A point object is placed at distance of 30 cm in front of a convex mirror of Focal length 30 cm. The image will form at

Options

A. infinity
B. pole
C. focus
D. 15 cm behind the mirror

Answer

To solve the problem of finding the image distance for a point object placed in front of a convex mirror, we can use the mirror formula:

\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]

Where:
- \( f \) is the focal length of the mirror,
- \( v \) is the image distance from the mirror,
- \( u \) is the object distance from the mirror.

### Step-by-step Solution:

1. **Identify the given values:**
- Focal length of the convex mirror, \( f = +30 \) cm (positive because for convex mirrors, the focal length is taken as positive).
- Object distance, \( u = -30 \) cm (negative because the object is placed in front of the mirror).

2. **Substitute the values into the mirror formula:**
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Plugging in the values:
\[ \frac{1}{30} = \frac{1}{v} + \frac{1}{-30} \]

3. **Rearranging the equation:**
\[ \frac{1}{30} + \frac{1}{30} = \frac{1}{v} \]
This simplifies to:
\[ \frac{2}{30} = \frac{1}{v} \]

4. **Finding \( v \):**
To find \( v \), take the reciprocal:
\[ v = \frac{30}{2} = 15 \text{ cm} \]

5. **Determine the nature of the image:**
Since the image distance \( v \) is positive, it indicates that the image is formed on the same side as the object, which is typical for a convex mirror. The image will be virtual and upright.

### Final Answer:
The image will be formed at a distance of 15 cm behind the mirror.