A plano-concave lens is made of glass (R.l. = 1.5) and the radius of curvature of the curved face is 50 cm. The power of the lens is

Options

A. -1.0D
B. -0.5D
C. +1.0D
D. +0.5 D

Answer

To find the power of a plano-concave lens made of glass with a refractive index of 1.5 and a radius of curvature of the curved face of 50 cm, we can follow these steps:

### Step 1: Understand the Lens Maker's Formula
The lens maker'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,
- \( R_1 \) is the radius of curvature of the first surface,
- \( R_2 \) is the radius of curvature of the second surface.

### Step 2: Identify the Parameters
For a plano-concave lens:
- The first surface is flat (plano), so \( R_1 = \infty \).
- The second surface is concave, and given that the radius of curvature is 50 cm, we take \( R_2 = -50 \) cm (the negative sign indicates that it is concave).

Given:
- \( \mu = 1.5 \)

### Step 3: Substitute Values into the Formula
Substituting the values into the lens maker's formula:
\[ \frac{1}{f} = (1.5 - 1) \left( \frac{1}{\infty} - \frac{1}{-50} \right) \]
This simplifies to:
\[ \frac{1}{f} = 0.5 \left( 0 - \left(-\frac{1}{50}\right) \right) \]
\[ \frac{1}{f} = 0.5 \left( \frac{1}{50} \right) \]
\[ \frac{1}{f} = \frac{0.5}{50} = \frac{1}{100} \]

### Step 4: Calculate the Focal Length
From the above, we find:
\[ f = 100 \text{ cm} = 1 \text{ m} \]
Since the lens is concave, the focal length is negative:
\[ f = -100 \text{ cm} = -1 \text{ m} \]

### Step 5: Calculate the Power of the Lens
The power \( P \) of the lens is given by:
\[ P = \frac{1}{f} \text{ (in meters)} \]
Substituting the focal length:
\[ P = \frac{1}{-1} = -1 \text{ diopter} \]

### Final Answer
The power of the plano-concave lens is \(-1.0\) diopter.

---