A short sighted person can see distinctly only those objects which lie between 10 cm and 100 cm from him. The power of the spectacle lens required to see a distant object is

Options

A. `+0.5D`
B. `-1.0D`
C. `-10D`
D. `+4.0D`

Explanation

To solve the problem of determining the power of the spectacle lens required for a short-sighted person to see distant objects, we will follow these steps:

### Step 1: Understand the condition of the short-sighted person
A short-sighted person, or myopic person, can see clearly only objects that are within a certain range. In this case, the person can see distinctly between 10 cm (0.1 m) and 100 cm (1 m).

### Step 2: Identify the far point of the person
The far point is the maximum distance at which the person can see clearly. Here, the far point is given as 100 cm (1 m).

### Step 3: Determine the focal length of the lens needed
To correct the vision of a short-sighted person, we need a concave lens. The focal length (f) of the lens is equal to the distance of the far point from the eye, but it will be negative since it is a concave lens. Thus, we have:
\[ f = -1 \, \text{m} \]

### Step 4: Calculate the power of the lens
The power (P) of a lens is given by the formula:
\[ P = \frac{1}{f} \]
where \( f \) is in meters. Substituting the value of \( f \):
\[ P = \frac{1}{-1} = -1 \, \text{diopter} \]

### Step 5: Conclusion
The power of the spectacle lens required for the short-sighted person to see distant objects clearly is:
\[ \text{Power} = -1 \, \text{diopter} \]

### Final Answer
The power of the spectacle lens required is **-1 diopter**.

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