When light is incident on a medium of refractive index `mu` from rarer medium at an angle 'i' and is refracted at an angle 'r', then Snell's law gives

Options

A. `mu=(sin i)/(sin r)`
B. `mu=(sin r)/(sin i)`
C. `mu=sin ixxsin r`
D. `(1)/(mu)=(sin i)/(sin r)`

Answer

To solve the problem using Snell's Law, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Mediums**:
- We have two mediums: a rarer medium (like air) and a denser medium (with refractive index `mu`).
- The refractive index of air is typically taken as 1.

2. **Identifying Angles**:
- The angle of incidence is denoted as `i`.
- The angle of refraction is denoted as `r`.

3. **Applying Snell's Law**:
- Snell's Law states that the product of the refractive index of the first medium and the sine of the angle of incidence is equal to the product of the refractive index of the second medium and the sine of the angle of refraction. Mathematically, this is expressed as:
\[ n_1 \sin(i) = n_2 \sin(r) \]

4. **Substituting Values**:
- For our case, we have:
- \( n_1 = 1 \) (for the rarer medium, air)
- \( n_2 = \mu \) (for the denser medium)
- Substituting these values into Snell's Law gives:
\[ 1 \cdot \sin(i) = \mu \cdot \sin(r) \]

5. **Rearranging the Equation**:
- We can rearrange the equation to isolate `mu`:
\[ \mu = \frac{\sin(i)}{\sin(r)} \]

6. **Final Result**:
- Thus, the relationship given by Snell's Law in this scenario is:
\[ \mu = \frac{\sin(i)}{\sin(r)} \]