A plano-convex lens has refractive index 1.6 and radius of curvature 60 cm. What is the focal length of the lens?

Options

A. 50 cm
B. 100 cm
C. 200 cm
D. 150 cm

Explanation

To find the focal length of a plano-convex lens with a refractive index of 1.6 and a radius of curvature of 60 cm, we can use the Lensmaker's Formula. Here’s the step-by-step solution:

### Step 1: Understand the Lensmaker's Formula
The Lensmaker's Formula is given by:

\[ \frac{1}{f} = (\mu - 1) \left( \frac{1}{R_1} - \frac{1}{R_2} \right) \]

Where:
- \( f \) is the focal length of the lens,
- \( \mu \) is the refractive index of the lens material relative to the surrounding medium,
- \( R_1 \) is the radius of curvature of the first surface,
- \( R_2 \) is the radius of curvature of the second surface.

### Step 2: Identify the Values
For a plano-convex lens:
- The refractive index \( \mu \) is given as 1.6 (for glass).
- The radius of curvature \( R_1 \) (convex surface) is +60 cm (positive because it is convex).
- The radius of curvature \( R_2 \) (plane surface) is infinity, which means \( R_2 = \infty \) and thus \( \frac{1}{R_2} = 0 \).

### Step 3: Calculate the Relative Refractive Index
Since the lens is in air, the relative refractive index \( \mu \) is simply:

\[ \mu = \frac{1.6}{1} = 1.6 \]

### Step 4: Substitute Values into the Formula
Now substituting the values into the Lensmaker's Formula:

\[ \frac{1}{f} = (1.6 - 1) \left( \frac{1}{60} - 0 \right) \]

This simplifies to:

\[ \frac{1}{f} = 0.6 \cdot \frac{1}{60} \]

### Step 5: Simplify the Equation
Calculating the right side:

\[ \frac{1}{f} = \frac{0.6}{60} = \frac{6}{600} \]

### Step 6: Find the Focal Length
Taking the reciprocal gives:

\[ f = \frac{600}{6} = 100 \text{ cm} \]

Thus, the focal length of the plano-convex lens is **100 cm**.

### Final Answer
The focal length of the lens is **100 cm**.

---