Report 8 Liquid light guide 2020124 Reporter Joshua

Report 8 Liquid light guide 2020/12/4 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? 2020/12/4 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 2020/12/4 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. 2020/12/4 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 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 4

Introduction h=46 cm Fig. 1 The liquid light guide apparatus 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 5

Theoretical Model According to Bernoulli’s equation, 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 6

Theoretical Model Assuming that and We can write And get In our case, We get 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 7

Theoretical Model 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. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 8

Relationship Between Horizontal Distance and Water Height Theoretical Prediction Experimental Results Horizontal Distance (cm) 70 70 60 60 50 50 40 40 theoretical 30 1 cm 1. 5 cm 2 cm 30 2. 5 cm 20 20 10 10 0 0 20 17. 5 15 12. 5 10 7. 5 5 2. 5 Height of Water (cm) 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 9

Theoretical Model • Assumption that surfaces of jet has the same shape as the center of the jet. • Ray tracing technique-> Coordinate geometry 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 10

Theoretical Model Let Then the reflecting point is Substituting P into we can write 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 11

To get the tangential line at a given point, it’s slope is: Tangential line is: Normal vector can be written: 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 12

Reflecting light beam is Because the incident angle and reflecting angle are the same, we can write 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 13

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, 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 14

• 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. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 15

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. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 16

Experiment • Experimental methods • Pictures are taken from the side of the basin to record the path of light inside the jet. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 17

Results and Discussion 1. 8 Direct Transmission 1. 6 Critical Height (cm) 1. 4 1. 2 Actual Theoretical 1 0. 8 0. 6 0. 4 1 cm 1. 5 cm 2. 5 cm Hole Diameter Chart 2. The actual critical water height for direct transmission and its theoretical prediction. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 18

Results and Discussion • In 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. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 19

Results and Discussion Fail vs. Success 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 20

Results and Discussion • Other Influential Factors: – Partially Functional Diameter: 1 cm Water Height: 5 cm 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 21

Results and Discussion • Other Influential Factors Diameter 1 cm 1. 5 cm 2. 5 cm Deformed End Drops <6 cm <3. 5 cm <4 cm N/A <3. 5 cm N/A <3 cm N/A 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 22

Results and Discussion • Other Influential Factors: 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 23

Results and Discussion Diameter 1 cm Effect 1. 5 cm 2. 5 cm Deformed End Drops <4 cm N/A <3. 5 cm N/A <3 cm N/A <6 cm <3. 5 cm Deformed Flow <2. 5 cm <3 cm <2. 5 cm Direct Pass <0. 61 cm <0. 87 cm <1. 2 cm Overall Range >6 cm >4 cm >3. 5 cm <2. 5 cm <1. 6 cm >3 cm Table 1. The critical height for all effects to happen and the overall range for the beam to work as a light guide. 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 24

Conclusions & Summary • In our experiment so far, 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 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 25

Conclusions & Summary • 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 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 26

THANK YOU 2020/12/4 Reporter: 儲君宇 Joshua Jun-Yu Chu 27