Lessons 52–53 · 2 lessons · P. Habibullayev, A. Boydedayev, A. Bahromov, K. Suyarov, J. Usarov, M. Yuldasheva. Physics Grade 9, revised and expanded 3rd edition. G‘afur G‘ulom Publishing House, Tashkent, 2019
52
Problem solving
Textbook: p. 142
GoalSolve problems on total internal reflection: sin α₀ = n₂/n₁, linked with n and v.
New words
limiting angle · chegaraviy burchakdense medium · zich muhitrare medium · siyrak muhitsine table · sinus jadvali
Explanation
In these problems first decide which medium the ray goes from and into: total reflection is possible only going from a denser to a rarer medium. The limiting angle is found from sin α₀ = n₂/n₁; if the second medium is air, sin α₀ = 1/n. If n₂/n₁ must be found from the law of refraction, use the sines of the two angles: n₂/n₁ = sin α/sin β. If the limiting angle is given, n = 1/sin α₀ follows, and then v = c/n gives the speed of light. If the angle of incidence exceeds α₀ the ray is totally reflected; if it is smaller the ray partly emerges. Sine values: sin 30° = 0.5; sin 37° ≈ 0.6; sin 45° ≈ 0.71; sin 53° ≈ 0.8; sin 60° ≈ 0.87.
Worked examples
At the substance–air boundary α₀ = 53°: n = 1/sin 53° ≈ 1/0.8 = 1.25; v = c/n = 3·10⁸/1.25 = 2.4·10⁸ m/s.
A ray goes from the dense to the rare medium, incident at 20° and refracted at 30°: n₂/n₁ = sin 20°/sin 30° ≈ 0.34/0.5 ≈ 0.68; so sin α₀ = 0.68, α₀ ≈ 43°.
Class activity
Drawing task: draw a ray falling perpendicular to one leg face of a glass prism (n = 1.5) whose cross-section is an isosceles right triangle. At what angle does it hit the hypotenuse (45°)? Check that 45° exceeds the limiting angle 42° and show in which direction the ray is totally reflected.
Practice
1
In which case can total internal reflection not occur?
When the ray goes from a rarer to a denser medium.
2
At the boundary with air sin α₀ = 0.625. What is the refractive index?
n = 1/0.625 = 1.6
3
In a substance n = 1.6. What is the speed of light in it, in m/s (c = 3·10⁸ m/s)?
187500000
4
Why does a diver see the water surface as a mirror at some angles?
The rays fall at angles above the limiting angle and are totally reflected.