A birthday candle 4 cm high is 10 cm from a converging lens whose focal length is 15 cm. Use a ray diagram on a suitable scale to find the location of the image, its height, and whether it is erect or inverted, real or virtual.
1/p + 1/q = 1/f
M = -q/p
where p is the distance of the object from the lens, q is the distance of the image from the lens, M is the magnification of the object. If M is positive the image is virtual and inverted; if M is negative the image is real and upright (erect).
f is positive for a converging lens:
1/10 + 1/q = 1/15
Solve for q, and then calculate M, and determine the rest of the answers. Sorry, I can't draw a ray diagram for you, but here are the rules:
To draw these ray diagrams, we will have to recall the three rules of refraction for a double convex lens:
Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens and travel through the focal point on the opposite side of the lens.
Any incident ray traveling through the focal point on the way to the lens will refract through the lens and travel parallel to the principal axis.
An incident ray that passes through the center of the lens will in effect continue in the same direction that it had when it entered the lens.
To find the location of the image, height, and its characteristics (erect or inverted, real or virtual), we can use the ray diagram method.
Here's how you can proceed:
Step 1: Draw the Principal Axis and the Lens
On a sheet of paper, draw a horizontal line which will represent the principal axis. Then, draw a vertical line perpendicular to the principal axis to represent the lens.
Step 2: Mark the Focal Point, Optical Center, and Object
Measure 15 cm from the lens along the principal axis and mark it as the focal point (F). Also, mark the center of the lens as the optical center (O). Draw an arrow above the principal axis to represent the object, with the height of the candle measured as 4 cm.
Step 3: Draw Rays from the Object
Draw three rays coming from the tip, center, and base of the candle, following these steps:
- Ray 1: Draw a ray parallel to the principal axis that passes through the optical center (O). This ray does not bend.
- Ray 2: Draw a ray passing through the focal point (F) on the lens. This ray bends and becomes parallel to the principal axis.
- Ray 3: Draw a ray that goes towards the lens, but passes through the center of the lens (O). This ray continues in a straight path without any bending.
Step 4: Locate the Image
Using the ray diagram, extend Ray 2 backwards, and extend Ray 3 through the lens. The point where these two rays meet after being extended is the location of the image. Mark this point as I.
Step 5: Measure the Image Characteristics
Measure the height of the image (h') from the principal axis. The measurement can be done using a ruler or a compass.
Step 6: Determine the Characteristics of the Image
By observing the ray diagram, you can determine the characteristics of the image:
- If the image is above the principal axis, it is erect. If it is below the principal axis, it is inverted.
- If the image is on the same side as the object (behind the lens), it is real. If it is on the opposite side (in front of the lens), it is virtual.
By following these steps and analyzing the ray diagram, you should be able to find the location of the image, its height, and determine whether it is erect or inverted, and real or virtual.