The critical angle for light traveling from a transparent medium to air s measured as 34º. The refractive index of the medium is

1. Analyze the question

We are given the critical angle ($c = 34^\circ$) for light traveling from a medium into air. We need to find the refractive index ($n$) of that medium.

2. Explain the concept

The relationship between the refractive index ($n$) of a medium and the critical angle ($c$) is defined by Snell's Law at the point of total internal reflection. When light travels from a denser medium to a rarer medium (like air), the formula is:

Where:

• $n$ is the refractive index.
• $c$ is the critical angle.

3. Show the solution

• Step 1: Identify the given value: $c = 34^\circ$.
• Step 2: Plug the value into the formula: $$n = \frac{1}{\sin(34^\circ)}$$
• Step 3: Calculate the sine of $34^\circ$: Using a calculator, $\sin(34^\circ) \approx 0.5592$.
• Step 4: Perform the division: $$n = \frac{1}{0.5592}$$ $$n \approx 1.788$$

Rounding this to two decimal places, we get 1.79.

4. Identify the answer

Comparing our result to the given options: A. 0.56 B. 1.50 C. 1.79 D. 2.02

The calculated value matches option C.

5. Tip

When dealing with critical angle problems, always remember that the refractive index $n$ must be greater than 1. If you calculate a value less than 1, you have likely inverted your formula (i.e., you calculated $\sin(c)$ instead of $1/\sin(c)$). Also, ensure your calculator is in Degree mode (DEG) and not Radians (RAD) before calculating trigonometric functions!