Nature of image of a real object formed by convex mirror is always

Options

A. Virtual, erect and magnified
B. Virtual, erect and diminished
C. Virtual, inverted and diminished
D. Real, inverted and diminished

Answer

To determine the nature of the image formed by a convex mirror for a real object, we can follow these steps:

### Step 1: Understanding Convex Mirrors
A convex mirror is a spherical mirror that is curved outward. The focal point (F) of a convex mirror is virtual and located behind the mirror. The focal length (f) is considered positive in the sign convention used for mirrors.

### Step 2: Sign Convention
For a real object placed in front of a convex mirror:
- The object distance (U) is negative (U < 0).
- The focal length (F) is positive (F > 0).

### Step 3: Using the Mirror Formula
The mirror formula is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]
Where:
- \( f \) = focal length
- \( v \) = image distance
- \( u \) = object distance

Substituting the signs into the formula:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{(-u)} \]
Rearranging gives:
\[ \frac{1}{v} = \frac{1}{f} + \frac{1}{u} \]

### Step 4: Finding the Image Distance (v)
Since \( f \) is positive and \( u \) is negative, the right-hand side of the equation will yield a positive value for \( v \). Thus, we can conclude that:
\[ v > 0 \]
This indicates that the image is formed on the same side as the object, which is the virtual side for a convex mirror.

### Step 5: Nature of the Image
From the above analysis, we can conclude:
- The image distance \( v \) is positive, indicating that the image is virtual.
- The image formed is always upright (erect).
- The image is diminished (smaller than the object).

### Conclusion
Thus, the nature of the image of a real object formed by a convex mirror is always **virtual, erect, and diminished**.

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