The formula for magnification m of a lens is :

Options

A. `v/u`
B. `(-v)/u`
C. `u/v`
D. `-u/v`

Answer

To derive the formula for magnification (M) of a lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Object and Image Heights**:
- Let the height of the object be denoted as \( H_o \) (height of object).
- Let the height of the image be denoted as \( H_i \) (height of image).

2. **Defining Magnification**:
- Magnification (M) is defined as the ratio of the height of the image to the height of the object. Therefore, the formula for magnification can be expressed as:
\[ M = \frac{H_i}{H_o} \]

3. **Understanding Object and Image Distances**:
- In addition to height, magnification can also be expressed in terms of distances from the lens. Let:
- \( V \) be the image distance (distance from the lens to the image).
- \( U \) be the object distance (distance from the lens to the object).

4. **Alternative Formula for Magnification**:
- The magnification can also be expressed as the ratio of the image distance to the object distance:
\[ M = \frac{V}{U} \]

5. **Conclusion**:
- Thus, the magnification of a lens can be represented using two formulas:
\[ M = \frac{H_i}{H_o} \quad \text{and} \quad M = \frac{V}{U} \]