A convex lens of focal length f forms an image which is 1/3 times the size of the object. Then, the distance of object from the lens is

Options

A. 2f
B. f
C. `(2)/(3)f`
D. `(3)/(2)f`

Explanation

To solve the problem step by step, we can follow these instructions:

### Step 1: Understand the given information
We have a convex lens with a focal length \( f \) that forms an image which is \( \frac{1}{3} \) times the size of the object.

### Step 2: Use the magnification formula
The magnification \( m \) is given by the formula:
\[ m = \frac{V}{U} \]
where \( V \) is the image distance and \( U \) is the object distance. Since the image is \( \frac{1}{3} \) times the size of the object, we can write:
\[ m = \frac{1}{3} \]
Thus, we have:
\[ \frac{V}{U} = \frac{1}{3} \]
From this, we can express \( V \) in terms of \( U \):
\[ V = \frac{U}{3} \]

### Step 3: Apply the lens formula
The lens formula is given by:
\[ \frac{1}{f} = \frac{1}{V} - \frac{1}{U} \]
Substituting \( V = \frac{U}{3} \) into the lens formula, we get:
\[ \frac{1}{f} = \frac{1}{\frac{U}{3}} - \frac{1}{U} \]

### Step 4: Simplify the equation
Now, simplify the right-hand side:
\[ \frac{1}{f} = \frac{3}{U} - \frac{1}{U} \]
Combining the fractions gives:
\[ \frac{1}{f} = \frac{3 - 1}{U} = \frac{2}{U} \]

### Step 5: Solve for \( U \)
To find \( U \), we can rearrange the equation:
\[ U = 2f \]

### Conclusion
Thus, the distance of the object from the lens is:
\[ U = 2f \]