How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

Plane (flat) mirrors have a reflective surface that bounces back light within 180 degrees of the mirror's face. We use these mirrors every day in our bathrooms, bedrooms, and cars. When you look in a plane mirror, you see a mirror image that is flipped backwards and opposite to the objects it is reflecting.

You’ve been tasked with projecting a line of text onto a glass screen for a magic show. However, the projector can’t be on stage, and is instead around a corner, and it’s too bright for the trick. You only have two mirrors. How can you project an image of the text on the glass screen that is dim but readable? Let’s do a mirror physics experiment and see if you can use what you learn to think of a clever solution!

How does the angle of two mirrors change the reflection of an object?

  • Protractor
  • Two identical, small plane mirrors
  • Modeling clay
  • Small object (coin, small figure, etc.)
  • Strip of paper
  • Pen
  • Plastic packing tape
  1. Tape your mirrors together so that they can be opened and closed like a hinge. You want to leave a slight gap between the two edges (around 1/16th of an inch) to do this.

How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

  1. Mark angles of 30, 36, 45, 60, 90, 120 and 180 degrees on a piece of paper using your protractor.
  2. Place the hinge of your mirrors at the vertex of your marked angles.
  3. The first angle you will test will be 180 degrees.
  4. Place your object (you can embed it in modeling clay if it won’t stand up on its own) in the middle of the mirrors and look at the reflection. How many objects do you see, including both reflected and real?
  5. Keeping the object equally between the two mirrors, move the mirrors together into the other angles you marked out with your protractor. How many objects do you see at each angle? Is there something about the angle can help you predict how many objects you will see? Is every reflected image the same brightness?

How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

  1. Write a word on a piece of paper, and place it in between the mirrors at 60 degrees. Look closely at the second reflection (the reflection of the reflection). Can you read the text? Why do you think this is happening?

You will see an ever-increasing number of objects as you move the mirrors closer together (reducing the angle between them). Whenever you can see a whole number of images reflected, the angle of the mirrors will perfectly divide into 360 degrees. When you look at the reflection of a reflection you will be able to read the text in the mirror, as if you pointed a camera at the object. The reflections should get dimmer (more silvery) as the number of times they are reflected increases

The mirrors reflect the reflections of other mirrors within 180 degrees of the mirror’s face. When mirrors reflect, the reflected image will be backwards, but if you reflect something twice, it will look normal.

Because light is traveling in a straight line to and from each mirror, the light will bounce a number of times back and forth between the mirrors before it travels from the object to your eye. The number of times the light bounces (and the number of objects that you see) will correlate to the number of times the angle divides into 360. As the mirrors get closer and closer to having zero angle between them, more and more images appear. At an angle of 0 degrees, or when the two mirrors are facing each other, there are an infinite number of reflections.

So, how are you going to accomplish your trick? You can make the text appear by lining up your mirrors and your projector so that the light bounces an even number of times before it gets to your eyes. Using multiple mirrors will also dim the image before it hits the glass plate for the trick.

How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

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How many images of a candle will be seen when two mirrors are set at 180 to each other and the candle is placed in between those mirrors?

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.

How many images of a candle will be formed if it is placed between two parallel plane mirrors separated by 40 cm?

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