Problem 5. Mirage

Mirage Create a mirage like a road or desert mirage in the laboratory and study its parameters.

Introduction What is mirage?What is mirage? How is it formed?How is it formed? Which are parameters of a mirage?Which are parameters of a mirage?

Experiment Effect: heated surface observed object

Formation of mirage Snell’s law: φ1φ1φ1φ1 φ2φ2φ2φ2 n1n1n1n1 n2n2n2n2 n 1 – index of refraction of first medium n 2 – index of refraction of second medium φ 1 – ray angle in first medium φ 2 – ray angle in second medium n 1 > n 2 → ray is refracting away from vertical

Formation of mirage - applying Snell’s law on sequence of parallel planes of infinitesimal thickness whose index of refraction is changing monotonously: Why would ray return ???

Formation of mirage In one moment (sooner or later), if sequence of n i isn’t convergent, will be: Total reflection occurs and ray is returning.

Mirage parameters index of refraction dependence of temperature index of refraction dependence of temperature temperature dependence of shift in direction parallel with temperature gradient temperature dependence of shift in direction parallel with temperature gradient n1n1n2n2n3n3……nNnNn1n1n2n2n3n3……nNnN… temperature index of refraction

Experiment horizontal line vessel with flourescein termometer

Experiment temperature distribution was measured with thermometer put in the water temperature distribution was measured with thermometer put in the water rays are photographed and deviation from horizontal line is measured rays are photographed and deviation from horizontal line is measured

Theoretical model It is sufficient to derive ray equation. assumptions: assumptions: linear dependence of temperature of depth i.e.: linear dependence of temperature of depth i.e.: linear dependence of index of refraction of temperature i.e.: linear dependence of index of refraction of temperature i.e.:

Theoretical model We will use following coordinate system and following equations: yxdx φ -dy ……. Snell’s law in differential form:

Theoretical model Ray equation: y 0 – initial depth n 0 – initial index of refraction φ 0 – initial ray angle

Results

Results k T1 =-0.78Kmm -1 k T3 =-0.40Kmm-1 k T2 =-0.32Kmm-1 k T4 =-0.27Kmm-1

Results

Results

Results k n1 =-4.86*10 -4 K -1 k n3 =-4.58*10 -4 K -1 k n2 =-4.68*10 -4 K -1 k n4 =-4.75*10 -4 K -1

Results For coefficient of dependence of index of refraction of water on temperature we got (in interval ≈ 318K – 358K): According to literature:

Conclusion we created mirage in a laboratory we created mirage in a laboratory we constructed theoretical model whose results are good compared to literature we constructed theoretical model whose results are good compared to literature mirage parameters are dependence of temperature on depth and dependence of index of refraction on temperature mirage parameters are dependence of temperature on depth and dependence of index of refraction on temperature for water: for water: for practical reasons we photographed and measured ray in water but we have also created mirage in air for practical reasons we photographed and measured ray in water but we have also created mirage in air