You are given water, mustard oil, glycerine and kerosene. In which of these media a ray of light incident obliquely at same angle would bend the most ?

Options

A. Kerosene
B. Water
C. Mustard oil
D. Glycerine

Explanation

To determine in which medium a ray of light will bend the most when incident obliquely at the same angle, we need to consider the refractive indices of the given media: water, mustard oil, glycerine, and kerosene.

### Step-by-Step Solution:

1. **Understand Refraction**: When light passes from one medium to another, it bends. The amount of bending depends on the refractive indices of the two media involved.

2. **Identify the Refractive Indices**: The refractive index (n) is a measure of how much light slows down in a medium compared to air. The refractive indices for the given media are approximately:
- Water: n ≈ 1.33
- Mustard Oil: n ≈ 1.47
- Glycerine: n ≈ 1.47
- Kerosene: n ≈ 1.44

3. **Apply Snell's Law**: Snell's Law states that:
\[ n_1 \sin(i) = n_2 \sin(r) \]
where \( n_1 \) is the refractive index of the first medium (air, which is approximately 1), \( i \) is the angle of incidence, \( n_2 \) is the refractive index of the second medium, and \( r \) is the angle of refraction.

4. **Analyze the Relationship**: From Snell's Law, we can derive that:
\[ \sin(r) = \frac{n_1}{n_2} \sin(i) \]
This implies that as \( n_2 \) (the refractive index of the second medium) increases, \( \sin(r) \) decreases, leading to a smaller angle of refraction \( r \). Thus, the bending of light is inversely proportional to the refractive index of the medium.

5. **Determine the Medium with the Highest Refractive Index**: The medium with the highest refractive index will cause the light to bend the most. From the values we have:
- Glycerine and mustard oil have the same refractive index (1.47), but glycerine is often noted to have a slightly higher effective refractive index in practical applications.

6. **Conclusion**: Since glycerine has the highest refractive index among the given options, a ray of light incident obliquely at the same angle will bend the most in glycerine.

### Final Answer:
The ray of light will bend the most in **glycerine**.