A birthday candle 4 cm high is 10 cm from a converging lens whose focal length is 15cm. Use a ray diagram on a suitable scale(say,1/3 full size) to find the location of the image, its height,and whether it is erect or inverted, real or virtual.
To find the location of the image, its height, and whether it is erect or inverted, real or virtual, we can use the ray diagram method. Here's how you can do it:
Step 1: Draw a horizontal line representing the principal axis. Place the converging lens horizontally along the principal axis.
Step 2: Place the object (the birthday candle) on the principal axis, 10 cm from the lens. Draw an arrow pointing upwards to represent the top of the candle.
Step 3: Draw three incident rays from the top, middle, and bottom of the candle towards the lens.
- The ray from the top should be drawn parallel to the principal axis, then it will pass through the focal point on the other side of the lens (15 cm away from the lens).
- The ray from the middle of the candle should pass through the center of the lens without bending.
- The ray from the bottom of the candle should be drawn towards the focal point before it enters the lens, then it will become parallel to the principal axis after passing through the lens.
Step 4: The point where the three refracted rays intersect after passing through the lens will represent the location of the image.
Step 5: Measure the distance from the lens to the point where the rays intersect. This distance represents the location of the image. In this case, let's say the distance is 20 cm.
Step 6: To determine if the image is erect or inverted, observe the direction of the arrow representing the top of the candle where the rays intersect. If the arrow is pointing upwards, the image will be erect. If it's pointing downwards, the image will be inverted. In this case, the arrow is pointing upwards, so the image is erect.
Step 7: Measure the height of the image from the principal axis to the point where the rays intersect. This will represent the height of the image. In this case, let's say the height is 2 cm.
Step 8: To determine whether the image is real or virtual, analyze the position of the image with respect to the lens. If the image is formed on the opposite side of the lens from the object, it's a real image. If it's formed on the same side as the object, it's a virtual image. In this case, the image is formed on the opposite side of the lens, so it's a real image.
So, using the ray diagram, we determined that the location of the image is 20 cm from the lens. The height of the image is 2 cm, and it is erect and real.