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Isaac physics: Underwater Ridge

Does anyone know the solution to this problem from Isaac physics?

"Under certain conditions the speed c,c of surface water waves is given by c = (gd)^1/2, where g,g is the gravitational acceleration and d,d is the depth of water (you may assume that this is valid for the whole of this question).

A flat-topped, parallel-sided ridge lies under the surface of a lake. The depth of water at the ridge is d 1, and the depth everywhere else is d 2.

Surface waves are travelling across the ridge (i.e. they are already travelling above the ridge) at an angle θ to the length of the ridge.

Find the minimum value of θ for which the waves will be able to travel past the ridge into the deeper region."

details to the problem: https://isaacphysics.org/questions/underwater_ridge_sym?board=refraction_and_tir&stage=a_level
Reply 1
As hints 3 and 4 suggests, just use snells rule with the given speeds. You also want the critical angle, so one of the angles is 90 to the normal.
Reply 2
Original post by mqb2766
As hints 3 and 4 suggests, just use snells rule with the given speeds. You also want the critical angle, so one of the angles is 90 to the normal.


i did try that. but they dont accept my answer.
(edited 10 months ago)
Reply 3
Original post by azimshurzo
i did try that. but the dont accept my answer.


So what did you enter/working?
Reply 4
Original post by mqb2766
So what did you enter/working?


i found that the critical angle would be sin^-1((d1/d2)^1/2)
so the minimum angle would be 90 - sin^-1((d1/d2)^1/2)
i hope that makes sense
Reply 5
Original post by azimshurzo
i found that the critical angle would be sin^-1((d1/d2)^1/2)
so the minimum angle would be 90 - sin^-1((d1/d2)^1/2)
i hope that makes sense


Sounds about right, but is there a very simple identity you could use so its in terms of another trig term?
(edited 10 months ago)
Reply 6
Original post by mqb2766
Sounds about right, but is there a very simple identity you could use so its in terms of another trig term?


i couldnt figure out. can you help?
Reply 7
Original post by azimshurzo
i couldnt figure out. can you help?


The minimum angle (to the ridge) and the critical angle (to the normal) are complementary. So instead of using sin, use ... The clues in the name.

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