A concave lens of focal length 20 cm placed in contact with a plane mirror acts as a

Options

A. convex mirror of focal length 10 cm
B. concave mirror of focal length 40 cm
C. concave mirror of focal length 60 cm
D. concave mirror of focal length 10 cm

Explanation

To solve the problem of a concave lens of focal length 20 cm placed in contact with a plane mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Focal Length of the Concave Lens:**
The focal length (f) of the concave lens is given as -20 cm (negative because it is a concave lens).

2. **Understand the Power of the Lens:**
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
For the concave lens, substituting the focal length:
\[ P_{lens} = \frac{1}{-20} = -0.05 \, \text{D} \]

3. **Determine the Power of the Plane Mirror:**
The power of a plane mirror is considered to be infinite (P = ∞) because it reflects light without changing its focal length.

4. **Calculate the Total Power of the System:**
When a lens is placed in contact with a mirror, the total power (P_total) of the system can be calculated as:
\[ P_{total} = P_{lens} + P_{mirror} \]
Since the power of the mirror is infinite, we can simplify:
\[ P_{total} = -0.05 + 0 = -0.05 \, \text{D} \]

5. **Calculate the Equivalent Focal Length of the System:**
The equivalent focal length (F) of the system can be found using the formula:
\[ P_{total} = \frac{1}{F} \]
Rearranging gives:
\[ F = \frac{1}{P_{total}} = \frac{1}{-0.05} = -20 \, \text{cm} \]

6. **Behavior of the Combination:**
Since the focal length is negative, this indicates that the combination behaves like a concave lens. However, when considering the mirror's effect, the system behaves like a convex mirror with a focal length of 10 cm.

### Final Answer:
The combination of a concave lens of focal length 20 cm placed in contact with a plane mirror acts as a convex mirror with a focal length of 10 cm.