A plano convex lens is made of glass of refractive index 1.5. The radius of curvature of its convex surface is R. Its focal length is

Options

A. R/2
B. R
C. 2R
D. 1.5R

Explanation

To find the focal length of a plano-convex lens made of glass with a refractive index of 1.5 and a convex surface radius of curvature \( R \), we can use the lens maker's formula:

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

### Step 1: Identify the parameters
- Refractive index \( \mu = 1.5 \)
- Radius of curvature of the convex surface \( R_1 = R \)
- The plane surface has an infinite radius of curvature \( R_2 = \infty \)

### Step 2: Substitute the values into the lens maker's formula
Using the values identified:
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{R} - \frac{1}{\infty} \right) \]

### Step 3: Simplify the equation
Since \( \frac{1}{\infty} = 0 \), the equation simplifies to:
\[ \frac{1}{f} = 0.5 \left( \frac{1}{R} - 0 \right) \]
\[ \frac{1}{f} = 0.5 \cdot \frac{1}{R} \]

### Step 4: Solve for \( f \)
To find \( f \), we can rearrange the equation:
\[ \frac{1}{f} = \frac{0.5}{R} \]
Taking the reciprocal gives:
\[ f = \frac{R}{0.5} = 2R \]

### Conclusion
The focal length \( f \) of the plano-convex lens is:
\[ f = 2R \]