Question

As a freelance sports photographer, you have secured the right to photograph the 2020 Olympics platform diving competition from just before divers initiate their dives by using a video camera on the bottom of the pool directly below the edge of diving platform. The pool is 6.5 meters deep, and the platform itself is 10 meters above the surface of the water. Show how to locate the image of the diving platform using qualitatively accurate ray diagrams and quantitatively accurate equations, explaining your logic along the way.

Answer 1

So as you can see in the picture, if the video camera is placed at O, the light ray from C will appear to camera as if it is coming from point B. So w.r.t the camera the length of the wedge is AB, not AC.

Now let, AC=h and AB=h₁,

and   

If the refractive index is , then from Snell's law,

..........(1)   

Now from triangle CDF,     

  

and ..........(2)

From triangle ODE,   

and   

   ...............(3)

Now from equation (1), (2) and (3) we can calculate .

Again triangle ODE and triangle OAB are similar. So,

  

     

................(4)

Now   we know AC=h, DF=AE=10 m and OE=6.5 m and if refractive index of water() is known to us then we can calculate the apparent length(AB) of the diving platform. Or inversely if the apparent length(AB) of the diving platform is known we can find out the actual length of the diving platform(AC) using equation (4)