Light Reflection. Not drawn to scale.

Transcription

1 Physics 25 Chapter 25 Dr. Alward Light Reflection In the figure at the right, the angle of reflection for Ray 1 equals the angle of incidence. The same is true for Ray 2. Not drawn to scale. Any image that is behind a mirror is said to be virtual, which means not real, because light is not really leaving that place, passing through the mirror to the eye. Rule: If the image is not on the eye-side, i.e., in back of the mirror, it s not real. Example: Two mirrors, M1 and M2, are joined at point P. A ray of light is incident on M1 from the left and is reflected onto M2. What is the angle θ? 70 o 1

2 Image Formation with Concave Mirrors Figure 1 Two Special Rays: Paraxial Rays, Focal Point Rays Paraxial rays reflect through the focal point. The focal length f is the distance from the mirror to the focal point. Focal lengths of concave mirrors are always Focal point rays are incident rays that lie on a line that passes through the focal point. Focal point rays reflect paraxially. Ray 2 behaves as if it originated at Point Q, a ray which would pass through F on its way to the mirror, so the ray originating at Point P is a focal point ray. Example: The focal length of the concave mirror in Figure 3 is f = 60 cm. An object 30 cm tall is placed 100 cm from the mirror. We follow the two special rays leaving the top of the object, and use their behavior to triangulate to the location of the top of the image. Similar rays leaving other parts of the object would map to corresponding points on the image. Figure 3 The image is real because it s on the eye-side. Image is inverted, taller, and in front of the mirror, about 40 cm tall. The image appears to be about 120 cm in front of the mirror. The value of knowing whether an image is real lies in the fact that real images can be projected onto a screen. If a camera film were placed where the real image is, the film would capture the image, because there really is light energy at that place that can cause chemical reactions on the film. Image capture is not possible for images that are not real, i.e., virtual images. 2

3 Mirror Equations Instead of estimating image location, size and orientation, one may use the mirror equations below to determine these properties. f = focal length f = 60 cm Focal lengths for concave mirrors are always x = object distance x = 100 cm Object distances for any type of mirror are always y = image distance Image distances can be positive, or negative. If the image is on the eye-side, y is positive; if it is in back of the mirror, i.e., not on the eye - side, y is negative. Recall: if the image is not on the eye-side, it is therefore in back of the mirror, which means the image is not real. Heights Ho = object height HI = image height Two Ways to Calculate Magnification 1. M = HI /Ho 2. M = -y/x The Mirror Equation Remember: f is always positive for concave mirrors. Example: x = 100 cm f = 60 cm (This is the data from Figure 3. repeated at the right.) 1/ /y = 1/60 y = 150 cm (we estimated 120 cm) M = -150/100 = HI = (30) = - 45 cm (we estimated -40 cm) Note that y is positive, as expected, because the image is in front of the mirror. Note also that M is negative, meaning that the image is inverted. Mnemonic: real is a positive attribute. If y is positive, the image is real, and the image is on the eyeside. 3

4 Example A: The focal length of a concave mirror is f = 60 cm. A 30-cm tall object is placed 30 cm from the mirror. Estimate the image height and location using the ray diagram method. 1/30 + 1/y = 1/60 y = -60 cm M = -y/x = -(-60)/30 = 2 HI = 2 (30) = 60 cm Rays 1 and 2e, extrapolated back, intersect behind the mirror. Image is about as far from the mirror as the focal point, so we estimate that y = -60 cm, and that its height is about 60 cm. Check this information using mirror equations at the right: HI is positive, which means that the image is upright, as the diagram confirms. y is not positive, so the image is not on the eye side, and therefore not real (it s virtual). Image Formation with Convex Mirrors Incident paraxial rays after reflection seem to have originated at the focal point. Incident rays aimed at the focal point reflect paraxially. Focal lengths of convex mirrors are negative. 4

5 Example A: The focal point of a convex mirror f = -20 cm. An object 12 cm tall is placed 30 cm from the mirror. What is the approximate height of the image? Rays 1 and 2, extrapolated back, intersect at a point behind the mirror. We estimate the height of the image to be about one-third the height of the object, or about 4 cm. Solve Example A problem exactly using the mirror equations. f = -20 cm Ho = 12 cm 1/30 + 1/y = -1/20 y = -12 cm M = -(-12)/30 = 0.4 HI = 0.4 (12) = 4.8 cm Image is upright, and shorter. Because y is not positive, the image is not real. Image is behind the mirror. Actual image height is 20% taller than the height that we estimated from the diagram. Image appears to be upright, and about one-third the height of the 12-cm tall object. Use the mirror equations at the right to confirm this information. Example B: Prove that convex mirrors cannot form inverted images, i.e., prove that M is always Recall: f is negative for convex mirrors 1/y = 1/f - 1/x = negative - positive y = negative Example C: Prove that convex mirrors cannot form real images. The work at the left shows that y is always negative. In order for an image to be real, it must be on the eye-side of the mirror, where y is positive, therefore, convex mirrors cannot form real images. M = -y/x = -(negative)/positive = positive/positive = positive 5