Aplanoconvex lens is made of material of refactive index 1.6 The radius olf curvature of the curred surface is 60 cm. The facal length of the lens is

Options

A. `50 cm`
B. `100 cm`
C. `200 cm`
D. `400 cm`

Answer

To find the focal length of a plano-convex lens, we can use the lens maker's formula:

\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{r_1} - \frac{1}{r_2} \right) \]

Where:
- \( f \) is the focal length of the lens,
- \( \mu \) is the refractive index of the lens material,
- \( r_1 \) is the radius of curvature of the first surface,
- \( r_2 \) is the radius of curvature of the second surface.

### Step 1: Identify the parameters
- The refractive index \( \mu = 1.6 \).
- For a plano-convex lens, one surface is flat (plane), so \( r_1 = \infty \).
- The radius of curvature of the curved surface \( r_2 = 60 \, \text{cm} \). Since it is convex, we take \( r_2 \) as positive, so \( r_2 = +60 \, \text{cm} \).

### Step 2: Substitute the values into the lens maker's formula
Using the lens maker's formula:

\[ \frac{1}{f} = (1.6 - 1) \left( \frac{1}{\infty} - \frac{1}{60} \right) \]

### Step 3: Simplify the equation
- Since \( \frac{1}{\infty} = 0 \), we can simplify:

\[ \frac{1}{f} = 0.6 \left( 0 - \frac{1}{60} \right) \]

This simplifies to:

\[ \frac{1}{f} = 0.6 \left( -\frac{1}{60} \right) = -\frac{0.6}{60} \]

### Step 4: Calculate \( \frac{1}{f} \)
Calculating \( \frac{1}{f} \):

\[ \frac{1}{f} = -\frac{0.6}{60} = -0.01 \, \text{cm}^{-1} \]

### Step 5: Find the focal length \( f \)
Taking the reciprocal to find \( f \):

\[ f = \frac{1}{-0.01} = -100 \, \text{cm} \]

Since we are interested in the magnitude of the focal length, we take the positive value:

\[ f = 100 \, \text{cm} \]

### Conclusion
The focal length of the plano-convex lens is \( 100 \, \text{cm} \).

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