1 / 20

Problem 5.

Problem 5. Mirage. Mirage. Create a mirage like a road or desert mirage in the laboratory and study its parameters. Introduction. What is mirage? How is it formed? W hi ch are parameters of a mirage?. Experiment. Effect :. heated surface. observed object. Formation of mirage.

ashton-larsen
Télécharger la présentation

Problem 5.

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Problem5. Mirage

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

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

  4. Experiment Effect: heated surface observedobject

  5. Formation of mirage Snell’slaw: φ1 n1 – index of refraction of first medium n2 – index of refraction of second medium φ1 – ray angle in first medium φ2 – ray angle in second medium n1 φ2 n2 n1 > n2 → ray is refracting away from vertical

  6. 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 ???

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

  8. Mirage parameters • index of refraction dependence of temperature • temperature dependence of shift in direction parallel with temperature gradient n1 n2 n3 … nN index of refraction temperature

  9. Experiment horizontal line vesselwith flourescein termometer

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

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

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

  13. Theoretical model Ray equation: y0 – initial depth n0 – initial index of refraction φ0 – initial ray angle

  14. Results

  15. Results kT1=-0.78Kmm-1 kT3=-0.40Kmm-1 kT2=-0.32Kmm-1 kT4=-0.27Kmm-1

  16. Results

  17. Results

  18. Results kn1=-4.86*10-4K-1 kn3=-4.58*10-4K-1 kn2=-4.68*10-4K-1 kn4=-4.75*10-4K-1

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

  20. Conclusion • we created mirage in a laboratory • 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 • for water: • for practical reasons we photographed and measured ray in water but we have also created mirage in air

More Related