The focal length of a concave mirror with radius of curvature 12 cm is

Options

A. 12 cm
B. - 24 cm
C. 6 cm
D. -6 cm

Answer

To find the focal length of a concave 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) is given as 12 cm.

### Step 3: Substitute the radius of curvature into the formula
Now, we can substitute the value of R into the formula:
\[ f = \frac{12 \, \text{cm}}{2} \]

### Step 4: Calculate the focal length
Now, perform the calculation:
\[ f = 6 \, \text{cm} \]

### Step 5: Apply the sign convention
Since we are dealing with a concave mirror, the focal length is considered negative. Therefore:
\[ f = -6 \, \text{cm} \]

### Final Answer
The focal length of the concave mirror is \(-6 \, \text{cm}\).

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