An object is placed on principal axis of concave mirror at distance of 1.5 f Image will be at

Options

A. -3f
B. 1.5f
C. -1.5f
D. 3f

Answer

To solve the problem of finding the image position when an object is placed at a distance of 1.5f from a concave mirror, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the given values**:
- Object distance (u) = -1.5f (the negative sign indicates that the object is in front of the mirror).
- Focal length (f) = -f (for a concave mirror, the focal length is considered negative).

2. **Use the mirror formula**:
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
where:
- \( f \) is the focal length,
- \( v \) is the image distance,
- \( u \) is the object distance.

3. **Substitute the values into the mirror formula**:
\[ \frac{1}{-f} = \frac{1}{v} + \frac{1}{-1.5f} \]

4. **Rearranging the equation**:
\[ \frac{1}{v} = \frac{1}{-f} - \frac{1}{1.5f} \]

5. **Finding a common denominator**:
The common denominator for the right side is \( 1.5f \):
\[ \frac{1}{v} = \frac{-1.5}{1.5f} + \frac{1}{1.5f} \]
\[ \frac{1}{v} = \frac{-1.5 + 1}{1.5f} = \frac{-0.5}{1.5f} \]

6. **Simplifying the equation**:
\[ \frac{1}{v} = \frac{-1}{3f} \]

7. **Taking the reciprocal to find v**:
\[ v = -3f \]

8. **Conclusion**:
The image will be formed at a distance of -3f from the mirror, which means it is located on the same side as the object, and it is a real and inverted image.

### Final Answer:
The image will be at a distance of -3f.