Report 8 Liquid light guide 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 0

Problem # 8 Liquid light guide A transparent vessel is filled with a liquid (e.g. water). A jet flows out of the vessel. A light source is placed so that a horizontal beam enters the liquid jet. Under what conditions does the jet operate like a light guide? 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 1

Overview Introduction – Observation – Problem Analysis Theoretical Model Experiment Results and Discussion – Direct Transmission – Other Factors Conclusions & Summary 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 2

Introduction Observation A laser beam can perform internal reflections in a jet. This makes the jet capable of serving as a light guide. However, when the jet strength decreases to a point, the jet can no longer act as a light guide. 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 3

Introduction Problem Analysis Water jet: near parabolic path Laser beam first comes into contact with the upper surface of jet Incident angle > critical angle: total internal reflection 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 4

Introduction 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 5 Fig.1 The liquid light guide apparatus h=46cm

Theoretical Model 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 6 The water jet should follow a path similar to a horizontal projectile motion. Therefore, we will use the formula to simulate the path of our light guide. An experiment is done to verify our hypothesis.

Theoretical Model 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 7 Horizontal Distance (cm) Height of Water (cm)

Theoretical Model 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 8 Assumption that surfaces of jet has the same shape as the center of the jet. Ray tracing technique-> Coordinate geometry

Theoretical Model 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 9 Let Then the reflecting point is Substituting P into we can write

2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 10 To get the tangential line at a given point, it’s slope is: Tangential line is: Normal vector can be written:

2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 11 Reflecting light beam is Because the incident angle and reflecting angle are the same, we can write

2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 12 According to Snell’s law, The critical angle for water is: When the stream acts as a light guide, the incident angle must be greater than the critical angle, Thus,

Continuous ray tracing – Incident angle grows larger with each reflection. Theoretically, the jet will operate as a light guide if the first reflection is a total internal reflection. 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 13

Experiment Experimental methods Water is filled into the reservoir and the jet ejects into a basin. The laser beam is turned on and aimed through the hole. The height of the beam is then adjusted to pass through the center of the jet. 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 14

Experiment Experimental methods Pictures are taken from the side of the basin to record the path of light inside the jet. 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 15

Results and Discussion 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 16 Chart 2. The actual critical water height for direct transmission and its theoretical prediction. Direct Transmission Hole Diameter Critical Height (cm)

Results and Discussion In the theory, the jet should act as a light guide until the water reaches the critical height. However, various other effects that causes the light guide to fail are observed. 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 17

Results and Discussion 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 18 Fail vs. Success

Results and Discussion Other Influential Factors: – Partially Functional 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 19 Diameter: 1cm Water Height: 5cm

Results and Discussion Other Influential Factors 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 20 Diameter: 1cm Water Height: 5cm Water Height: 3cm

Results and Discussion Other Influential Factors: – Deformed Flow 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 21 Diameter: 1.5cm Water Height: 2cm

Results and Discussion 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 22 Diameter Effect 1cm1.5cm2cm2.5cm Turbulent End<6cm<4cm<3.5cm<3cm Drops<3.5cmN/A Deformed Flow<2.5cm<3cm<2.5cm Direct Pass<0.65cm<0.8cm<1.3cm<1.9cm Overall Range>6cm>4cm>3.5cm>3cm Table 1. The critical height for all effects to happen and the overall range for the beam to work as a light guide.

Conclusions & Summary 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 23 In our experiment so far, the theory shows the trend of the critical height of the water. Possible causes of bias are: 1.Path of jet is not completely parabolic 2.Turbulent jet surface

Conclusions & Summary 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 24 The jet will act as a light guide except in the following cases: 1.Incident angle < Critical angle -Speed of jet is too slow -Surface becomes too turbulent -Jet becomes deformed 2.The flow breaks into drops

THANK YOU 2016/6/3 Reporter: 儲君宇 Joshua Jun-Yu Chu 25 THANK YOU