Cambridge Pre-U Physics
θ1 air
A O
θ1
LY
θ2
apparent depth
θ1
B
C
O
water refractive index n
N
θ2
Figure S13.8 Refraction means that water appears to be less deep than it really is.
EV IE
W
A ray of light coming from the bottom of the container of water at an angle to the normal is refracted away from the normal as it leaves the water and passes into air (ray CO). A ray of light that comes from the bottom of the container but is normal to the surface passes through without changing angle (ray CA). If we trace the first ray back into the water (dotted line OB), then it meets the ray that came out along the normal at point B. The distance AB is the apparent depth (the real depth is the distance AC). If you redraw Figure S13.8 with a larger angle θ1, then you will notice that the rays cross higher up in the water and the apparent depth is reduced. So to find the maximum possible apparent depth, we need to work out what happens as θ1 tends to zero. Snell’s law tells us that: sin θ1 = n sin θ 2
R
Trigonometry tells us that in triangle AOB
sin θ1 =
OA OB
sin θ 2 =
OA OC
FO R
and that in triangle AOC
Combining these two equations with Snell’s law tells us that: OA OA =n OB OC
However, as we make θ1 smaller, length OB tends to length AB and OC tends to AC (it doesn’t make sense to say what they are when θ1 = 0, but just before it becomes zero, these pairs of lengths are nearly equal). Applying this to our equation above tells us that OA OA =n AB AC real depth AC h= = AB apparent depth
Original material © Cambridge University Press 2016
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