A swimming pool is 1.4 m deep and 12 m long. Is it possible for you to dive to t

Question

A swimming pool is 1.4 m deep and 12 m long. Is it possible for you to dive to the very bottom of the pool so people standing on the deck at the end of the pool do not see you? Assume you dive to the very bottom of the pool so people standing on the deck at the end of the pool can see you. Find the minimum height of the personprimes eyes at the far side of the pool, so you would be observable by this person. Take an angle 48.5degree for a ray that is incident at the water-air interface (n_water = 1.33). Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

we know that the difraction is defined as

n1*sin(theta)=n2*sin(theta2)

now theta2 is the angle of the ray in the water then

theta2=sin^-1((n1/n2)*sin(theta1)=sin^-1((1/1.33)*sin(45))=32.11 degrees

sin(theta1)=(h/(12-x)) (1)

where h is the height of the person X is the distance which the ray is the deck

tan(theta2)=((12-x)/1.4)

we clear X x=11.12m

we clear H of 1

h=0.622m

h is the hieght minimun

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