The focal length of a convex mirror is 20 cm its radius of curvature will be

Options

A. (a)10 cm
B. (b)20 cm
C. (c)30 cm
D. (d)40 cm

Answer

To find the radius of curvature of a convex mirror given its focal length, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the relationship between focal length and radius of curvature**:
The radius of curvature (R) of a mirror is related to its focal length (F) by the formula:
\[ R = 2F \]

2. **Identify the given focal length**:
From the problem, we know that the focal length (F) of the convex mirror is given as:
\[ F = 20 \text{ cm} \]

3. **Substitute the focal length into the formula**:
Now, we can substitute the given focal length into the formula for radius of curvature:
\[ R = 2 \times F = 2 \times 20 \text{ cm} \]

4. **Calculate the radius of curvature**:
Performing the multiplication:
\[ R = 40 \text{ cm} \]

5. **State the final answer**:
Therefore, the radius of curvature of the convex mirror is:
\[ R = 40 \text{ cm} \]

### Final Answer:
The radius of curvature of the convex mirror is **40 cm**.

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