To determine the refractive index of a medium when a ray of light travels from air into that medium, we can use Snell's Law. Snell's Law relates the angles of incidence and refraction to the refractive indices of the two media involved. ### Step-by-Step Explanation 1. **Understanding Snell's Law**: Snell's Law states that: \[ n_1 \sin(\alpha) = n_2 \sin(\beta) \] where: - \( n_1 \) is the refractive index of the first medium (air in this case, which is approximately 1), - \( n_2 \) is the refractive index of the second medium (the transparent medium), - \( \alpha \) is the angle of incidence (the angle between the incident ray and the normal), - \( \beta \) is the angle of refraction (the angle between the refracted ray and the normal). 2. **Setting Up the Equation**: Since we are interested in finding the refractive index of the medium (\( n_2 \)), we can rearrange Snell's Law: \[ n_2 = \frac{n_1 \sin(\alpha)}{\sin(\beta)} \] Given that \( n_1 \) (the refractive index of air) is approximately 1, we can simplify this to: \[ n_2 = \frac{\sin(\alpha)}{\sin(\beta)} \] 3. **Identifying the Correct Option**: From the derived formula, we see that the refractive index of the medium is given by: \[ n_2 = \frac{\sin(\alpha)}{\sin(\beta)} \] This corresponds to option **B**. ### Why the Other Options are Incorrect - **Option A: \( \frac{\cos(\alpha)}{\sin(\beta)} \)**: This option incorrectly uses cosine for the angle of incidence. The refractive index is defined in terms of sine, not cosine, so this option is not valid. - **Option C: \( \frac{\cos(\beta)}{\sin(\alpha)} \)**: This option also incorrectly uses cosine for the angle of refraction and does not follow the correct relationship defined by Snell's Law. - **Option D: \( \frac{\sin(\beta)}{\sin(\alpha)} \)**: This option is the inverse of the correct relationship. It suggests that the refractive index is the ratio of the sine of the angle of refraction to the sine of the angle of incidence, which is not correct according to Snell's Law. ### Common Pitfalls - **Confusing Sine and Cosine**: A common mistake is to confuse the sine and cosine functions when applying Snell's Law. Remember that the refractive index is always related to the sine of the angles. - **Ignoring the Medium's Refractive Index**: When calculating the refractive index, ensure you know the refractive index of the first medium (air is approximately 1). - **Misinterpreting Angles**: Ensure that angles are measured from the normal line, not from the surface of the medium. ### Revision Summary - Snell's Law relates the angles of incidence and refraction to the refractive indices of two media. - The refractive index of a medium can be calculated using the formula \( n_2 = \frac{\sin(\alpha)}{\sin(\beta)} \). - The correct answer to the question is option **B**. - Avoid confusing sine and cosine functions when applying Snell's Law.