Two plane mirrors are placed parallel to each other and 40 cm apart. An a object is placed 10 cm from one mirror .What is the distance from the object to the image for each of the five images that are closest to the object?

Explanation

To solve the problem of finding the distances from the object to the five closest images formed by two parallel mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Setup**:
- We have two parallel mirrors, Mirror 1 (M1) and Mirror 2 (M2), placed 40 cm apart.
- An object (O) is placed 10 cm away from Mirror 1.

2. **Determine the Position of the First Image (I1)**:
- The first image (I1) is formed by the reflection of the object in Mirror 1.
- Since the object is 10 cm from Mirror 1, the distance from the object to the first image (I1) is:
\[ D_{O \to I1} = 10 \, \text{cm} + 10 \, \text{cm} = 20 \, \text{cm} \]

3. **Determine the Position of the Second Image (I2)**:
- The second image (I2) is formed by the reflection of the first image (I1) in Mirror 2.
- The distance from I1 to Mirror 2 is:
\[ D_{I1 \to M2} = 40 \, \text{cm} - 10 \, \text{cm} = 30 \, \text{cm} \]
- Therefore, the distance from the object to I2 is:
\[ D_{O \to I2} = 30 \, \text{cm} + 30 \, \text{cm} = 60 \, \text{cm} \]

4. **Determine the Position of the Third Image (I3)**:
- The third image (I3) is formed by the reflection of I2 in Mirror 1.
- The distance from I2 to Mirror 1 is:
\[ D_{I2 \to M1} = 60 \, \text{cm} - 10 \, \text{cm} = 50 \, \text{cm} \]
- Therefore, the distance from the object to I3 is:
\[ D_{O \to I3} = 50 \, \text{cm} + 30 \, \text{cm} = 80 \, \text{cm} \]

5. **Determine the Position of the Fourth Image (I4)**:
- The fourth image (I4) is formed by the reflection of I3 in Mirror 2.
- The distance from I3 to Mirror 2 is:
\[ D_{I3 \to M2} = 80 \, \text{cm} - 30 \, \text{cm} = 50 \, \text{cm} \]
- Therefore, the distance from the object to I4 is:
\[ D_{O \to I4} = 50 \, \text{cm} + 30 \, \text{cm} = 80 \, \text{cm} \]

6. **Determine the Position of the Fifth Image (I5)**:
- The fifth image (I5) is formed by the reflection of I4 in Mirror 1.
- The distance from I4 to Mirror 1 is:
\[ D_{I4 \to M1} = 80 \, \text{cm} - 10 \, \text{cm} = 70 \, \text{cm} \]
- Therefore, the distance from the object to I5 is:
\[ D_{O \to I5} = 70 \, \text{cm} + 30 \, \text{cm} = 100 \, \text{cm} \]

### Summary of Distances:
- Distance from O to I1: 20 cm
- Distance from O to I2: 60 cm
- Distance from O to I3: 80 cm
- Distance from O to I4: 80 cm
- Distance from O to I5: 100 cm

### Final Distances:
1. **I1**: 20 cm
2. **I2**: 60 cm
3. **I3**: 80 cm
4. **I4**: 80 cm
5. **I5**: 100 cm