A person has a minimum distance of distinct vision as 50cm. The power of lenses required to read a book at a distance of 25cm is

Options

A. 3D
B. 1D
C. 2D
D. 4D

Answer

To solve the problem step by step, we will use the lens formula and the concept of power of a lens.

### Step 1: Identify the given values
- The minimum distance of distinct vision (V) = -50 cm (the negative sign indicates that the image is formed on the same side as the object).
- The object distance (u) = -25 cm (the book is placed at 25 cm in front of the lens, hence the negative sign).

### Step 2: Use the lens formula
The lens formula is given by:
\[ \frac{1}{F} = \frac{1}{V} - \frac{1}{U} \]
Substituting the values we have:
\[ \frac{1}{F} = \frac{1}{-50} - \frac{1}{-25} \]

### Step 3: Simplify the equation
Calculating the right-hand side:
\[ \frac{1}{F} = -\frac{1}{50} + \frac{1}{25} \]
To combine these fractions, we need a common denominator. The least common multiple of 50 and 25 is 50:
\[ \frac{1}{F} = -\frac{1}{50} + \frac{2}{50} = \frac{1}{50} \]

### Step 4: Find the focal length (F)
From the equation, we have:
\[ \frac{1}{F} = \frac{1}{50} \]
Thus, the focal length \( F \) is:
\[ F = 50 \text{ cm} \]

### Step 5: Calculate the power of the lens
The power \( P \) of a lens is given by the formula:
\[ P = \frac{100}{F} \text{ (in cm)} \]
Substituting the value of \( F \):
\[ P = \frac{100}{50} = 2 \text{ diopters} \]

### Conclusion
The power of the lens required to read a book at a distance of 25 cm is **2 diopters**.