A thin glass (refractive index 1.5) lens has optical power of `-5D` in air. Its optical power in a liquid medium with refractive index 1.6 will be

Options

A. 1D
B. `-1D`
C. 25D
D. 20

Explanation

To find the optical power of a thin glass lens in a liquid medium, we can follow these steps:

### Step 1: Understand the given data
- The refractive index of the lens (glass) \( \mu_2 = 1.5 \)
- The optical power of the lens in air \( P_{air} = -5D \) (indicating it is a diverging lens)
- The refractive index of the surrounding medium (liquid) \( \mu_1 = 1.6 \)

### Step 2: Use the lens maker's formula
The lens maker's formula is given by:
\[ \frac{1}{F} = \left( \mu_2 - \mu_1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
In air, the surrounding medium has a refractive index of 1. Therefore, we can rewrite the formula for the lens in air:
\[ \frac{1}{F_{air}} = \left( 1.5 - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Given that \( P_{air} = -5D \), we have:
\[ \frac{1}{F_{air}} = -5 \]

### Step 3: Substitute values for the air condition
Substituting the known values into the formula:
\[ -5 = (0.5) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
This leads to:
\[ \frac{1}{R_1} - \frac{1}{R_2} = -10 \]

### Step 4: Analyze the lens in the liquid medium
Now, we need to find the optical power of the lens when it is in the liquid medium:
\[ \frac{1}{F_{liquid}} = \left( 1.5 - 1.6 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
This simplifies to:
\[ \frac{1}{F_{liquid}} = (-0.1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

### Step 5: Substitute the previous result into the liquid condition
We already found that:
\[ \frac{1}{R_1} - \frac{1}{R_2} = -10 \]
Substituting this into our equation for the liquid:
\[ \frac{1}{F_{liquid}} = (-0.1)(-10) = 1 \]

### Step 6: Calculate the optical power in the liquid
The optical power \( P \) is given by:
\[ P_{liquid} = \frac{1}{F_{liquid}} = 1D \]

### Conclusion
Thus, the optical power of the lens in the liquid medium with a refractive index of 1.6 is:
\[ \boxed{1D} \]