Report 8 Liquid light guide 2015/11/28 Reporter: 儲君宇 Joshua Jun-Yu Chu 0.

Report 8 Liquid light guide

112/04/18 Reporter: 儲君宇 Joshua Jun-Yu Chu 1

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?


Overview• Introduction

– Observation– Problem Analysis

• Theoretical Model• Experiment• Results and Discussion

– Direct Transmission– Other Factors

• Conclusions & Summary


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.


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


Introduction


Fig.1 The liquid light guide apparatus

h=46cm

Theoretical Model


According to Bernoulli’s equation,

2 21 1 1 2 2 2

1 1

2 2P v gy P v gy

2v

1v

1P

2P

2 1y y

Theoretical Model


1 2 12 ( )v g y y

2 0v Assuming that and1 2 atmP P P

2v

1v

1P

2P

2 1y y

We can write 21 1 2

1

2v gy gy

And get

In our case, 2 1H y y

We get 2v gH

Theoretical Model


2

4

xy h

H

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.


Horizontal D

istance (cm)

Height of Water (cm)

Relationship Between Horizontal Distance and Water Height

Theoretical Prediction Experimental Results

Theoretical Model


•Assumption that surfaces of jet has the same shape as the center of the jet.•Ray tracing technique-> Coordinate geometry

2

4 2

x dy h

H

Theoretical Model


Let Then the reflecting point is

Substituting P into we can write

1 (1,0)d

( , )P t h2

4 2

x dy h

H

2

4 2

t dh h

H 2t dH

( 2 , )P dH h


To get the tangential line at a given point, it’s slope is:

Tangential line is:

Normal vector can be written:

2

dy x

dx H

1

2:

2

dHT y x h d

H

1 ( 2 ,2 )n dH H


Reflecting light beam is

Because the incident angle and reflecting angle are the same, we can write

2 (1, )d a

1 1 2 2

1 1 2 2

cosn d n d

n d n d


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,

48.8

2

20 cos 48.8 0.66

2 4

dH

dH H

2

2

(1 0.66 ) 2

4 0.66

dH

0.648H d

1 1 2 2sin sinn n

1 2

1

sin ( ) 48.8n

n

• 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.


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.


Experiment• Experimental methods• Pictures are taken from the side of the

basin to record the path of light inside the jet.


Results and Discussion


Chart 2. The actual critical water height for direct transmission and its theoretical prediction.

Direct Transmission

Hole Diameter

Critical H

eight (cm

)


• 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.




Fail vs. Success


• Other Influential Factors:– Partially Functional


Diameter: 1cmWater Height: 5cm

Results and Discussion• Other Influential Factors


Diameter 1cm 1.5cm 2cm 2.5cmDeformed End <6cm <4cm <3.5cm <3cmDrops <3.5cm N/A N/A N/A

Results and Discussion• Other Influential Factors:




DiameterEffect

1cm 1.5cm 2cm 2.5cm

Deformed End <6cm <4cm <3.5cm <3cmDrops <3.5cm N/A N/A N/ADeformed Flow <2.5cm <3cm <2.5cm <2.5cmDirect Pass <0.61cm <0.87cm <1.2cm <1.6cmOverall 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


• 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 parabolic2. Turbulent jet surface

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 deformed2. The flow breaks into drops

THANK YOU


THANK YOU

Report 8 Liquid light guide 2015/11/28 Reporter: 儲君宇 Joshua Jun-Yu Chu 0.

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Transcript of Report 8 Liquid light guide 2015/11/28 Reporter: 儲君宇 Joshua Jun-Yu Chu 0.