":1,"stem":"For total internal reflection to occur, light must travel from the optically denser medium to the less dense one. Which setup allows it?","stemZh":"要发生全反射，光必须从光密介质射向光疏介质。下列哪种情形可以发生？","options":[{"id":"A","text":"air $(n = 1.0) →$ glass $(n = 1.5)$"},{"id":"B","text":"glass $(n = 1.5) →$ air $(n = 1.0)$"},{"id":"C","text":"air $→$ water $(n = 1.33)$"},{"id":"D","text":"water $→$ glass"}],"optionsZh":[{"id":"A","text":"$空气（n=1.0）→ 玻璃（n=1.5）$"},{"id":"B","text":"$玻璃（n=1.5）→ 空气（n=1.0）$"},{"id":"C","text":"空气 $→ 水（n=1.33）$"},{"id":"D","text":"$水 →$ 玻璃"}],"answer":"B","explanation":"Total internal reflection requires starting in the higher-index (denser) medium: glass $(1.5)$ to air $(1.0)$, with the incidence angle above the critical angle.","explanationZh":"全反射要求从折射率较大的介质（光密）出发：玻璃（1.5）到空气（1.0），且入射角大于临界角。","tags":["basic","total-internal-reflection","condition"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-002","images":[{"src":"/physics/diagrams/critical-angle.svg","alt":"Critical angle $θc$ at a glass–air $boundary: \\sin θc = n_air / n_glass$; beyond $θc$ the ray is totally reflected.","altZh":"玻璃–空气界面的临界角 θc：\\sin θc = n_空气 / n_玻璃；超过 θc 光线发生全反射。"}],"moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":1,"stem":"For light going from glass $(n_1 = 1.5)$ to air $(n_2 = 1.0)$, the critical angle satisfies $\\sin\\theta_c = \\dfrac{n_2}{n_1}$. Find $\\theta_c$.","stemZh":"$光从玻璃（n_1=1.5）到空气（n_2=1.0），临界角满足 \\sin\\theta_c=\\dfrac{n_2}{n_1}，求 \\theta_c。$","options":[{"id":"A","text":"$48^{\\circ}$"},{"id":"B","text":"$60^{\\circ}$"},{"id":"C","text":"$42^{\\circ}$"},{"id":"D","text":"$90^{\\circ}$"}],"answer":"C","explanation":"$\\sin\\theta_c = \\dfrac{1.0}{1.5} = 0.667$, so $\\theta_c = \\arcsin(0.667) \\approx 41.8^{\\circ} \\approx 42^{\\circ}$.","explanationZh":"$\\sin\\theta_c=\\dfrac{1.0}{1.5}=0.667，故 \\theta_c=\\arcsin(0.667)\\approx41.8^{\\circ}\\approx42^{\\circ}。$","tags":["basic","total-internal-reflection","critical-angle"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-003","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":1,"stem":"At a glass–air boundary, the critical angle is $42^{\\circ}. A$ ray inside the glass strikes the boundary at $i = 30^{\\circ}$. What happens?","stemZh":"在玻璃–空气界面，临界角为 $42^{\\circ}。玻璃内的光线以 i=30^{\\circ}$ 射向界面，会发生什么？","options":[{"id":"A","text":"Total internal reflection"},{"id":"B","text":"No light emerges"},{"id":"C","text":"It reflects completely"},{"id":"D","text":"It refracts into the air"}],"optionsZh":[{"id":"A","text":"全反射"},{"id":"B","text":"没有光射出"},{"id":"C","text":"完全反射"},{"id":"D","text":"折射进入空气"}],"answer":"D","explanation":"Total internal reflection only occurs when $i > \\theta_c$. Here $30^{\\circ} < 42^{\\circ}$, so the ray refracts into the air.","explanationZh":"全反射只在 $i>\\theta_c$ 时发生。此处 $30^{\\circ}<42^{\\circ}，故光线折射进入空气。$","tags":["basic","total-internal-reflection","below-critical"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-004","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":2,"stem":"Find the critical angle for light going from water $(n_1 = 1.33)$ to air $(n_2 = 1.0)$.","stemZh":"$求光从水（n_1=1.33）到空气（n_2=1.0）的临界角。$","options":[{"id":"A","text":"$49^{\\circ}$"},{"id":"B","text":"$41^{\\circ}$"},{"id":"C","text":"$60^{\\circ}$"},{"id":"D","text":"$30^{\\circ}$"}],"answer":"A","explanation":"$\\sin\\theta_c = \\dfrac{1.0}{1.33} = 0.752$, so $\\theta_c = \\arcsin(0.752) \\approx 48.8^{\\circ} \\approx 49^{\\circ}$.","explanationZh":"$\\sin\\theta_c=\\dfrac{1.0}{1.33}=0.752，故 \\theta_c=\\arcsin(0.752)\\approx48.8^{\\circ}\\approx49^{\\circ}。$","tags":["basic","total-internal-reflection","critical-angle"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-005","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":2,"stem":"At a glass–air boundary the critical angle is $42^{\\circ}. A$ ray inside the glass strikes at $i = 50^{\\circ}$. What happens?","stemZh":"玻璃–空气界面临界角为 $42^{\\circ}。玻璃内光线以 i=50^{\\circ}$ 入射，会发生什么？","options":[{"id":"A","text":"It refracts"},{"id":"B","text":"Total internal reflection occurs"},{"id":"C","text":"It stops"},{"id":"D","text":"It reflects only partially"}],"optionsZh":[{"id":"A","text":"折射"},{"id":"B","text":"发生全反射"},{"id":"C","text":"停止"},{"id":"D","text":"仅部分反射"}],"answer":"B","explanation":"Since $i = 50^{\\circ} > \\theta_c = 42^{\\circ}$, the conditions for total internal reflection are met and the ray is completely reflected.","explanationZh":"$因 i=50^{\\circ}>\\theta_c=42^{\\circ}，满足全反射条件，光线被完全反射。$","tags":["basic","total-internal-reflection","above-critical"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-006","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":3,"stem":"Light goes from a medium of $n_1 = 1.4$ to air $(n_2 = 1.0)$. Find the critical angle $\\theta_c$.","stemZh":"光从折射率 $n_1=1.4 的介质到空气（n_2=1.0），求临界角 \\theta_c。$","options":[{"id":"A","text":"$44^{\\circ}$"},{"id":"B","text":"$60^{\\circ}$"},{"id":"C","text":"$46^{\\circ}$"},{"id":"D","text":"$35^{\\circ}$"}],"answer":"C","explanation":"$\\sin\\theta_c = \\dfrac{1.0}{1.4} = 0.714$, so $\\theta_c = \\arcsin(0.714) \\approx 45.6^{\\circ} \\approx 46^{\\circ}$.","explanationZh":"$\\sin\\theta_c=\\dfrac{1.0}{1.4}=0.714，故 \\theta_c=\\arcsin(0.714)\\approx45.6^{\\circ}\\approx46^{\\circ}。$","tags":["applied","total-internal-reflection","critical-angle"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-007","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":3,"stem":"An optical fibre guides light by repeated total internal reflection at the core–cladding boundary. Which statement is correct?","stemZh":"光纤利用纤芯–包层界面上的多次全反射来传导光。下列说法正确的是？","options":[{"id":"A","text":"Light escapes at every bounce"},{"id":"B","text":"The cladding has a higher n than the core"},{"id":"C","text":"TIR requires going from less dense to denser"},{"id":"D","text":"Light is trapped by repeated TIR because the core is denser than the cladding"}],"optionsZh":[{"id":"A","text":"光在每次反射时都会逸出"},{"id":"B","text":"包层的折射率比纤芯高"},{"id":"C","text":"全反射要求从光疏介质射向光密介质"},{"id":"D","text":"由于纤芯比包层更光密，光被多次全反射约束在纤芯内"}],"answer":"D","explanation":"TIR needs the ray to start in the denser medium $(core$, higher n) striking the less dense cladding (lower n) above the critical angle, so light stays trapped in the core.","explanationZh":"全反射要求光线从光密介质（纤芯，较大 n）射向光疏介质（包层，较小 n）且入射角大于临界角，因此光被约束在纤芯内。","tags":["applied","total-internal-reflection","optical-fibre"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-008","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":3,"stem":"In a fibre, light in the core $(n_2 = 1.5,\\text{ the }cladding)$ has a critical angle of $60^{\\circ}$ with the cladding. Find the core's refractive index $n_1 (n_2 = 1.5)$.","stemZh":"某光纤中，纤芯到包层的临界角为 $60^{\\circ}（包层 n_2=1.5），求纤芯折射率 n_1。$","options":[{"id":"A","text":"1.73"},{"id":"B","text":"1.50"},{"id":"C","text":"1.30"},{"id":"D","text":"2.00"}],"answer":"A","explanation":"$\\sin\\theta_c = \\dfrac{n_2}{n_1} \\Rightarrow n_1 = \\dfrac{n_2}{\\sin\\theta_c} = \\dfrac{1.5}{\\sin 60^{\\circ}} = \\dfrac{1.5}{0.866} \\approx 1.73$.","explanationZh":"$\\sin\\theta_c=\\dfrac{n_2}{n_1}\\Rightarrow n_1=\\dfrac{n_2}{\\sin\\theta_c}=\\dfrac{1.5}{\\sin60^{\\circ}}=\\dfrac{1.5}{0.866}\\approx1.73。$","tags":["applied","total-internal-reflection","critical-angle","fibre"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-009","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":3,"stem":"For glass $(n_1 = 1.5)$ to air $(n_2 = 1.0)$, the critical angle is $42^{\\circ}$. When does total internal reflection occur?","stemZh":"$玻璃（n_1=1.5）到空气（n_2=1.0）的临界角为 42^{\\circ}。何时发生全反射？$","options":[{"id":"A","text":"$i < 42^{\\circ}$"},{"id":"B","text":"$i > 42^{\\circ}$"},{"id":"C","text":"$i = 42^{\\circ}$ only"},{"id":"D","text":"For all angles"}],"answer":"B","explanation":"TIR occurs only when the incidence angle exceeds the critical $angle: i > \\theta_c = 42^{\\circ}$.","explanationZh":"全反射只在入射角大于临界角时发生，即 $i>\\theta_c=42^{\\circ}。$","tags":["applied","total-internal-reflection","condition"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-010","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":3,"stem":"Diamond has $n = 2.42$. Find its critical angle for light going to air $(n = 1.0)$.","stemZh":"钻石折射率 $n=2.42，求光从钻石到空气（n=1.0）的临界角。$","options":[{"id":"A","text":"$48^{\\circ}$"},{"id":"B","text":"$90^{\\circ}$"},{"id":"C","text":"$24^{\\circ}$"},{"id":"D","text":"$66^{\\circ}$"}],"answer":"C","explanation":"$\\sin\\theta_c = \\dfrac{1.0}{2.42} = 0.413$, so $\\theta_c = \\arcsin(0.413) \\approx 24.4^{\\circ} \\approx 24^{\\circ} —$ the small angle gives diamond its sparkle.","explanationZh":"$\\sin\\theta_c=\\dfrac{1.0}{2.42}=0.413，故 \\theta_c=\\arcsin(0.413)\\approx24.4^{\\circ}\\approx24^{\\circ}；小的临界角使钻石更闪耀。$","tags":["applied","total-internal-reflection","critical-angle","diamond"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-011","images":[{"src":"/physics/diagrams/critical-angle.svg","alt":"At a glass–air boundary, TIR only happens for rays starting in the glass with $i > θc; air→glass$ cannot give TIR.","altZh":"玻璃–空气界面，只有从玻璃出发且 i > θc 的光线才会全反射；空气→玻璃不可能发生全反射。"}],"moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":4,"stem":"A student says total internal reflection happens when light goes from air into water, 'because water has a larger refractive index.' What is wrong?","stemZh":"有学生说，当光从空气进入水中时会全反射，“因为水的折射率更大”。错在哪里？","options":[{"id":"A","text":"TIR has nothing to do with refractive index"},{"id":"B","text":"Water has the lower refractive index"},{"id":"C","text":"TIR needs the ray to start in the lower-n medium"},{"id":"D","text":"TIR needs the ray to start in the higher-n (denser) medium with $i > \\theta_c$"}],"optionsZh":[{"id":"A","text":"全反射与折射率无关"},{"id":"B","text":"水的折射率较小"},{"id":"C","text":"全反射要求光线从较小 n 的介质出发"},{"id":"D","text":"全反射要求光线从较大 n（光密）介质出发，且 $i>\\theta_c$"}],"answer":"D","explanation":"$Air→water$ goes from the LESS dense to the MORE dense medium, so TIR cannot occur. TIR requires starting in the denser medium (higher n) with incidence above the critical angle.","explanationZh":"$空气→水是从光疏到光密，不可能全反射。全反射要求从光密（较大$ n）介质出发且入射角大于临界角。","tags":["trap","total-internal-reflection","condition","direction"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-012","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":4,"stem":"A student computes the critical angle as $\\theta_c = \\arcsin\\!\\left(\\dfrac{n_1}{n_2}\\right)$ with $n_1 > n_2$, getting $\\arcsin(1.5)$, which is impossible. What is the correct formula?","stemZh":"某学生把临界角算成 $\\theta_c=\\arcsin\\!\\left(\\dfrac{n_1}{n_2}\\right)（n_1>n_2），得到 \\arcsin(1.5)$ 无意义。正确公式是什么？","options":[{"id":"A","text":"$\\sin\\theta_c = \\dfrac{n_2}{n_1}$ with $n_1 > n_2$"},{"id":"B","text":"$\\sin\\theta_c = \\dfrac{n_1}{n_2}$"},{"id":"C","text":"$\\theta_c = \\dfrac{n_1 - n_2}{n_1}$"},{"id":"D","text":"$\\sin\\theta_c = n_1 n_2$"}],"answer":"A","explanation":"The ratio must be less than 1, so $\\sin\\theta_c = \\dfrac{n_2}{n_1}$ where the incident (denser) medium is $n_1$ and the other is $n_2 < n_1$.","explanationZh":"比值必须小于 $1，故 \\sin\\theta_c=\\dfrac{n_2}{n_1}，其中入射（光密）介质为 n_1，另一介质 n_2 \\theta_c$"},{"id":"C","text":"No light refracts at $i = \\theta_c$"},{"id":"D","text":"The ray is absorbed"}],"optionsZh":[{"id":"A","text":"仅在 $i=\\theta_c$ 时发生全反射"},{"id":"B","text":"$i<\\theta_c 时折射；i>\\theta_c$ 时才全反射"},{"id":"C","text":"$i=\\theta_c$ 时无光折射"},{"id":"D","text":"光线被吸收"}],"answer":"B","explanation":"TIR begins only when i exceeds $\\theta_c$. At and below $\\theta_c$ there is still a refracted ray $(at \\theta_c\\text{ it skims the }surface)$.","explanationZh":"全反射仅在 i 超过 $\\theta_c$ 后才开始。在 $\\theta_c 及以下仍有折射光线（\\theta_c$ 时沿界面掠射）。","tags":["trap","total-internal-reflection","threshold"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-014","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":5,"stem":"A fibre has core $n_1 = 1.6$ and cladding $n_2 = 1.4$. At the core–cladding boundary, with incidence $i = 50^{\\circ}$, what happens?","stemZh":"某光纤纤芯 $n_1=1.6、包层 n_2=1.4。在纤芯–包层界面上，入射角 i=50^{\\circ}$ 时会发生什么？","options":[{"id":"A","text":"TIR occurs"},{"id":"B","text":"Light is fully absorbed"},{"id":"C","text":"Light refracts into the cladding (no TIR)"},{"id":"D","text":"The ray travels along the boundary"}],"optionsZh":[{"id":"A","text":"发生全反射"},{"id":"B","text":"光被完全吸收"},{"id":"C","text":"折射进入包层（未发生全反射）"},{"id":"D","text":"光线沿界面传播"}],"answer":"C","explanation":"Critical $angle: \\sin\\theta_c = \\dfrac{1.4}{1.6} = 0.875$, so $\\theta_c \\approx 61^{\\circ}$. Since $i = 50^{\\circ} < 61^{\\circ}$, TIR does NOT occur; the ray refracts into the cladding.","explanationZh":"$临界角：\\sin\\theta_c=\\dfrac{1.4}{1.6}=0.875，故 \\theta_c\\approx61^{\\circ}。因 i=50^{\\circ}<61^{\\circ}，不发生全反射，光线折射进入包层。$","tags":["trap","total-internal-reflection","fibre","angle-check"]},{"subject":"physics","type":"single-choice","status":"published","id":"physics-total-internal-reflection-015","moduleId":"optics","unitId":"geometric-optics","topicId":"total-internal-reflection","difficulty":5,"stem":"A glass block $(n_1 = 1.5)$ is immersed in water $(n_2 = 1.33)$. Can total internal reflection occur at the glass–water boundary, and if so when?","stemZh":"$玻璃块（n_1=1.5）浸在水中（n_2=1.33）。在玻璃–水界面能否发生全反射？若能，何时发生？$","options":[{"id":"A","text":"No, glass and water are too similar"},{"id":"B","text":"Only at $i = 0^{\\circ}$"},{"id":"C","text":"Yes, but only if $i > 90^{\\circ}$"},{"id":"D","text":"Yes, for $i > 62.5^{\\circ}$"}],"optionsZh":[{"id":"A","text":"不能，玻璃和水太接近"},{"id":"B","text":"仅在 $i=0^{\\circ} 时$"},{"id":"C","text":"能，但需 $i>90^{\\circ}$"},{"id":"D","text":"能，当 $i>62.5^{\\circ} 时$"}],"answer":"D","explanation":"Glass is denser than water $(1.5 > 1.33)$, so TIR is possible. $\\sin\\theta_c = \\dfrac{1.33}{1.5} = 0.887, \\theta_c \\approx 62.5^{\\circ}$; TIR occurs for $i > 62.5^{\\circ} (not\\text{ only at an air }boundary)$.","explanationZh":"$玻璃比水光密（1.5>1.33），故可发生全反射。\\sin\\theta_c=\\dfrac{1.33}{1.5}=0.887，\\theta_c\\approx62.5^{\\circ}；当 i>62.5^{\\circ}$ 时发生全反射（并非只发生在空气界面）。","tags":["trap","total-internal-reflection","condition","non-air"]}]

Optics