If the speed of light in material A is 1.25 times its speed in material B, then the ratio of the refractive indices of these materials is

Options

A. 1.5
B. 1
C. 0.8
D. 1.25

Explanation

To solve the problem, we need to find the ratio of the refractive indices of two materials A and B, given that the speed of light in material A is 1.25 times the speed of light in material B.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
- Let \( V_A \) be the speed of light in material A.
- Let \( V_B \) be the speed of light in material B.
- According to the problem, \( V_A = 1.25 \times V_B \).

2. **Using the Definition of Refractive Index**:
- The refractive index \( \mu \) of a material is defined as:
\[ \mu = \frac{c}{V} \]
where \( c \) is the speed of light in vacuum and \( V \) is the speed of light in the material.

3. **Expressing Refractive Indices**:
- For material A:
\[ \mu_A = \frac{c}{V_A} \]
- For material B:
\[ \mu_B = \frac{c}{V_B} \]

4. **Finding the Ratio of Refractive Indices**:
- We need to find the ratio \( \frac{\mu_A}{\mu_B} \):
\[ \frac{\mu_A}{\mu_B} = \frac{\frac{c}{V_A}}{\frac{c}{V_B}} = \frac{V_B}{V_A} \]

5. **Substituting the Relationship Between Speeds**:
- From the given information, we know \( V_A = 1.25 \times V_B \).
- Therefore:
\[ \frac{V_B}{V_A} = \frac{V_B}{1.25 \times V_B} = \frac{1}{1.25} \]

6. **Calculating the Final Ratio**:
- Simplifying \( \frac{1}{1.25} \):
\[ \frac{1}{1.25} = 0.8 \]

7. **Conclusion**:
- The ratio of the refractive indices of materials A and B is:
\[ \frac{\mu_A}{\mu_B} = 0.8 \]

### Final Answer:
The ratio of the refractive indices of materials A and B is \( 0.8 \).

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