The student is expected to describe and predict image formation as a consequence of reflection from a plane mirror and refraction through a thin convex lens.
Mirrors and lenses can be used to form images of objects. Real images are formed when the rays of light from the object come back together at the location of the image. Virtual images are formed when the rays of light from the object appear to come from the location of the image, but don’t actually pass through that location. Only real images can be visualized using a screen.
The position and size of an image reflected from a plane mirror, or refracted from a thin convex lens can be predicted by drawing a ray diagram and by mathematical calculations.
Flat, or plane, mirrors form a virtual upright image in the space behind the reflective surface of the mirror. The image is located at the same distance from the mirror as the object, is left-right reversed and is the same size as the object.
A lens is a device that produces an image using the refraction of light rays. The size and position of the image depends on the design of the lens and the size and position of the object.
A thin convex lens is also called a converging lens, because it causes parallel light rays to converge to a single point. The image formed by a thin convex lens can be either real, inverted and located in the space on the opposite side of the lens from the object, or virtual, upright and located on the same side of the lens as the object.
Reflection From a Plane Mirror
Virtual Images: Flat, or plane mirrors, form a virtual image in the space behind the reflective surface of the mirror that can be seen by the reflection of the light waves. Virtual images refer to the light rays that the observer sees, but do not actually come from the image. Virtual images formed by a plane mirror are located behind the mirror, are reversed left to right, are the same distance from the mirror as the object, and are the same size as the object.
Prediction of the Position and Size of the Image: The location of a reflected and virtual image can be predicted knowing the angle of incidence equals the angle of reflection. The Law of Reflection can be briefly illustrated in this figure:
Law of Reflection
MN is the reflective surface, OB is the normal and AO is the incident ray. The reflective angle COB must equal the incident angle AOB. The position and size of an image reflected from a plane mirror, or refracted from a thin convex lens can be determined by drawing a ray diagram and by mathematical calculations. Therefore, as shown below, the mirror MN serves as the reflective surface. The object ST presents an upright and virtual image by the mirror. Every light wave that hits the mirror obeys the Law of Reflection, and thus the image S’T’ is formed.
Image formation as a consequence of the Law of Reflection from a plane mirror
Refraction Through a Thin Convex Lens
A lens is a device that produces an image of an object using the refraction of light rays. The size and position of the image depends on the design of the lens and the size and position of the object. A thin convex lens is also called a converging lens, because it causes parallel light rays to converge to a single point. We can use this fact to locate the image produce by the lens using the technique of ray tracing, as shown in the diagrams below.
Ray Tracing Steps
1. In ray tracing, we first draw a cross section of the lens.
2. Next, we draw a line through the center of the lens perpendicular to the plane of the lens. This line is the principal axis. Rays of light that enter the lens parallel to this axis will converge on the other side of the lens at a common point known as the focal point. Because light can come from either side of a lens, there are focal points on both sides of the lens. (These points are labeled “F” in the diagrams below.)
3. Next, we draw our object at the appropriate scaled distance away from our lens.
4. We then draw a ray of light from a point on our object to the lens, parallel to the principal axis. The lens will refract this light ray through the focal point
5. We then draw a second light ray from the same point on our object through the focal point to the lens. Because the lens is symmetric, this light ray will be refracted parallel to the principal axis.
6. Finally, we draw a third light ray from the point to the center of the lens. This ray will not be refracted at all. The point where the refracted rays of light meet (or, in the case of a virtual image, the point where the refracted rays appear to come from) is the location of the image.
Applications
Applications vary depending on the function of the instrument. When focusing a smaller image inside an eye or camera, the object is located more than twice the focal length away from the lens. However, on a telescope eyepiece, the need is to focus the image already captured by the main lens or mirror, so the image remains the same size with the object at exactly the focal length of the lens. Searchlights and lighthouses need to have light reflected in an ever widening beam to infinity. Other applications require the image to be enlarged close up such as a magnifying glass.
Thin Lens Equation
The location and size of an image can also be determined mathematically using the Thin Lens Equation:
1/d-o + 1/d-i = 1/f
In this equation, d-o is the distance from the object to the lens, and f is the distance from the lens to the focal point, known as the focal length. d-i is the distance from the lens to the image. For a single convex lens, d-o and f will always be positive. If d-i is positive, the image is real, and located on the opposite side of the lens from the object. If d-i is negative, the image is virtual and located on the same side of the lens as the object.