If the radius of curvature of a convex mirror is 40 cm, then its focal length is

Options

A. -20 cm
B. 20 cm
C. 40 cm
D. -40 cm

Answer

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

### Step 1: Understand the relationship between focal length and radius of curvature
The focal length (f) of a mirror is related to its radius of curvature (R) by the formula:
\[ f = \frac{R}{2} \]

### Step 2: Identify the radius of curvature
In this problem, the radius of curvature (R) of the convex mirror is given as 40 cm.

### Step 3: Determine the sign of the radius of curvature
For a convex mirror, the radius of curvature is considered positive when using the sign convention. Therefore, we have:
\[ R = +40 \, \text{cm} \]

### Step 4: Substitute the radius of curvature into the formula
Now, we can substitute the value of R into the formula for focal length:
\[ f = \frac{R}{2} = \frac{40 \, \text{cm}}{2} \]

### Step 5: Calculate the focal length
Now, performing the calculation:
\[ f = \frac{40}{2} = 20 \, \text{cm} \]

### Conclusion
The focal length of the convex mirror is:
\[ f = 20 \, \text{cm} \]

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