A concave lens and a convex lens have same focal length of `20 cm` and both put in contact this combination is used to view an object `5 cm` long kept at `20 cm` from the lens combination. As compared to object the image will be

Options

A. Magnified and inverted
B. Reduced and erect
C. Of the same size and erect
D. Of the same size and inverted

Explanation

To solve the problem step by step, we need to determine the nature of the image formed by the combination of a concave lens and a convex lens, both having the same focal length of 20 cm.

### Step 1: Identify the Focal Lengths
- The focal length of the concave lens (F1) is negative:
\[ F_1 = -20 \, \text{cm} \]
- The focal length of the convex lens (F2) is positive:
\[ F_2 = 20 \, \text{cm} \]

### Step 2: Calculate the Equivalent Focal Length of the Combination
To find the equivalent focal length (F) of the combination of the two lenses in contact, we use the formula:
\[ \frac{1}{F} = \frac{1}{F_1} + \frac{1}{F_2} \]
Substituting the values:
\[ \frac{1}{F} = \frac{1}{-20} + \frac{1}{20} \]
This simplifies to:
\[ \frac{1}{F} = -\frac{1}{20} + \frac{1}{20} = 0 \]
Thus, the equivalent focal length is:
\[ F = \infty \]

### Step 3: Interpret the Equivalent Focal Length
An equivalent focal length of infinity means that the lens combination behaves like a plane glass slab. This indicates that it has no converging or diverging power.

### Step 4: Determine the Image Characteristics
Since the lens combination acts like a plane glass, it does not change the size of the image. Therefore, whatever object is placed in front of this combination will have its image formed at the same size and position as the object.

### Step 5: Conclusion
The object is 5 cm long and is placed at a distance of 20 cm from the lens combination. The image formed will be:
- **Same size as the object**
- **Not inverted or magnified**

Thus, the answer to the question is that the image will be the same size as the object.

### Final Answer
As compared to the object, the image will be the same size.

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