Question

(Modeling) Speed of Light When a light ray travels from one medium, such as air, to another medium, such as water or glass, the speed of the light changes, and the light ray is bent, or refracted, at the boundary between the two media. (This is why objects under water appear to be in a different position from where they really are.) It can be shown in physics that these changes are related by Snell's law c₁ = sin θ₁ , c₂ sin θ₂ where c₁ is the speed of light in the first medium, c₂ is the speed of light in the second medium, and θ₁ and θ₂ are the angles shown in the figure. In Exercises 81 and 82, assume that c₁ = 3 x 10⁸ m per sec. Find the speed of light in the second medium for each of the following. a. θ₁ = 46°, θ₂ = 31° b. θ₁ = 39°, θ₂ = 28°

Accepted Answer

Identify the given values: the speed of light in the first medium $$c_1 = 3$$ 	imes $$10^8 m/s$$, and the angles $$\$$theta_1$$ and $$\$$theta_2$$ for each part of the problem. Recall Snell's law as given: $$c_1$$ \sin \$$theta_1$$ = $$c_2$$ \sin \$$theta_2. $$This relates the speeds and angles of the light ray in the two media. Rearrange Snell's law to solve for the unknown speed $$c_2 in $$the second medium: $$c_2$$ = \frac{$$c_1$$ \sin \$$theta_1$$}{\sin \$$theta_2$$}$$. For each part (a and b), substitute the given values of $$\$$theta_1$$ and $$\$$theta_2$$ into the formula. Make sure to convert the angles to radians if your calculator requires it, or use degree mode. Calculate the sine values for $$\$$theta_1$$ and $$\$$theta_2$$, then compute c_2$ using the formula. This will give you the speed of light in the second medium for each case.

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Key Concepts

Snell's Law

Refraction and Speed of Light in Different Media

Trigonometric Functions in Angle Calculations