Industrial inspection equipment directs a narrow infrared beam inside a diamond rod…
PHYSICS · Multi-part · CBSE · Physics · Ray Optics and Optical Instruments · Ray Optics and Optical Instruments
Problem
Industrial inspection equipment directs a narrow infrared beam inside a diamond rod (index 2.42) toward a polished end face that is in direct contact with water (index 1.33). The beam makes an angle of 35∘ with the normal to that end face while still inside the diamond.
Respond to the prompts below, showing all necessary steps and clearly articulating your reasoning.
(a) Calculate the angle that the beam would make with the normal in the water if refraction occurs.
(b) Determine the critical angle (in diamond) for the diamond–water interface and decide whether total internal reflection actually occurs for the given 35∘ internal angle. Support your conclusion numerically.
(c) Suppose the beam inside the diamond is instead directed at θinc (still measured from the normal), where θinc is just small enough to permit refraction into the water without undergoing total internal reflection. Express the emerging angle in the water in terms of θinc and the two indices of refraction, and evaluate it numerically at that limiting condition.
(d) Discuss qualitatively how replacing the water with air would alter both the critical angle and the behavior of the infrared beam, referencing your quantitative findings from parts (a)–(c).