A convex mirror offocal length fforms an image which is 1/n times the object. The distance of the object from the mirror is:

Options

A. (a)(n-1)f
B. (b)`((n-1)/n)f`
C. (c)`((n+1)/n)f`
D. (d)(n+1)f

Explanation

To solve the problem of finding the distance of the object from a convex mirror, given that the image formed is \( \frac{1}{n} \) times the object, we can follow these steps:

### Step 1: Understand the relationship between magnification and object/image distances
The magnification \( M \) for a mirror is given by the formula:
\[ M = \frac{-V}{U} \]
where \( V \) is the image distance and \( U \) is the object distance.

### Step 2: Set up the equation using the given magnification
From the problem, we know that the image is \( \frac{1}{n} \) times the object. Therefore, we can write:
\[ M = \frac{1}{n} \]
Substituting into the magnification formula, we have:
\[ \frac{1}{n} = \frac{-V}{U} \]
Cross-multiplying gives:
\[ V = -\frac{U}{n} \]

### Step 3: Use the mirror formula
The mirror formula for a convex mirror is given by:
\[ \frac{1}{f} = \frac{1}{V} + \frac{1}{U} \]
Substituting \( V = -\frac{U}{n} \) into the mirror formula:
\[ \frac{1}{f} = \frac{1}{-\frac{U}{n}} + \frac{1}{U} \]
This simplifies to:
\[ \frac{1}{f} = -\frac{n}{U} + \frac{1}{U} \]

### Step 4: Combine the fractions
Combining the terms on the right-hand side:
\[ \frac{1}{f} = \frac{-n + 1}{U} \]

### Step 5: Rearranging to find U
Rearranging the equation to solve for \( U \):
\[ U = \frac{(1 - n)f}{1} \]
This simplifies to:
\[ U = (1 - n)f \]

### Step 6: Final expression for the distance of the object
Since \( U \) represents the distance of the object from the mirror, we conclude:
\[ U = (1 - n)f \]

### Conclusion
Thus, the distance of the object from the convex mirror is:
\[ U = (1 - n)f \]