What is the formula to find number of images formed when two plane mirrors are inclined at an angle?

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Take two plane mirrors (without frame). Place both the mirrors side by side and fix the junction where they meet with a cello tape. Now you will be able to open and close the mirrors like a book. Place both the mirrors at a small angle apart in the upright position on the floor. Place a lighted candle in the space between the two mirrors. You will observe many images of the candle which makes a beautiful scene.

Now, by gradually decreasing the angle between the mirrors observe the images being formed. You will now observe more and more numbers of images of the candle. Similarly, if the angle between the mirrors is increased the number of images decreases and when this angle is 180 degree, only one image is visible.

When the angle between the two mirrors is 180 degree they together act like a single mirror so that only one image is visible. As the angle between the mirrors gradually decreased, not only the candle but the mirrors themselves get imaged in one another. That is why when the angle between the mirrors is decreased one observe image within image, and image within that image, and so on. In this way one observes a lot many images. If the angle between the mirrors is finally decreased to zero, infinite images are expected to be formed.

1. Place both the mirrors vertically with 180 degree angle between the them.
2. Place a lighted candle in the space between the two mirrors.
3. You will see single image of the candle in mirror. Reduce the angle between mirrors and observe multiple images of the candle which makes a beautiful scene.
4. Now, measure the maximum angle between two mirrors when you get 1, 3, 5, 7, and 9 images. These angles are \(\theta_\text{measured}\).
5. Calculate \(\theta_\text{calculated}\) for \(n=1,3,5,7,9\) by using the formula given above.
6. Draw the ray diagram when angle between two mirrors is 90 degree.

Question 8 Exercise 7B

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Answer:

(a) The number of images formed when an object is placed between the two plane mirrors at an angle of 90°, is 3. Three images are formed.

We know that two mirrors kept perpendicular to each other, produce three images for an object that is placed in between them.

i.e, the angle between two mirrors is 60°, n=360°/90° = 4, number of images = n-1 = 4-1 = 3.

(b) The number of images formed if an object is placed between two plane mirrors with an angle of 60°, is five. Five images are formed:

i.e, the angle between two mirrors is 60°, n=360°/60° = 6, number of images = n-1 = 6-1 = 5.

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