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- Homework Statement
- A person looks at the surface of water with an angle of 30 degrees and sees a coin 0.5 m further than it really is. What is the depth (h) of the pool.

The answer I should get is around 16 cm, but I get 0.289 m. What is wrong with my solution?

- Relevant Equations
- Snell's law; basic trigonometry

α=30°; l=0.5 m; n1=1; n2=1.33

α+β=90°, so β=90°-30°=60°.

Using Snell's law:

sinβ/sinγ = n2/n1

sinγ≈0.651

γ≈41°.

β=γ+θ (vertical angles)

θ=60°-41°=19°

tan(θ+β)=l/h

h=l/tan(θ+γ)

h=0.5/(tan(19+41))≈0.289 m

α+β=90°, so β=90°-30°=60°.

Using Snell's law:

sinβ/sinγ = n2/n1

sinγ≈0.651

γ≈41°.

β=γ+θ (vertical angles)

θ=60°-41°=19°

tan(θ+β)=l/h

h=l/tan(θ+γ)

h=0.5/(tan(19+41))≈0.289 m

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