if `mu_21` is `1.5,` then find the value of `lambda_1/lambda_2.`

Explanation

To solve the problem, we need to find the value of \(\frac{\lambda_1}{\lambda_2}\) given that \(\mu_{21} = 1.5\).

### Step-by-Step Solution:

1. **Understand the given information**: We know that \(\mu_{21} = 1.5\). This is the refractive index of medium 2 with respect to medium 1.

2. **Use the definition of refractive index**: The refractive index \(\mu_{21}\) can be expressed as:
\[ \mu_{21} = \frac{\mu_2}{\mu_1} \]
where \(\mu_2\) is the speed of light in medium 2 and \(\mu_1\) is the speed of light in medium 1.

3. **Relate the refractive index to the wavelengths**: The relationship between the refractive index and the wavelengths in the two media is given by:
\[ \mu = \frac{\lambda_1}{\lambda_2} \]
This means that the refractive index is inversely proportional to the wavelengths of light in the respective media.

4. **Substitute the value of \(\mu_{21}\)**: Since we have \(\mu_{21} = 1.5\), we can write:
\[ \frac{\lambda_1}{\lambda_2} = \frac{1}{\mu_{21}} = \frac{1}{1.5} \]

5. **Calculate \(\frac{\lambda_1}{\lambda_2}\)**:
\[ \frac{\lambda_1}{\lambda_2} = \frac{2}{3} \]

6. **Final answer**: Therefore, the value of \(\frac{\lambda_1}{\lambda_2}\) is:
\[ \frac{\lambda_1}{\lambda_2} = \frac{2}{3} \]