A real image is formed by a convex lens. Then it is put in contact with a concave lens and again a real image is formed. This image will
shift towards the lens system
shift away from the lens system
remain in its original position
shift to infinity

Options

A. shift towards the lens system
B. shift away from the lens system
C. remain in its original position
D. shift to infinity

Answer

To solve the problem step by step, we need to analyze the situation involving a convex lens and a concave lens placed in contact with each other.

### Step 1: Understand the formation of a real image by the convex lens
- A convex lens forms a real image when the object is placed beyond its focal length (F). This means that the object distance (u) is less than -F (using the sign convention where distances measured against the direction of incident light are negative).

### Step 2: Introduce the concave lens
- When the convex lens is placed in contact with a concave lens, we need to consider the effect of the concave lens. A concave lens always produces a virtual image when an object is placed in front of it. However, in this case, since the convex lens already formed a real image, we need to analyze how the combination of these two lenses affects the position of the image.

### Step 3: Analyze the powers of the lenses
- The power of the convex lens (P1) is positive, and the power of the concave lens (P2) is negative. The total power (P) of the lens system can be calculated as:
\[ P = P1 + P2 \]
- Since P1 is positive and P2 is negative, the overall power of the system will be less than that of the convex lens alone, which means the focal length (f) of the combined system will increase.

### Step 4: Use the lens formula
- The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
where \( f \) is the focal length of the lens system, \( v \) is the image distance, and \( u \) is the object distance.
- Since \( u \) remains constant (the object position does not change), and \( f \) increases (the focal length of the combined system is larger), it follows that \( v \) must also increase to satisfy the lens formula.

### Step 5: Conclusion on the position of the image
- As \( v \) increases, this indicates that the image formed by the lens system shifts away from the lens. Therefore, the correct answer to the question is that the image will shift away from the lens system.

### Final Answer:
The image will shift away from the lens system.

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