Two plane mirrors A and B are parallel to each other and spaced 20 cm apart. An object is kept in between them at 15 cm from a. Out of the following, at which point, image is not formed in mirror a (distance measured from mirror A)

Options

A. 15 cm
B. 25 cm
C. 45 cm
D. 55 cm

Answer

To solve the problem of determining at which point an image is not formed in mirror A, we will follow these steps:

### Step 1: Understand the Configuration
We have two parallel mirrors, A and B, separated by a distance of 20 cm. An object is placed 15 cm away from mirror A.

### Step 2: Determine the Position of the Object
- The object is positioned at a distance of 15 cm from mirror A.
- This means that the distance from mirror B (which is 20 cm away from A) is:
\[ \text{Distance from B} = 20 \text{ cm} - 15 \text{ cm} = 5 \text{ cm} \]

### Step 3: Find the Image Formed by Mirror A
- When light reflects off mirror A, it forms a virtual image behind the mirror at the same distance as the object.
- Therefore, the image \( I_1 \) formed by mirror A will be at:
\[ \text{Distance of } I_1 \text{ from A} = 15 \text{ cm} \]

### Step 4: Find the Image Formed by Mirror B
- The image \( I_1 \) acts as a virtual object for mirror B.
- The distance of this virtual object from mirror B is 5 cm (as calculated earlier).
- The image \( I_2 \) formed by mirror B will be at:
\[ \text{Distance of } I_2 \text{ from B} = 5 \text{ cm} \implies \text{Distance of } I_2 \text{ from A} = 20 \text{ cm} + 5 \text{ cm} = 25 \text{ cm} \]

### Step 5: Find Further Reflections
- The image \( I_2 \) will now act as a virtual object for mirror A.
- The distance of this virtual object from mirror A is 25 cm.
- Therefore, the image \( I_3 \) formed by mirror A will be at:
\[ \text{Distance of } I_3 \text{ from A} = 25 \text{ cm} \]

### Step 6: Continue the Process
- The image \( I_3 \) will act as a virtual object for mirror B.
- The distance from mirror B will be:
\[ \text{Distance from B} = 45 \text{ cm} - 20 \text{ cm} = 25 \text{ cm} \]
- The image \( I_4 \) formed by mirror B will be at:
\[ \text{Distance of } I_4 \text{ from A} = 45 \text{ cm} \]

### Conclusion
From the above calculations, we can see that images are formed at distances of 15 cm, 25 cm, and 45 cm from mirror A. However, since the mirrors are only 20 cm apart, there cannot be an image formed at a distance greater than 20 cm from mirror A without it being reflected back into the space between the mirrors.

Thus, the point at which an image is **not formed** in mirror A is:
- **Any point greater than 20 cm from mirror A**.