Which of the following represents correct mirror formula ?

Options

A. `(1)/(f)=(1)/(v)-(1)/(u)`
B. `(1)/(f)=(1)/(v)+(1)/(u)`
C. `f=v+u`
D. `(1)/(f)=v+u`

Answer

To solve the question regarding the correct mirror formula, we will follow these steps:

### Step 1: Identify the Mirror Formula
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where:
- \(f\) is the focal length of the mirror,
- \(v\) is the image distance,
- \(u\) is the object distance.

### Step 2: Rearranging the Formula
We can rearrange the formula to express \(f\) in terms of \(u\) and \(v\):
\[ \frac{1}{f} = \frac{u + v}{uv} \]
This implies:
\[ f = \frac{uv}{u + v} \]

### Step 3: Analyzing the Options
Now, we will analyze the provided options to determine which one is correct:
1. **Option 1**: \( \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \) - This is incorrect; it is the lens formula, not the mirror formula.
2. **Option 2**: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \) - This is correct as it matches the mirror formula.
3. **Option 3**: \( f = \frac{u + v}{uv} \) - This is incorrect; it does not represent the correct relationship.
4. **Option 4**: \( \frac{1}{f} = \frac{u + b}{uv} \) - This is also incorrect; it has an erroneous term \(b\).

### Step 4: Conclusion
The correct mirror formula is:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

### Final Answer
The correct option representing the mirror formula is:
**Option 2: \( \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \)**

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