Two plane mirrors are plaved 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 first five images formed by two parallel mirrors, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have two plane mirrors (let's call them Mirror A and Mirror B) placed parallel to each other, 40 cm apart.
- An object (let's call it O) is placed 10 cm from Mirror A.

2. **Determine the Position of the Object**:
- Since the object O is 10 cm from Mirror A, it is 30 cm from Mirror B (because the total distance between the mirrors is 40 cm).

3. **Calculate the First Image (I1)**:
- The first image (I1) is the reflection of the object O in Mirror A.
- The distance from O to I1 is equal to twice the distance from O to Mirror A.
- Distance I1O = 2 * 10 cm = 20 cm.

4. **Calculate the Second Image (I2)**:
- The second image (I2) is the reflection of the object O in Mirror B.
- The distance from O to I2 is equal to twice the distance from O to Mirror B.
- Distance I2O = 2 * 30 cm = 60 cm.

5. **Calculate the Third Image (I3)**:
- The third image (I3) is the reflection of I1 in Mirror B.
- The distance from I1 to Mirror B is 30 cm (since O is 10 cm from A, and A is 40 cm from B).
- Therefore, the distance from O to I3 is I1B + BO = 30 cm + 40 cm = 80 cm.

6. **Calculate the Fourth Image (I4)**:
- The fourth image (I4) is the reflection of I2 in Mirror A.
- The distance from I2 to Mirror A is 70 cm (since I2 is 60 cm from O and O is 10 cm from A).
- Therefore, the distance from O to I4 is I2A + AO = 70 cm + 10 cm = 80 cm.

7. **Calculate the Fifth Image (I5)**:
- The fifth image (I5) is the reflection of I3 in Mirror A.
- The distance from I3 to Mirror A is 50 cm (since I3 is 80 cm from O and O is 10 cm from A).
- Therefore, the distance from O to I5 is I3A + AO = 50 cm + 10 cm = 100 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 Answer:
The distances from the object to the first five images are:
1. 20 cm
2. 60 cm
3. 80 cm
4. 80 cm
5. 100 cm