A thin lens of focal length `+10.0 cm` lies on a horizontal plane mirror. How far above the lens should an object be be held if its image is to coincide with the object?

Explanation

To solve the problem, we need to determine how far above the lens an object should be held so that its image coincides with the object itself. Here’s a step-by-step solution:

### Step 1: Understand the Setup
We have a thin lens with a focal length (f) of +10.0 cm placed on a horizontal plane mirror. The lens will create an image of an object placed above it, and this image will be reflected by the mirror.

### Step 2: Identify the Focal Length
The focal length of the lens is given as +10.0 cm. This indicates that it is a converging lens.

### Step 3: Determine the Image Formation by the Lens
When an object is placed at the focal point of a converging lens, the rays of light coming from the object will diverge after passing through the lens. However, if the object is placed at the focal point (10 cm above the lens), the rays will exit the lens parallel to the principal axis.

### Step 4: Reflection by the Mirror
Since the lens is placed on a horizontal mirror, the parallel rays coming from the lens will strike the mirror and reflect back. The reflection will cause the rays to retrace their path back through the lens.

### Step 5: Coinciding Image and Object
When the rays reflect off the mirror and return through the lens, they will converge at the same point where the object was originally placed. Therefore, the image formed by the lens will coincide with the position of the object.

### Step 6: Conclusion
Thus, to have the image coincide with the object, the object must be placed at the focal point of the lens, which is 10 cm above the lens.

### Final Answer
The object should be held **10 cm above the lens**.

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