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 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 eye from the ground is 1.5 m.
- The height of the lower end of the mirror from the ground is 0.8 m.
- The length of the mirror is 0.3 m.

### Step 2: Determine the height of the upper end of the mirror
- Since the lower end of the mirror is at 0.8 m and the mirror is 0.3 m long, the upper end of the mirror is at:
\[ \text{Height of upper end} = 0.8 \, \text{m} + 0.3 \, \text{m} = 1.1 \, \text{m} \]

### Step 3: Analyze the image formation
- In a plane mirror, the image formed is of the same height as the object and appears at the same distance behind the mirror as the object is in front of it.
- The image of the person's eye will be located at a height equal to the height of the eye above the ground, which is 1.5 m.

### Step 4: Determine the effective height for the image
- The person's eye is at 1.5 m, and since the mirror's upper end is at 1.1 m, the image will be reflected from the mirror.
- The distance from the person's eye (1.5 m) to the upper end of the mirror (1.1 m) is:
\[ \text{Distance from eye to upper end of mirror} = 1.5 \, \text{m} - 1.1 \, \text{m} = 0.4 \, \text{m} \]
- The image will appear at the same height as the person's eye, which is 1.5 m, but since the mirror only goes up to 1.1 m, we need to consider the height of the image that can be seen in the mirror.

### Step 5: Determine the visible height of the image
- The height of the image that can be seen in the mirror is limited by the height of the mirror. Since the mirror is 0.3 m long and starts at 0.8 m, it can reflect the image from 0.8 m to 1.1 m.
- The height of the image seen in the mirror will be:
\[ \text{Height of image} = \text{Height of eye} - \text{Height of lower end of mirror} = 1.5 \, \text{m} - 0.8 \, \text{m} = 0.7 \, \text{m} \]

### Step 6: Conclusion
- Therefore, the length of the image that the person sees of himself in the mirror is:
\[ \text{Length of the image} = 0.3 \, \text{m} \]

### Final Answer
The length of the image he sees of himself is **0.3 m**.

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