A 4 diopter lens is used as a magnifier. Where should the object be placed to obtain maximum angular magnification for normal eye?

Answer

To solve the problem of where to place the object for maximum angular magnification using a 4 diopter lens as a magnifier, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The power (P) of the lens is given as 4 diopters (D).
- We need to find the focal length (f) of the lens.

2. **Calculate the Focal Length**:
- The relationship between power and focal length is given by the formula:
\[ f = \frac{1}{P} \]
- Substituting the value of power:
\[ f = \frac{1}{4} \text{ meters} = 0.25 \text{ meters} = 25 \text{ cm} \]

3. **Use the Magnification Formula**:
- The angular magnification (M) for a magnifying lens is given by:
\[ M = 1 + \frac{D}{f} \]
- Where D is the least distance of distinct vision, which is typically taken as 25 cm for a normal eye.

4. **Substituting Values into the Magnification Formula**:
- Substitute D = 25 cm and f = 25 cm into the magnification formula:
\[ M = 1 + \frac{25}{25} = 1 + 1 = 2 \]

5. **Relate Magnification to Object Distance**:
- The magnification can also be expressed in terms of object distance (u):
\[ M = \frac{D}{u} \]
- Setting the magnification equal to 2:
\[ 2 = \frac{25}{u} \]

6. **Solve for Object Distance (u)**:
- Rearranging the equation to find u:
\[ u = \frac{25}{2} = 12.5 \text{ cm} \]

### Final Answer:
The object should be placed at a distance of **12.5 cm** from the lens to obtain maximum angular magnification for a normal eye.