An equiconvex lens of refractive index 1.6 has power 4D in air. Its power in water is:

Options

A. (a)1.5 D
B. (b)2.0 D
C. (c)1.3 D
D. (d)3.2 D

Answer

To find the power of the equiconvex lens in water, we can follow these steps:

### Step 1: Understand the given information
We know:
- The refractive index of the lens (μ) = 1.6
- The power of the lens in air (P) = 4D
- The refractive index of water (n_water) = 1.33

### Step 2: Use the lens maker's formula
The power (P) of a lens is given by the formula:
\[ P = \left( \mu - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
Where:
- μ is the refractive index of the lens
- R1 and R2 are the radii of curvature of the lens surfaces.

### Step 3: Calculate the mean refractive index when the lens is in water
The mean refractive index of the lens in water (μ') can be calculated as:
\[ \mu' = \frac{\mu}{n_{water}} = \frac{1.6}{1.33} \]

### Step 4: Calculate the power of the lens in water
Using the modified lens maker's formula for the power in water:
\[ P' = \left( \mu' - 1 \right) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]
We can express this in terms of the power in air (P):
\[ P' = P \cdot \frac{\mu' - 1}{\mu - 1} \]

### Step 5: Substitute the values
From the previous steps:
1. Calculate μ':
\[ \mu' = \frac{1.6}{1.33} \approx 1.202 \]
2. Calculate (μ' - 1):
\[ \mu' - 1 \approx 1.202 - 1 = 0.202 \]
3. Calculate (μ - 1):
\[ \mu - 1 = 1.6 - 1 = 0.6 \]

Now substitute these values into the power formula:
\[ P' = 4D \cdot \frac{0.202}{0.6} \]

### Step 6: Calculate P'
\[ P' = 4D \cdot 0.3367 \approx 1.347D \]

### Final Result
The power of the lens in water is approximately **1.35 D**.