As shown in the figure, there is a glass cylinder with a refractive index of 2 in the air, and its cross section is a fan-shaped OAB with a central angle of 90 and a radius of R, and a beam of parallel light is parallel. (1) According to the law of refraction, SIN 45 SINR = 2.

Sinr= 12。

Solution: r = 30.

(2) The velocity of the beam in the glass column is v = cn = 3×1082 = 2.1×108m/s. 。

(3) The light passing through O enters the AB interface vertically and exits at point C, and there is no light between C and B; The closer to A, the greater the incident angle of light incident on AB interface, and the greater the possibility of total reflection.

According to the critical angle formula: sinC= 12, and the critical angle is 45. If the critical point on AB interface is D, and the light is incident on E point on AO interface, the angle between OD and the horizontal direction in triangle ODE is180-(120+45) = 65438+.

So the arc length of the light part is14 π r.

Answer: The arc length of the part with light on arc AB is14 π r. 。