Calculate the focal length of a reading glass of a person, if the distance of distinct vision is 75cm.

Options

A. 75.2cm
B. 25.6cm
C. 100.4cm
D. 37.5cm

Explanation

To solve the problem of calculating the focal length of a reading glass for a person with a distance of distinct vision of 75 cm, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Values:**
- The distance of distinct vision (V) is given as 75 cm. Since this is a virtual image formed by the lens, we will take it as negative:
\[ V = -75 \text{ cm} \]

2. **Determine the Object Distance (U):**
- The distance of distinct vision for a normal eye is typically considered to be 25 cm. Since this is the object distance, we also take it as negative:
\[ U = -25 \text{ cm} \]

3. **Use the Lens Formula:**
- The lens formula relates the focal length (f), object distance (U), and image distance (V):
\[ \frac{1}{f} = \frac{1}{V} + \frac{1}{U} \]

4. **Substitute the Values:**
- Now, substituting the values of V and U into the lens formula:
\[ \frac{1}{f} = \frac{1}{-75} + \frac{1}{-25} \]

5. **Calculate Each Term:**
- Calculate \(\frac{1}{-75}\) and \(\frac{1}{-25}\):
\[ \frac{1}{-75} = -\frac{1}{75}, \quad \frac{1}{-25} = -\frac{1}{25} \]

6. **Find a Common Denominator:**
- The common denominator for 75 and 25 is 75. Convert \(\frac{1}{-25}\) to have the same denominator:
\[ \frac{1}{-25} = -\frac{3}{75} \]

7. **Combine the Fractions:**
- Now combine the two fractions:
\[ \frac{1}{f} = -\frac{1}{75} - \frac{3}{75} = -\frac{4}{75} \]

8. **Invert to Find Focal Length:**
- To find the focal length (f), take the reciprocal:
\[ f = -\frac{75}{4} = -18.75 \text{ cm} \]

9. **Interpret the Result:**
- The negative sign indicates that the focal length is for a converging lens (reading glass), and the absolute value gives us the focal length:
\[ f = 18.75 \text{ cm} \]

### Final Answer:
The focal length of the reading glass is **18.75 cm**.