The power of a lens is -4.0 D. what is the nature of the lens?

Options

A. Plane
B. Concave
C. Convex
D. Plano convex

Explanation

To determine the nature of the lens based on its power, we can follow these steps:

### Step 1: Understand the relationship between power and focal length
The power (P) of a lens is defined by the formula:
\[ P = \frac{1}{f} \]
where \( P \) is the power in diopters (D) and \( f \) is the focal length in meters (m).

### Step 2: Identify the given power
In this problem, the power of the lens is given as:
\[ P = -4.0 \, D \]

### Step 3: Relate power to focal length
Since we have the formula for power, we can rearrange it to find the focal length:
\[ f = \frac{1}{P} \]

### Step 4: Substitute the value of power
Now, substituting the given power into the equation:
\[ f = \frac{1}{-4.0} \]
\[ f = -0.25 \, m \]

### Step 5: Determine the nature of the lens
The focal length \( f \) is negative. In optics, a lens with a negative focal length is a concave lens. Therefore, since the focal length is negative, we conclude that the lens is a concave lens.

### Final Answer:
The nature of the lens is **concave**.

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