# Angle of incidence and reflection relationship help

### BBC Bitesize - GCSE Physics (Single Science) - Reflection and refraction - AQA - Revision 1

specular reflection, the angle of incidence θi equals the angle of .. in figure , then Snell's law gives a relationship between the angle. The law of reflection states that the incident ray, the reflected ray, and the normal to the surface of the mirror all lie in the same plane. Furthermore, the angle of. The law of reflection states that for each incident ray the angle of incidence equals What is the relationship between the angle of incidence and the angle of.

### The Optical Society: Exploring the Science of Light | Optics For Kids

In this case, for light from the object to reflect off the mirror and travel to the eye, the light would have to reflect in such a way that the angle of incidence is more than the angle of reflection. Neither of these cases would follow the law of reflection. In fact, in each case, the image is not seen when sighting along the indicated line of sight.

It is because of the law of reflection that an eye must sight at the image location in order to see the image of an object in a mirror. Check Your Understanding 1. Consider the diagram at the right. Which one of the angles A, B, C, or D is the angle of incidence? Angle C is the angle of reflection angle between the reflected ray and the normal.

A ray of light is incident towards a plane mirror at an angle of degrees with the mirror surface. What will be the angle of reflection? See Answer The angle of reflection is 60 degrees. Note that the angle of incidence is not 30 degrees; it is 60 degrees since the angle of incidence is measured between the incident ray and the normal.

Perhaps you have observed the image of the sun in the windows of distant buildings near the time that the sun is rising or setting. However, the image of the sun is not seen in the windows of distant building during midday. Use the diagram below to explain, drawing appropriate light rays on the diagram. See Answer A ray of light drawn from the sun's position at 7 pm to the distant window reflects off the window and travel to the observer's eye.

On the other hand, a ray of light drawn from the 1 pm sun position to the window will reflect and travel to the ground, never making it to the distant observer's eye. A ray of light is approaching a set of three mirrors as shown in the diagram. The light ray is approaching the first mirror at an angle of degrees with the mirror surface. Trace the path of the light ray as it bounces off the mirror.

• The Law of Reflection
• All Things Equal

Continue tracing the ray until it finally exits from the mirror system. How many times will the ray reflect before it finally exits? See Answer The light reflects twice before it finally exits the system. Draw a normal at the point of incidence to the first mirror; measure the angle of incidence 45 degrees ; then draw a reflected ray at 45 degrees from the normal. Spherical mirrors Light reflecting off a flat mirror is one thing, but what happens when light reflects off a curved surface?

We'll take a look at what happens when light reflects from a spherical mirror, because it turns out that, using reasonable approximations, this analysis is fairly straight-forward. The image you see is located either where the reflected light converges, or where the reflected light appears to diverge from. A spherical mirror is simply a piece cut out of a reflective sphere. It has a center of curvature, C, which corresponds to the center of the sphere it was cut from; a radius of curvature, R, which corresponds to the radius of the sphere; and a focal point the point where parallel light rays are focused to which is located half the distance from the mirror to the center of curvature.

The focal length, f, is therefore: Parabolic mirrors are really the only mirrors that focus parallel rays to a single focal point, but as long as the rays don't get too far from the principal axis then the equation above applies for spherical mirrors.

CRITICAL ANGLE AND TOTAL INTERNAL REFLECTION

The diagram shows the principal axis, focal point Fand center of curvature for both a concave and convex spherical mirror. Spherical mirrors are either concave converging mirrors or convex diverging mirrors, depending on which side of the spherical surface is reflective. If the inside surface is reflective, the mirror is concave; if the outside is reflective, it's a convex mirror.

Concave mirrors can form either real or virtual images, depending on where the object is relative to the focal point. A convex mirror can only form virtual images. A real image is an image that the light rays from the object actually pass through; a virtual image is formed because the light rays can be extended back to meet at the image position, but they don't actually go through the image position.

Ray diagrams To determine where the image is, it is very helpful to draw a ray diagram. The image will be located at the place where the rays intersect. You could just draw random rays from the object to the mirror and follow the reflected rays, but there are three rays in particular that are very easy to draw.

Only two rays are necessary to locate the image on a ray diagram, but it's useful to add the third as a check. The first is the parallel ray; it is drawn from the tip of the object parallel to the principal axis. It then reflects off the mirror and either passes through the focal point, or can be extended back to pass through the focal point.

The second ray is the chief ray. This is drawn from the tip of the object to the mirror through the center of curvature. The chief and parallel rays meet at the tip of the image.

The third ray, the focal ray, is a mirror image of the parallel ray.

## Reflection and refraction

The focal ray is drawn from the tip of the object through or towards the focal point, reflecting off the mirror parallel to the principal axis. All three rays should meet at the same point. A ray diagram for a concave mirror is shown above.

This shows a few different things. For this object, located beyond the center of curvature from the mirror, the image lies between the focal point F and the center of curvature. The image is inverted compared to the object, and it is also a real image, because the light rays actually pass through the point where the image is located.

With a concave mirror, any object beyond C will always have an image that is real, inverted compared to the object, and between F and C. You can always trade the object and image places that just reverses all the arrows on the ray diagramso any object placed between F and C will have an image that is real, inverted, and beyond C.

What happens when the object is between F and the mirror? You should draw the ray diagram to convince yourself that the image will be behind the mirror, making it a virtual image, and it will be upright compared to the object.

A ray diagram for a convex mirror What happens with a convex mirror? In this case the ray diagram looks like this: As the ray diagram shows, the image for a convex mirror is virtual, and upright compared to the object. A convex mirror is the kind of mirror used for security in stores, and is also the kind of mirror used on the passenger side of many cars "Objects in mirror are closer than they appear.

A convex mirror will reflect a set of parallel rays in all directions; conversely, it will also take light from all directions and reflect it in one direction, which is exactly how it's used in stores and cars.

The mirror equation Drawing a ray diagram is a great way to get a rough idea of how big the image of an object is, and where the image is located. We can also calculate these things precisely, using something known as the mirror equation. The textbook does a nice job of deriving this equation in section Magnification In most cases the height of the image differs from the height of the object, meaning that the mirror has done some magnifying or reducing.

The magnification, m, is defined as the ratio of the image height to the object height, which is closely related to the ratio of the image distance to the object distance: A magnification of 1 plus or minus means that the image is the same size as the object.

If m has a magnitude greater than 1 the image is larger than the object, and an m with a magnitude less than 1 means the image is smaller than the object. If the magnification is positive, the image is upright compared to the object; if m is negative, the image is inverted compared to the object.

Sign conventions What does a positive or negative image height or image distance mean?

To figure out what the signs mean, take the side of the mirror where the object is to be the positive side. Any distances measured on that side are positive. Distances measured on the other side are negative. When the image distance is positive, the image is on the same side of the mirror as the object, and it is real and inverted.

### The reflection and refraction of light

When the image distance is negative, the image is behind the mirror, so the image is virtual and upright. A negative m means that the image is inverted.

Positive means an upright image. Steps for analyzing mirror problems There are basically three steps to follow to analyze any mirror problem, which generally means determining where the image of an object is located, and determining what kind of image it is real or virtual, upright or inverted.

Step 1 - Draw a ray diagram.

The more careful you are in constructing this, the better idea you'll have of where the image is. Step 2 - Apply the mirror equation to determine the image distance.