Find the distance of an object from a convex lens if image is
two times magnified. Focal length of the lens is `10cm`

Explanation

To find the distance of an object from a convex lens when the image is two times magnified, we can follow these steps:

### Step 1: Understand the Magnification Formula
The magnification (m) for a lens is given by the formula:
\[ m = \frac{v}{u} \]
where \( v \) is the image distance and \( u \) is the object distance. Given that the image is two times magnified, we have:
\[ m = 2 \]
Thus, we can write:
\[ \frac{v}{u} = 2 \]
This implies:
\[ v = 2u \]

### Step 2: Consider the Lens Formula
The lens formula relates the object distance (u), image distance (v), and focal length (f) of the lens:
\[ \frac{1}{f} = \frac{1}{v} - \frac{1}{u} \]
Given that the focal length \( f = 10 \, \text{cm} \), we can substitute \( v = 2u \) into the lens formula.

### Step 3: Substitute and Rearrange the Lens Formula
Substituting \( v = 2u \) into the lens formula gives:
\[ \frac{1}{10} = \frac{1}{2u} - \frac{1}{u} \]
To simplify, we can find a common denominator:
\[ \frac{1}{10} = \frac{1 - 2}{2u} \]
This simplifies to:
\[ \frac{1}{10} = \frac{-1}{2u} \]

### Step 4: Solve for Object Distance (u)
Now, we can solve for \( u \):
\[ 2u = -10 \]
\[ u = -5 \, \text{cm} \]

### Step 5: Interpret the Result
The negative sign indicates that the object is on the same side as the incoming light, which is consistent with the sign convention for lenses.

### Final Answer
The distance of the object from the convex lens is:
\[ |u| = 5 \, \text{cm} \]

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