Solve Index of Refraction Homework Statement

[ObliviousSage]

Homework Statement

Index of refraction of air is being treated as 1, index of refraction for water is 1.33.
W is given as 6.1 cm, the problem is to find H.

Homework Equations

By Snell's Law, n₁sin$$\Theta$$₁=n₂sin$$\Theta$$₂.

We can also use at least one of the trigonometric equations, tan$$\Theta$$=opposite/adjacent.

The Attempt at a Solution

Since we know n₁ and n₂, we can reduce the Snell's Law equation to: sin$$\Theta$$₁=1.33*sin$$\Theta$$₂.

We can also get that tan$$\Theta$$₁=6.1/H and tan$$\Theta$$₂=3.05/H via basic trig, and these can be combined to get tan$$\Theta$$₁=2*tan$$\Theta$$₂.

The problem is that I can't see any way to combine any of those equations that will let me isolate a single variable (H, $$\Theta$$₁, or $$\Theta$$₂) so that I can find its value and plug it into solve for the other variables.

 

[SammyS]

In the figure on the left, the angle from the side of the glass to the ray, is equal to the angle of refraction in the figure on the right. You called this angle, θ₁.

Therefore,  $$\sin(\theta_1)=\frac{W}{\sqrt{W^2+H^2\,}\,}\ .$$

From the given conditions, it's clear that  $$\sin(\theta_2)=\frac{W/2}{\sqrt{(W/2)^2+H^2\,}\,}\ .$$

Since, you know W, n₁, and n₂, you should be able to write Snell's Law with only one unknown.

 

[ObliviousSage]

Oh wow, I can't believe I forgot about that! Yeah, that should do it, thanks!