Dunman High 1999 Prelims P2 Q4
The diagram shows a ray of monochromatic light incident normally on a triangular glass prism of critical angle 39.5°.
(a) Find the refractive index of glass.
(b) Explain why the ray will not emerge into the air from the face XY.
(c) What is the angle of incidence at which the ray meets the face YZ.
(d) Hence find the angle of refraction when the ray emerges into the air again.
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Answer:
(a) refractive index = 1 / sin 39.5° = 1.57
(b) The angle of incidence is 60°. This is clearly higher than the critical angle of 39.5°. Hence, the ray will undergo total internal reflection, and thus will not emerge into the air from face XY.
(c) Angle of incidence = (180° - 30° - 30°) - 90° = 30°
(d) refractive index = sin (angle of refraction) / sin 30°
sin (angle of refraction) = 1.57 * sin 30°
angle of refraction = 51.7°
