Question

In winter a lake has a 0.30m thick ice layer over 1.20m of water. A light beam from above strikes a spot on the ice, making a 29? angle with the normal.

Part A

How far horizontally from that spot does the light ray strike the lake bottom?

Answer 1

According to Snell's law,

                    

Here, is the refrctive index of the ice, is the refractive index of the water, is the angle of incidence and is the angle of refraction.

Rearrange the equation for .

                   

                   

                        

The displacement at this point is,

                  

                     

                       

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Now, the angle od refraction on the surface of the lake is considered as the angle of incidence of the light ray as it strikes the bottom of the lake. so, from the Snell's law,

Rearrange the equation for .

                   

                   

                   

The displacement at this point is,

                  

                     

                       

Thus, the total horizontal distance is,

                  

                     

                     

Therefore, the horizontal distance at which the light ray strikes the bottom of the lake is .