Shashank went to the optician to get his eyes checked. He observed that the doctor combined two lenses and put these in front of his eyes so that he could see clearly. The powers of the two lenses used in the combination were -3 D and 4 D.
Which of the following does the negative sign in the power -3 D signify?

Options

A. The focus is on the same side of the lens as the object.
B. The focus is on the opposite side of the lens as the object.
C. The principal focus is situated outside the principal axis.
D. The focal length on one side of the lens is smaller than that on the other.

Answer

To solve the question regarding the significance of the negative sign in the power of the lens, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Lens Power**:
The power (P) of a lens is defined as the reciprocal of its focal length (f) in meters. The formula is given by:
\[ P = \frac{1}{f} \]
where P is in diopters (D) and f is in meters.

2. **Identifying the Given Values**:
In this case, we have two lenses with powers:
- Lens 1: \( P_1 = -3 \, D \)
- Lens 2: \( P_2 = 4 \, D \)

3. **Analyzing the Negative Power**:
The negative sign in the power of the lens indicates that the focal length is negative. Therefore, for the lens with power -3 D:
\[ f_1 = \frac{1}{P_1} = \frac{1}{-3} \, \text{m} = -\frac{1}{3} \, \text{m} \]

4. **Understanding Focal Length Significance**:
According to the Cartesian sign convention:
- Focal lengths of converging lenses (convex lenses) are positive.
- Focal lengths of diverging lenses (concave lenses) are negative.

5. **Conclusion**:
Since the focal length is negative, it signifies that the lens is a diverging lens (concave lens). This means that the focus of the lens is on the same side as the object, which is why the light rays diverge.

### Final Answer:
The negative sign in the power of -3 D signifies that the lens is a diverging lens (concave lens) and that its focal length is negative, indicating that the focus is on the same side as the object.

---