A boy stands straight in front of a mirror at a distance of 30 cm from it. He sees his erect image whose height is `(1)/(5)` of his real height. The mirror he is using is

Options

A. Plane
B. Convex
C. Concave
D. Plano-convex

Explanation

To determine the type of mirror the boy is using, we can analyze the information provided step by step.

### Step 1: Understand the Image Characteristics
The boy sees an erect image that is \( \frac{1}{5} \) of his real height. This means that the image is diminished and virtual.

**Hint:** Remember that an erect image is typically virtual and cannot be projected onto a screen.

### Step 2: Identify the Type of Mirror
1. **Plane Mirror:** A plane mirror produces an image that is the same size as the object (height remains unchanged). Therefore, it cannot produce an image that is \( \frac{1}{5} \) of the height. So, a plane mirror is not the answer.

2. **Concave Mirror:** A concave mirror can produce a virtual image, but this occurs when the object is placed between the focal point (F) and the mirror (P). However, concave mirrors generally produce magnified images in this position, not diminished ones. Therefore, a concave mirror is also not the answer.

3. **Convex Mirror:** A convex mirror always produces a virtual image that is diminished and erect, regardless of the position of the object. This matches the characteristics of the image seen by the boy.

**Hint:** Recall that convex mirrors always produce virtual images that are smaller than the object.

### Step 3: Conclusion
Based on the characteristics of the image (diminished, erect, and virtual), we conclude that the mirror the boy is using is a **convex mirror**.

**Final Answer:** The mirror he is using is a **convex mirror**.