How To Draw A Ray Diagram For A Plane Mirror

In this explainer, we will learn how to draw diagrams of light rays interacting with concave mirrors.

Earlier starting to depict ray diagrams, information technology will be useful to outset consider a concave mirror equally a three-dimensional solid object.

A concave mirror is a hollow curved object, like a bowl.

A concave mirror is shown in the following effigy. The optical axis of the mirror is shown.

The optical axis of a concave mirror is an imaginary line that passes through the bespeak at the back of the mirror.

The optical axis of a spherical mirror is equidistant from the surface of the mirror in every direction perpendicular to this centrality. This means that the cerise and blue lines shown in the following effigy are really the aforementioned length.

If the mirror is viewed along the optical centrality, it is clearer to run across that the mirror is symmetrical effectually this axis.

An incident lite ray tin travel along the optical axis of the mirror. This is shown in the following figure.

Nosotros can see that an incident light ray that travels along the optical axis of the mirror will striking the signal at the back of the mirror and exist reflected back along its incoming path.

For rays with paths that are parallel to the optical axis, merely rays that travel along the optical axis of a concave mirror are reflected back along their incoming path. Whatsoever other path that such a ray travels along results in the ray existence reflected on a path different from its incoming path.

The following effigy shows how we can stand for a cross section of a concave mirror with a curve in a 2-dimensional drawing.

The following figure shows light rays incident on a curve representing a cross section of a concave mirror.

Of the 3 incident light rays shown, simply the ray shown in greenish will reflect along its incoming path. The 2 rays shown in black will reflect along different paths from their incoming paths.

The following figure shows a magnified view of the part of the mirror where ane of the rays shown in blackness hits the mirror.

We come across that where the ray hits the mirror, at that place is a line normal to the surface of that point on the mirror.

The following figure shows the constabulary of reflection determining how this incident ray would reflect from the mirror.

As we retrieve from the law of reflection, the incident bending equals the reflection angle. Each of these angles is between a light ray and the line normal to the surface of the mirror.

Allow us await at an example involving the reflection of a light ray from a concave mirror.

Example ane: Identifying the Path of a Ray Reflected from a Concave Mirror

The following figure shows three light rays incident on a concave mirror. Which is a correctly fatigued reflected ray, ray A or ray B?

Answer

The correct path of the reflected ray is either that of ray A or of ray B shown in the question.

Information technology would be easy to mistake how to depict the path for the correct ray past incorrectly comparing a concave mirror to a plane mirror.

Reflection of the incident ray shown in red from a plane mirror would be as shown in the following figure.

This would correspond to ray B in the question.

Yet, the incident ray is reflecting from a concave mirror, not a airplane mirror.

This means that we can eliminate ray B. This only leaves ray A, which must exist correct.

Let us consider why ray A is correct.

The post-obit figure shows that the ray shown in red is symmetrical about the optical axis of the mirror to the ray shown in blue.

The rays shown in red and in blueish are parallel to the optical axis, at equal distances from it. The angle made where the reddish incident ray crosses the blueish reflected ray is equal to the bending made where the blue incident ray crosses the ruddy reflected ray; ray A.

When drawing ray diagrams with mirrors, ordinarily we may consider parallel incident rays.

The post-obit figure shows iii parallel incident rays and how each ray reflects from a concave mirror.

We run across that all the reflected rays pass through a point that is on the optical centrality of the mirror.

In that location are two special points on the optical axis of whatsoever curved mirror. These points are called

• the center of curvature of the mirror,
• the focal signal of the mirror.

The centre of curvature of a mirror is a point that is at the same distance from the surface of the mirror in every direction.

The focal point of a curved mirror is a point at which the reflected rays of parallel incident rays all cantankerous each other's paths.

Let us look at an example involving the reflection of parallel incident lite rays from a concave mirror.

Example ii: Identifying a Point along the Optical Centrality of a Concave Mirror

The following figure shows iii parallel light rays incident on a concave mirror. Which of the following is the term for point P, which is shown by the blackness dot?

1. Focal point of the mirror
2. Center of curvature of the mirror

Answer

The center of curvature of a mirror is a betoken that is at the same distance from the surface of the mirror in every management.

In the following effigy, nosotros tin compare the lengths of the two dashed lines from P to different parts of the surface of the mirror.

It is clear that these two dashed lines have unequal lengths. This tells us that P is not the center of curvature of the mirror.

The focal point of a curved mirror is a point at which the reflected rays of parallel incident rays all cross each other'due south paths.

We see that all the incident rays are parallel. We see as well that all the reflected ray paths cross at P.

Therefore, P is the focal point of the mirror.

Suppose that an object is placed in front of a concave mirror. We can consider the light from i indicate on the object.

The following figure shows low-cal rays from a point on an object that are incident on a concave mirror.

The light rays from the point travel in different directions.

The following figure shows how these 2 rays reflect from the mirror.

Two special points are marked. Point A is the bespeak from which light rays start.

We tin see that at the other special point, betoken B, the paths of the two reflected rays cross each other.

We encounter that betoken B is at the opposite stop of the object to point A.

Nosotros have just shown two directions in which lite rays from point A could travel.

It is very important to understand though that calorie-free rays from point A that travel in any management will meet at bespeak B.

Information technology is of import to sympathize that this is simply truthful for light rays that reflect from the mirror. A light ray from point A that travels to the left will not reverberate from the mirror and so will not arrive at point B.

This means that all light rays from point A that are reflected past the mirror will meet at point B.

This means that at point B, a real image is formed of the function of the object at point A.

This tells u.s. that if a screen was placed at indicate B, we would exist able to run into on the screen any was at point A.

We can apply this to every point on an object.

Light rays from each point on the object will be reflected to some other signal, forming an image of that point.

Each unlike betoken on an object produces an image at a different point. Light rays from points on an object that are next to each other are reflected to points on an prototype that are next to each other.

This ways that an image of an unabridged object is formed.

We tin can see here an paradigm formed by a concave mirror.

We cannot actually see the object that produced the image.

We can reasonably judge, however, that the incident calorie-free rays on the mirror came from the sky, some trees, and the ground; we meet these things in the epitome.

It is important to detect that the epitome is upside down. The heaven is at the lesser of the mirror and the basis is at the pinnacle.

This should not surprise us when we recall how light rays are reflected from a point by a concave mirror, shown in the following figure.

The prototype is of an prototype of betoken A, which is at the elevation of the object, is at point B, which is at the lesser of the object.

We see then that a concave mirror can produce an inverted image of an object.

The prototype produced by a concave mirror changes depending on how far in front of the mirror an object is.

We have seen examples and then far of an object that is at a distance from the dorsum of the mirror equal to the distance from the back of the mirror to the center of curvature of the mirror. This is shown in the post-obit figure.

We take seen that for an object at this distance from the back of the mirror, the image is inverted.

We can see that a point at the pinnacle of the object appears in the paradigm at the bottom of the object.

The following figure shows that this means that the image must be the same size every bit the object.

If an object is moved toward or away from the dorsum of a concave mirror, this changes the size of the epitome.

The formation of images for objects backside and in forepart of the center of curvature of a concave mirror is shown in the post-obit figure.

Nosotros can run into that the images produced are however inverted.

We tin see though that for both cases, the vertical distance from the heart of curvature to point A is not equal to the vertical distance from the center of curvature to betoken B.

This tells us that in both these cases, the size of the paradigm is not equal to the size of the object.

Allow united states at present expect at an example involving the image of an object formed by reflection from a concave mirror.

Example 3: Comparing the Size of an Image Formed by a Concave Mirror to an Object

The post-obit figure shows two calorie-free rays from the aforementioned point on an object that are incident on a concave mirror. The object is between the heart of curvature of the mirror and the focal indicate of the mirror. A real prototype is produced. Which of the following is true?

1. The image is larger than the object.
2. The object is larger than the image.
3. The prototype and the object are the same size.

Reply

The image formed by a concave mirror for an object located between the heart of curvature and focal bespeak of the mirror is an inverted image.

The height of the paradigm is at the point where the paths of light rays reflected from the top of the object cross each other.

We can see two things about this betoken.

• The point is further from the back of the mirror than the altitude from the surface of the mirror to its center of curvature.
• The vertical altitude from the center of curvature to the tiptop of the paradigm is greater than the vertical distance from the centre of curvature to the top of the object.

The image would appear with the size and position shown in the following figure.

We see that the epitome is larger than the object.

Information technology would not exist possible in practice to see all of this image, as the object would cake some of the light rays that would be needed to course the image.

Nosotros tin see that there is a pattern relating the altitude of an object from the back of a lens and the size of the image produced.

• When an object is located between the focal betoken and heart of curvature of a concave mirror, the epitome is larger than the object.
• When an object is located at the center of curvature of a concave mirror, the image is the same size as the object.
• When an object is located further from the dorsum of a concave mirror than the distance from the centre of curvature to the surface of the mirror, the epitome is smaller than the object.

If an object is located closer to the dorsum of a concave mirror than the distance from the focal point to the back of the mirror, an interesting thing happens. This is shown in the post-obit effigy.

We see that none of the paths of the reflected rays cross each other. This means that no real prototype is formed.

However, if the paths of the reflected rays are traced back, they meet at a signal.

The top of the point that the reflected ray paths come across at is the top of a virtual image.

This is shown in the following figure.

We can run into that the virtual prototype is the same way upward as the object.

We tin see that the virtual image is larger than the object.

A virtual paradigm cannot grade on a screen just can exist seen by the human eye.

The fact that a concave mirror can brand inverted existent images and upright virtual images ways that a concave mirror tin show some objects inverted and others upright at the same time, every bit shown beneath.

Let us at present summarize what has been learned in this explainer.

Key Points

• A concave mirror can produce existent images and virtual images.
• A concave mirror produces virtual images of objects nearer to the back of the mirror than the distance between the dorsum of the mirror and the focal betoken of the mirror.
• Virtual images produced past a concave mirror are upright and larger than the object imaged.
• A concave mirror produces real images of objects further from the dorsum of the mirror than the altitude between the back of the mirror and the focal signal of the mirror.
• Real images produced by a concave mirror are inverted.
• Objects that are located betwixt the focal betoken and middle of curvature of a concave mirror produce images that are larger than the object.
• Objects that are located at the center of curvature of a concave mirror produce images of equal size to the object.
• Objects that are located further from the back of a concave mirror than the distance from the dorsum of the mirror to the center of curvature produce images that are smaller than the object.

Source: https://www.nagwa.com/en/explainers/395143514640/

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