A plano convex lens has a thickness of 6cm. Its radius of curvature is 25 cm. When its curved surface is kept on a horizontal surface and viewed from the top, its bottom appears to be raised by 2 cm. The focal power of lens is

Options

A. 1D
B. 4D
C. 2D
D. 3D

Explanation

To find the focal power of the plano-convex lens, we will follow these steps:

### Step 1: Identify the Given Data
- Thickness of the lens (t) = 6 cm
- Radius of curvature (R) = 25 cm
- The bottom of the lens appears raised by 2 cm when viewed from the top.

### Step 2: Calculate the Apparent Depth
The apparent depth (d') can be calculated as:
\[ d' = t - \text{raised height} = 6 \, \text{cm} - 2 \, \text{cm} = 4 \, \text{cm} \]

### Step 3: Calculate the Refractive Index (μ)
Using the formula for refractive index:
\[ \mu = \frac{\text{Real Depth}}{\text{Apparent Depth}} \]
Substituting the values:
\[ \mu = \frac{6 \, \text{cm}}{4 \, \text{cm}} = \frac{3}{2} \]

### Step 4: Use the Lensmaker's Formula
The lensmaker's formula for a plano-convex lens is given by:
\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R} \right) \]
Substituting the values we have:
\[ \frac{1}{f} = \left( \frac{3}{2} - 1 \right) \left( \frac{1}{25} \right) \]
\[ \frac{1}{f} = \left( \frac{1}{2} \right) \left( \frac{1}{25} \right) \]
\[ \frac{1}{f} = \frac{1}{50} \]

### Step 5: Calculate the Focal Length (f)
Taking the reciprocal gives us:
\[ f = 50 \, \text{cm} = 0.5 \, \text{m} \]

### Step 6: Calculate the Focal Power (P)
The focal power (P) is given by:
\[ P = \frac{1}{f} \]
Substituting the focal length in meters:
\[ P = \frac{1}{0.5} = 2 \, \text{D} \]

### Conclusion
The focal power of the lens is **2 Diopters (D)**.

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