A person's eye is at a height of 1.5 m . He stands infront of a 0.3 m long plane mirror whose lower end is 0.8m above the ground. The length of the image he sees of himself is

Options

A. 1.5 m
B. 1.0 m
C. 0.8 m
D. 0.6 m

Answer

To solve the problem, we need to determine the length of the image that a person sees in a plane mirror. Here’s a step-by-step solution:

### Step 1: Understand the Setup
- The height of the person's eyes from the ground is 1.5 m.
- The length of the plane mirror is 0.3 m.
- The lower end of the mirror is 0.8 m above the ground.

### Step 2: Determine the Position of the Mirror
- The top end of the mirror can be calculated as:
\[ \text{Height of the top end of the mirror} = \text{Height of the lower end} + \text{Length of the mirror} = 0.8 \, \text{m} + 0.3 \, \text{m} = 1.1 \, \text{m} \]

### Step 3: Identify the Relevant Distances
- The person's eyes are at 1.5 m, which is above the top of the mirror (1.1 m). Therefore, the person can see their reflection in the mirror.
- The distance from the person's eyes to the top of the mirror is:
\[ \text{Distance from eyes to top of mirror} = 1.5 \, \text{m} - 1.1 \, \text{m} = 0.4 \, \text{m} \]

### Step 4: Determine the Length of the Image
- The length of the image seen in the mirror can be determined using the properties of similar triangles. The image will appear to be as tall as the distance from the eyes to the top of the mirror, doubled (because the image in a plane mirror is the same height as the object).
- The distance from the eyes to the bottom of the mirror is:
\[ \text{Distance from eyes to bottom of mirror} = 1.5 \, \text{m} - 0.8 \, \text{m} = 0.7 \, \text{m} \]
- The total height of the image is the distance from the eyes to the top of the mirror plus the distance from the eyes to the bottom of the mirror:
\[ \text{Length of image} = 0.4 \, \text{m} + 0.7 \, \text{m} = 1.1 \, \text{m} \]
- However, the effective length of the image seen in the mirror is determined by the height of the mirror itself, which gives us:
\[ \text{Length of image seen} = 2 \times \text{Length of mirror} = 2 \times 0.3 \, \text{m} = 0.6 \, \text{m} \]

### Final Answer
Thus, the length of the image that the person sees of himself is **0.6 m**.

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