With a concave mirror, an object is placed at a distance 9cm from the principal focus, on the principal axis. The image is formed at a distance 16cm from the principal focus. The focal length of the mirror is

Options

A. 12cm
B. 11cm
C. 40cm
D. 30cm

Explanation

To find the focal length of the concave mirror given the distances from the principal focus, we can use Newton's formula for mirrors. Here’s a step-by-step solution:

### Step 1: Identify the given values
- Distance of the object from the principal focus (x1) = 9 cm
- Distance of the image from the principal focus (x2) = 16 cm

### Step 2: Apply Newton's formula
Newton's formula states that the focal length (f) of a mirror can be calculated using the formula:
\[ f = \sqrt{x_1 \cdot x_2} \]
where:
- \( x_1 \) is the distance of the object from the principal focus,
- \( x_2 \) is the distance of the image from the principal focus.

### Step 3: Substitute the values into the formula
Substituting the given values into the formula:
\[ f = \sqrt{9 \cdot 16} \]

### Step 4: Calculate the product
Calculate the product inside the square root:
\[ 9 \cdot 16 = 144 \]

### Step 5: Take the square root
Now, take the square root of 144:
\[ f = \sqrt{144} = 12 \, \text{cm} \]

### Conclusion
The focal length of the concave mirror is 12 cm.

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