The mirror formula is given by
`1/v+1/u=1/f`
where the symbols have their usual meanings. Then the lens formula is given by

Options

A. `1/v+1/u=1/f`
B. `1/v-1/u=1/f`
C. `1/v+1/u=-1/f`
D. none of these

Answer

To derive the lens formula from the mirror formula, we can follow these steps:

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

### Step 2: Transition to Lens Formula
For lenses, the formula is slightly different. The lens formula is given by:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]
where:
- \( v \) = distance of the image from the lens
- \( u \) = distance of the object from the lens
- \( f \) = focal length of the lens

### Step 3: Identify the Differences
The main difference between the mirror and lens formulas is the sign in front of the object distance \( u \). In the lens formula, it is subtracted, while in the mirror formula, it is added.

### Step 4: Conclusion
Thus, the lens formula can be stated as:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

### Final Answer
The lens formula is:
\[ \frac{1}{v} - \frac{1}{u} = \frac{1}{f} \]

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