A person can see clearly objects between 15 and 100 cm from his eye. The range of his vision if he wears close fitting spetancles having a power of -0.8 diopter is

Options

A. 5 to 500 cm
B. 12 to 250 cm
C. 17 to 500 cm
D. 17 to 250 cm

Explanation

To solve the problem, we need to determine the new range of vision for a person who can normally see objects clearly between 15 cm and 100 cm from his eye when he wears spectacles with a power of -0.8 diopters.

### Step-by-Step Solution:

1. **Understanding the Power of the Lens:**
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is the focal length in meters. Given that the power of the spectacles is -0.8 diopters, we can find the focal length:
\[ f = \frac{1}{P} = \frac{1}{-0.8} = -1.25 \text{ meters} = -125 \text{ cm} \]

2. **Finding the New Near Point:**
The near point of the eye without spectacles is 15 cm. When wearing spectacles, the effective near point (D) can be calculated using the lens formula:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]
Here, \( u \) is the object distance (the near point), and \( v \) is the image distance (the new near point with spectacles). We can rearrange the formula to find \( v \):
\[ \frac{1}{v} = \frac{1}{-125} + \frac{1}{-15} \]

Calculating the right-hand side:
\[ \frac{1}{v} = -0.008 + -0.0667 = -0.0747 \]
Therefore,
\[ v = \frac{1}{-0.0747} \approx -13.39 \text{ cm} \]
Since we are interested in the absolute value, the new near point is approximately 13.39 cm.

3. **Finding the New Far Point:**
The far point of the eye without spectacles is 100 cm. We will use the same lens formula to find the new far point:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]
Here, \( u \) is the object distance (the far point), and we want to find \( v \) (the new far point with spectacles):
\[ \frac{1}{v} = \frac{1}{-125} + \frac{1}{-100} \]

Calculating:
\[ \frac{1}{v} = -0.008 + -0.01 = -0.018 \]
Therefore,
\[ v = \frac{1}{-0.018} \approx -55.56 \text{ cm} \]
Again, taking the absolute value, the new far point is approximately 55.56 cm.

4. **Final Range of Vision:**
The new range of vision for the person wearing the spectacles is from approximately 13.39 cm to 55.56 cm.

### Conclusion:
The range of vision for the person wearing spectacles with a power of -0.8 diopters is approximately **13.39 cm to 55.56 cm**.