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 two lenses can form a real image?

Options

A. only the lens with power -3 D
B. only the lens with power 4 D
C. both the lenses
D. neither of the lenses

Answer

To determine which of the two lenses can form a real image, we need to analyze the powers of the lenses given in the problem.

### Step 1: Understand the relationship between power and focal length
The power (P) of a lens is related to its focal length (F) by the formula:
\[ P = \frac{1}{F} \]
Where:
- P is the power in diopters (D)
- F is the focal length in meters (m)

### Step 2: Calculate the focal lengths of the lenses
Given the powers of the two lenses:
- Lens 1: P1 = -3 D
- Lens 2: P2 = 4 D

Using the formula \( F = \frac{1}{P} \):
1. For Lens 1 (P1 = -3 D):
\[ F_1 = \frac{1}{-3} = -\frac{1}{3} \text{ m} \quad (\text{negative focal length indicates a concave lens}) \]

2. For Lens 2 (P2 = 4 D):
\[ F_2 = \frac{1}{4} = \frac{1}{4} \text{ m} \quad (\text{positive focal length indicates a convex lens}) \]

### Step 3: Determine which lens can form a real image
A real image is formed by a converging lens (convex lens) when the object is placed outside its focal length.

- Lens 1 (concave lens) cannot form a real image because it diverges light rays.
- Lens 2 (convex lens) can form a real image since it converges light rays.

### Conclusion
The lens that can form a real image is the convex lens with a power of +4 D.