International Young Physicist Tournament presentation of Team Slovakia created by Lukas Bosko

2. Task When a photo is taken with a flash, bright “disks” may appear as shown in the picture. Investigate and explain the phenomenon.

3. The Ghost The ghost is the image of a little flashed object, that was located out ofthefield depth.

4. Principle of the phenomenon The light from a flash reflectsfrom a small surface in the unfocused area – it acts as a small source of light. Focused object Object out of field depth Photosensitive layer lens

5. Camera Can always be approximated to a single convex lens with one aperture. Photosensitive layer A system of lenses Photosensitive layer Convex lens Aperture 5

6. Focus Object located further than focused objects Focused object Object located closer than focused object photosensitive layer focus depth lens iris

7. Aperture Smallaperture, big focusdepth Big aperture, smallfocusdepth

8. Focusingtheobjects

9. Lensmaker’s equation L0– focused object distance L0’ – distance of the object’s projection – distance of the ph. layer L1– distance of the ghost-generating object L1’– distance of it’s projection

10. F-stop number (aperture) f – focus distance d – the size of the aperture

11. d – diameter of the aperture s – diameter of the ghostly image L0´ – distance between the ghostly image and the aperture = f L1´ – distance of the particle’s projection Size of the ghost for infinite focused object distance

12. Size of the ghost The particle is not a perfect point source of light, it has a certain diameter p (we have to count it in). There is an increase in the size of the ghostly image described by our final formula:

13. We wanted to measure the exact size of the ghostly image on the chip, thus we introduced a size coefficient. One pixels size: wm –width of the ph. layer wpx –width of the image in pixels Actual size of the ghostly image in pixels – Dpx Experiments Used in our experiments to determine the size of a ghostly image.

14. Experimental setup Independent variables Aperture Distance from the lighted object to the lens Dependent variables Size of a ghost Small particle Focusedobject

15. Method of measurement f1.8 f19

16. Varying distance Constant parameters Focal length f = 50 mm Aperture numberA = 1,8 (d = 27,8 mm) Focused object distance L0 = 6 m Particle size p: negligible Varied parameter –L1(the distance of the particles from the lens)

17. Varying distance [m] 5,5 5 4,5 4 3,5 3 2,5 2 1,5 1

18. Varying distance Projected ghostly image size [mm] Particle distance [mm]

19. Constant parameters L1 = 1500 mm f = 50 mm L0 = 6 m p = negligible Varied parameter A(by altering the diameter of the aperture) Varying aperture size

20. Varying aperture size f1.8f2.8f3.3f5.6 f8f13f19f22

21. Varying aperture size Projected ghostly image [mm] F-stop number (Aperture)

22. Constant parameters L1 = 1500 mm f = 50 mm L0 = 6 m p = 6mm Varied parameter A(by altering the diameter of the aperture) Varying aperture size

23. f1.8f2.8f3.3f5.6 f8f13f19f22 Varying aperture size

25. on the distortions induced by the lens

26. on the structure of the aperture Different color of the edges of the ghostly image The texture of the ghostly image Particles with non-typical light reflection Other observed effects

28. Increasing theF-stop number increases the visibility of thiseffectShapeoftheghost

30. Colored borders between light and shadow – caused by chromatic aberration Dependency of the refraction index of light on it’s wavelength Colored edges

31. Texture of the ghostly image Small particles (with their size comparable with the wavelength of light) (1<λ<100) have an easily observable texture This texture consists of concentric circles Diffraction occurs on the small particles Other, larger particles do not create ghostlyimages with these circles

32. Conclusion Ghostly images are created when a particle outside the depth of field is lit The diameter of the ghostly image is mainly dependent on the particle distance and aperture size The experiments confirm our theory with remarkable precision Other effects can be observed in the ghostly image and we have described and explained their influence Thank you for your attention

38. Task Task When a photo is taken with a flash, bright “disks” may appear as shown in the picture. Investigate and explain the phenomenon.

39. Ghostly images

41. A lot of interesting effects were explained

42. Type of photosensitive layer (film or pixels) has no influence

43. Opponent did not accept my approach through geometric optics to a taskOverview

44. Conclusion Ghostly images are created when a particle outside the depth of field is lit The diameter of the ghostly image is mainly dependent on the particle distance and aperture size, which were investigated The experiments confirm our theory with remarkable precision Other effects can be observed in the ghostly image and we have described and explained their influence Thank you for your attention