Showing posts with label LIGHT AND OPTICS. Show all posts
Showing posts with label LIGHT AND OPTICS. Show all posts

## Total Internal Reflection of Light Simulation

#### Quiz

Q1) Total internal reflection occurs when the angle of incidence is

A. greater than the angle of refraction
B. equal to the critical angle
C. greater than the critical angle
D. greater than 45°

Q2) Total internal reflection

A. refers to light being reflected from a plane mirror
B. may occur when a fisherman looks at a fish in a lake
C. may occur when a fish looks at a fisherman on a lake

#### Total Internal Reflection of Light Simulation

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Total Internal Reflection
When you’re in a physics mood and you’re going to take a bath, fill the tub extra deep and bring a waterproof flashlight into the tub with you. Turn the bathroom light off. Shine the submerged light straight up and then slowly tip it and note how the intensity of the emerging beam diminishes and how more light is reflected from the water surface to the bottom of the tub.

The Critical Angle
At a certain angle, called the critical angle, you’ll notice that the beam no longer emerges into the air above the surface. The critical angle is the angle of incidence that results in the light being refracted at an angle of 90° with respect to the normal. As a result, the intensity of the emerging beam reduces to zero. When the flashlight is tipped beyond the critical angle (48° from the normal in water), the beam cannot enter the air; it is only reflected. The beam is experiencing total internal reflection, which is the complete reflection of light back into its original medium.
FIGURE 1. You can observe total internal reflection in your bathtub. a–d. Light emitted in the water at angles below the critical angle is partly refracted and partly reflected at the surface. e. At the critical angle, the emerging beam skims the surface. f. Past the critical angle, there is total internal reflection.

Total internal reflection occurs when the angle of incidence is larger than the critical angle. The only light emerging from the water surface is that which is diffusely reflected from the bottom of the bathtub. This procedure is shown in Figure 1. The proportions of light refracted and reflected are indicated by the relative lengths of the solid arrows. The light reflected beneath the surface obeys the law of reflection: The angle of incidence is equal to the angle of reflection. The critical angle for glass is about 43°, depending on the type of glass. This means that within the glass, rays of light that are more than 43° from the normal to a surface will be totally internally reflected at that surface.

Figure 2. (a) This photo demonstrates several different paths of light radiated from the bottom of an aquarium. (b) At the critical angle, $\theta_{c}$ , a light ray will travel parallel to the boundary. Any rays with an angle of incidence greater than $\theta_{c}$  will be totally internally reflected at the boundary.

Snell’s law can be used to find the critical angle. When the angle of incidence, $\theta_{i}$ , equals the critical angle, $\theta_{c}$ , then the angle of refraction, $\theta_{r}$ , equals 90°. Substituting these values into Snell’s law gives the following relation.

$\ n_{i} sin\theta_{c} = n_{r} sin90°$

Because the sine of 90° equals 1, the following relationship results.

 CRITICAL ANGLE $\sin\theta_{c} = \frac{n_{r}}{n_{i}}~~~~~for~n_{i}>n_{r}$

Note that this equation can be used only when $\ n_{i}$ is greater than $\ n_{r}$. In other words, total internal reflection occurs only when light moves along a path from a medium of higher index of refraction to a medium of lower index of refraction. If ni were less than $\ n_{r}$, this equation would give $\ sin\theta_{c} > 1$, which is an impossible result because by definition the sine of an angle can never be greater than 1. When the second substance is air, the critical angle is small for substances with large indices of refraction.Diamonds, which have an index of refraction of 2.419, have a critical angle of 24.4°. By comparison, the critical angle for crown glass, a very clear optical glass, where $\ n$ = 1.52, is 41.0°. Because diamonds have such a small critical angle, most of the light that enters a cut diamond is totally internally reflected. The reflected light eventually exits the diamond from the most visible faces of the diamond. Jewelers cut diamonds so that the maximum light entering the upper surface is reflected back to these faces.

## Convex and Concave Lens Ray Diagrams

#### Quiz

Quiz 1. When light passing through a lens, the light is bent, causing the rays of light to diverge. The type of lens is a ...

a. convex lens
b. concave lens
c. optic lens
d. diamond prism lens

A lens that causes light rays initially parallel to the central axis to converge is (reasonably) called a concave (converging) lens

Quiz 2. The lens of the human eye is a convex lens. That means that when it takes in light from an object, it refracts the light rays, by focussing them on the retina. If the eye is too long, the image will form in front of the retina. This condition is called ...

a. retina dysfunction
b. optical illusion
c. near-sightedness
d. far-sightedness

Near-sightedness is when people have trouble seeing distant objects, because the object is in focus in front of the retina and then out of focus when it reaches the retina

#### Convex and Concave Lens Simulation

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Thin Lenses
A lens is a transparent object with two refracting surfaces whose central axes coincide. The common central axis is the central axis of the lens. When a lens is surrounded by air, light refracts from the air into the lens, crosses through the lens, and then refracts back into the air. Each refraction can change the direction of travel of the light.
A lens that causes light rays initially parallel to the central axis to converge is (reasonably) called a converging lens. If, instead, it causes such rays to diverge, the lens is a diverging lens. When an object is placed in front of a lens of either type, light rays from the object that refract into and out of the lens can produce an image of the object.

Fig 1. When rays of light pass through (a) a converging lens (thicker at the middle), they are bent inward. When they pass through (b) a diverging lens (thicker at the edge), they are bent outward.

Locating Images of Extended Objects by Drawing Rays
Fig2 (a) shows an object O outside focal point $\ F_1$ of a converging lens. We can graphically locate the image of any off-axis point on such an object (such as the tip of the arrow in Fig2 (a) by drawing a ray diagram with any two of three special rays through the point.These special rays, chosen from all those that pass through the lens to form the image, are the following:

 1. A ray that is initially parallel to the central axis of the lens will pass through focal point $\ F_2$ (ray 1 in Fig2 (a). 2. A ray that initially passes through focal point $\ F_1$ will emerge from the lens parallel to the central axis (ray 2 in Fig2 (a). 3. A ray that is initially directed toward the center of the lens will emerge from the lens with no change in its direction (ray 3 in Fig2 (a). because the ray encounters the two sides of the lens where they are almost parallel.

The image of the point is located where the rays intersect on the far side of the lens. The image of the object is found by locating the images of two or more of its points. Fig2 (b) shows how the extensions of the three special rays can be used to locate the image of an object placed inside focal point $\ F_1$ of a converging lens.
Note that the description of ray 2 requires modification (it is now a ray whose backward extension passes through $\ F_1$).
You need to modify the descriptions of rays 1 and 2 to use them to locate an image placed (anywhere) in front of a diverging lens. In Fig2 (c), for example, we find the point where ray 3 intersects the backward extensions of rays 1 and 2.

Images Created by Converging Lenses : Ray diagrams

Diverging lenses produce virtual images from real objects
A diverging lens creates a virtual image of a real object placed anywhere with respect to the lens. The image is upright, and the magnification is always less than one; that is, the image size is reduced. Additionally, the image appears inside the focal point for any placement of the real object.

Fig3. The image created by a diverging lens is always a virtual,  smaller image.

The ray diagram shown in Fig3. for diverging lenses was created using the rules given in Table. The first ray, parallel to the axis, appears to come from the focal point on the same side of the lens as the object. This ray is indicated by the oblique dashed line. The second ray passes through the center of the lens and is not refracted. The third ray is drawn as if it were going to the focal point in back of the lens. As this ray passes through the lens, it is refracted parallel to the principal axis and must be extended backward, as shown by the dashed line. The location of the tip of the image is the point at which the three rays appear to have originated.

#### Related Videos : Convex and Concave Lens Experiment

Following video is experiment of convex and concave lens

## Concave and Convex Mirrors Simulation

#### QUIZ

Q1) For a spherical concave mirror, virtual images are formed when the object is located

A. between F and C
B. beyond C
C. at C
D. inside F

Q2) Which of the following is not true when an image is formed by an object located between C and F of a concave mirror?
A. Negative magnification
B. Negative image distance
C. Inverted image
D. Enlarged image

#### Concave and Convex Mirrors Simulation

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If you look at the surface of a shiny spoon, you will notice that your reflection is different from what you see in a plane mirror. The spoon acts as a curved mirror, with one side curved inward and the other curved outward. The properties of curved mirrors and the images that they form depend on the shape of the mirror and the object’s position.

Concave Mirrors
The inside surface of a shiny spoon, the side that holds food, acts as a concave mirror. A concave mirror has a reflective surface, the edges of which curve toward the observer. Properties of a concave mirror depend on how much it is curved. Figure 1 shows how a spherical concave mirror works. In a spherical concave mirror, the mirror is shaped as if it were a section of a hollow sphere with an inner reflective surface. The mirror has the same geometric center, C, and radius of curvature, r, as a sphere of radius, r. The line that includes line segment CM is the principal axis, which is the straight line perpendicular to the surface of the mirror that divides the mirror in half. Point M is the center of the mirror where the principal axis intersects the mirror.

Figure 1. The focal point r of a spherical concave mirror is located halfway between the center of curvature and the mirror surface. Rays entering parallel to the principal axis are reflected to converge at the focal point, F.

When you point the principal axis of a concave mirror toward the Sun, all the rays are reflected through a single point. You can locate this point by moving a sheet of paper toward and away from the mirror until the smallest and sharpest spot of sunlight is focused on the paper. This spot is called the focal point of the mirror, the point where incident light rays that are parallel to the principal axis converge after reflecting from the mirror.
The Sun is a source of parallel light rays because it is very far away. All of the light that comes directly from the Sun must follow almost parallel paths to Earth, just as all of the arrows shot by an archer must follow almost parallel paths to hit within the circle of a bull’s-eye.
When a ray strikes a mirror, it is reflected according to the law of reflection. Figure 1 shows that a ray parallel to the principal axis is reflected and crosses the principal axis at point F, the focal point. F is at the halfway point between M and C. The focal length, f, is the position of the focal point with respect to the mirror along the principal axis and can
be expressed as f r/2. The focal length is positive for a concave mirror.

Figure 2. The real image, as seen by the unaided eye (a). The unaided eye cannot see the real image if it is not in a location to catch the rays that form the image (b). The real image as seen on a white opaque screen (c).

Graphical Method of Finding the Image
You have already drawn rays to follow the path of light that reflects off plane mirrors. This method is even more useful when applied to curved mirrors.
Not only can the location of the image vary, but so can the orientation and size of the image. You can use a ray diagram to determine properties of an image formed by a curved mirror. Figure 2 shows the formation of a real image, an image that is formed by the converging of light rays. The image is inverted and larger than the object. The rays actually converge at the point where the image is located. The point of intersection, I, of the two reflected rays determines the position of the image. You can see the image floating in space if you place your eye so that the rays that form the image fall on your eye, as in Figure 2a. As Figure 2b shows, however, your eye must be oriented so as to see the rays coming from the image location. You cannot look at the image from behind. If you were to place a movie screen at this point, the image would appear on the screen, as shown in Figure 2c. You cannot do this with virtual images.
To more easily understand how ray tracing works with curved mirrors, you can use simple, one-dimensional objects, such as the arrow shown in Figure 3a. A spherical concave mirror produces an inverted real image if the object position, do, is greater than twice the focal length, f. The object is then beyond the center of curvature, C. If the object is placed between the center of curvature and the focal point, F, as shown in Figure 3b, the image is again real and inverted. However, the size of the image is now greater than the size of the object.

Figure 3. When the object is farther from the mirror than C, the image is a real image that is inverted and smaller compared to the object (a). When the object is located between C and F, the real image is inverted, larger than the object, and located beyond C (b).

Mathematical Method of Locating the Image
The spherical mirror model can be used to develop a simple equation for spherical mirrors. You must use the paraxial ray approximation, which states that only rays that are close to and almost parallel with the principal axis are used to form an image. Using this, in combination with the law of reflection, leads to the mirror equation, relating the focal length, f, object position, do, and image position, di, of a spherical mirror.

 Mirror Equation $\ \frac{1}{f}=\frac{1}{d_i}+\frac{1}{d_0}$ The reciprocal of the focal length of a spherical mirror is equal to the sum of the reciprocals of the image position and the object position.

When using this equation to solve problems, it is important to remember that it is only approximately correct. It does not predict spherical aberration, because it uses the paraxial ray approximation. In reality, light coming from an object toward a mirror is diverging, so not all of the light is close to or parallel to the axis. When the mirror diameter is small relative to the radius of curvature to minimize spherical aberration, this
equation predicts image properties more precisely.

Magnification Another property of a spherical mirror is magnification, m, which is how much larger or smaller the image is relative to the object.
In practice, this is a simple ratio of the image height to the object height. Using similar-triangle geometry, this ratio can be written in terms of image position and object position.

 Magnification m $\ m=\frac{h_i}{h_0}=\frac{-d_i}{d_0}$ The magnification of an object by a spherical mirror, defined as the image height divided by the object height, is equal to the negative of the image position, divided by the object position.

Image position is positive for a real image when using the preceding equations. Thus, the magnification is negative, which means that the image is inverted compared to the object. If the object is beyond point C, the absolute value of the magnification for the real image is less than 1.
This means that the image is smaller than the object. If the object is placed between point C and point F, the absolute value of the magnification for the real image is greater than 1. Thus, the image is larger than the object.

Figure 4. When an object is located between the focal point and a spherical concave mirror, a virtual image that is upright and larger compared to the object is formed behind the mirror (a), as shown with the stack of blocks (b). What else do you see in this picture?

Virtual Images with Concave Mirrors
You have seen that as an object approaches the focal point, F, of a concave mirror, the image moves farther away from the mirror. If the object is at the focal point, all reflected rays are parallel. They never meet, therefore, and the image is said to be at infinity, so the object could never be seen. What happens if the object is moved even closer to the mirror? What do you see when you move your face close to a concave mirror?
The image of your face is right-side up and behind the mirror. A concave mirror produces a virtual image if the object is located between the mirror and the focal point, as shown in the ray diagram in Figure 4a. Again, two rays are drawn to locate the image of a point on an object. As before, ray 1 is drawn parallel to the principal axis and reflected through the focal point. Ray 2 is drawn as a line from the point on the object to the mirror, along a line defined by the focal point and the point on the object.
At the mirror, ray 2 is reflected parallel to the principal axis. Note that ray 1 and ray 2 diverge as they leave the mirror, so there cannot be a real image. However, sight lines extended behind the mirror converge, showing that the virtual image forms behind the mirror.
When you use the mirror equation to solve problems involving concave mirrors for which an object is between the mirror and the focal point, you will find that the image position is negative. The magnification equation gives a positive magnification greater than 1, which means that the image is upright and larger compared to the object, like the image in Figure 4b.

Figure 5. A convex mirror always produces virtual images that are upright and smaller compared to the object.

Convex Mirrors
In the first part of this chapter, you learned that the inner surface of a shiny spoon acts as a concave mirror. If you turn the spoon around, the outer surface acts as a convex mirror, a reflective surface with edges that curve away from the observer. What do you see when you look at the back of a spoon? You see an upright, but smaller image of yourself.
Properties of a spherical convex mirror are shown in Figure 5. Rays reflected from a convex mirror always diverge. Thus, convex mirrors form virtual images. Points F and C are behind the mirror. In the mirror equation, f and di are negative numbers because they are both behind the mirror.
The ray diagram in Figure 5 represents how an image is formed by a spherical convex mirror. The figure uses two rays, but remember that there are an infinite number of rays. Ray 1 approaches the mirror parallel to the principal axis. The reflected ray is drawn along a sight line from F through the point where ray 1 strikes the mirror. Ray 2 approaches the mirror on a path that, if extended behind the mirror, would pass through F.
The reflected part of ray 2 and its sight line are parallel to the principal axis. The two reflected rays diverge, and the sight lines intersect behind the mirror at the location of the image. An image produced by a single convex mirror is a virtual image that is upright and smaller compared to the object.
The magnification equation is useful for determining the apparent dimensions of an object as seen in a spherical convex mirror. If you know the diameter of an object, you can multiply by the magnification fraction to see how the diameter changes. You will find that the diameter is smaller,
as are all other dimensions. This is why the objects appear to be farther away than they actually are for convex mirrors.

Figure 6. Convex mirrors produce images that are smaller than the objects. This increases the field of view for observers.

Field of view
It may seem that convex mirrors would have little use because the images that they form are smaller than the objects. However, this property of convex mirrors does have practical uses. By forming smaller images, convex mirrors enlarge the area, or field of view, that an observer sees, as shown in Figure 6. Also, the center of this field of view is visible from any angle of an observer off the principal axis of the mirror;
thus, the field of view is visible from a wide perspective. For this reason, convex mirrors often are used in cars as passenger-side rearview mirrors.

Mirror Comparison
How do the various types of mirrors compare? Table 1 compares the properties of single-mirror systems with objects that are located on the principal axis of the mirror. Virtual images are always behind the mirror, which means that the image position is negative. When the absolute value of a magnification is between zero and one, the image is smaller than the object. A negative magnification means the image is inverted relative to the object. Notice that the single plane mirror and convex mirror produce only virtual images, whereas the concave mirror can produce real images or virtual images. Plane mirrors give simple reflections, and convex mirrors expand the field of view. A concave mirror acts as a magnifier when an object is within the focal length of the mirror.

## Law of Reflection Simulation

Quiz

Quiz 1. Reflection is the process in which light strikes a surface and bounces off that surface. The reflected ray will bounce back directly to the light source if it is lined up with the ...

a. incident ray
b. reflected ray
c. normal line
d. reflecting surface

Quiz 2. When you attempt to focus an image on a screen, using a concave mirror, but cannot, yet, you can see an image when are looking into the same concave mirror, the image is called a ...

a. convex distortion
b. concave image
c. virtual image
d. reflected distortion

When a mirror cannot focus an image on a screen, but you can see an image in the mirror, it is called a virtual image

Law of Reflection Simulation

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REFLECTION OF LIGHT

Suppose you have just had your hair cut and you want to know what the back of your head looks like. You can do this seemingly impossible task by using two mirrors to direct light from behind your head to your eyes. Redirecting light with mirrors reveals a basic property of light’s interaction with matter.

Light traveling through a uniform substance, whether it is air, water, or a vacuum, always travels in a straight line. However, when the light encounters a different substance, its path will change. If a material is opaque to the light, such as the dark, highly polished surface of a wooden table, the light will not pass into the table more than a few wavelengths. Part of the light is absorbed, and the rest of it is deflected at the surface. This change in the direction of the light is called reflection. All substances absorb at least some incoming light and reflect the rest. A good mirror can reflect about 90 percent of the incident light, but no surface is a perfect reflector.

The texture of a surface affects how it reflects light
The manner in which light is reflected from a surface depends on the surface’s smoothness. Light that is reflected from a rough, textured surface, such as paper, cloth, or unpolished wood, is reflected in many different directions, as shown in Fig 1(a). This type of reflection is called diffuse reflection.
Light reflected from smooth, shiny surfaces, such as a mirror or water in a pond, is reflected in one direction only, as shown in Fig 1(b). This type of reflection is called specular reflection. A surface is considered smooth if its surface variations are small compared with the wavelength of the incoming light.
For our discussion, reflection will be used to mean only specular reflection.
(a)                                            (b)
Fig 1. Diffusely reflected light is reflected in many directions (a), whereas specularly reflected light is reflected in the same forward direction only (b).

(a)
(b)
Fig 2. The symmetry of reflected light (a) is described by the law of reflection, which states that the angles of the incoming and reflected rays are equal (b).

Incoming and reflected angles are equal
You probably have noticed that when incoming rays of light strike a smooth reflecting surface, such as a polished table or mirror, at an angle close to the surface, the reflected rays are also close to the surface.When the incoming rays are high above the reflecting surface, the reflected rays are also high above the surface. An example of this similarity between incoming and reflected rays is shown in Fig 2(a).
If a straight line is drawn perpendicular to the reflecting surface at the point where the incoming ray strikes the surface, the angle of incidence and the angle of reflection can be defined with respect to the line. Careful measurements of the incident and reflected angles q and q , respectively, reveal that the angles are equal, as illustrated in Fig 2(b).
(angle of incidence : the angle between a ray that strikes a surface and the line perpendicular to that surface at the point of contact
angle of reflection : the angle formed by the line perpendicular to a surface and the direction in which a reflected ray moves)

$\theta = \theta'$

angle of incoming light ray = angle of reflected light ray

The line perpendicular to the reflecting surface is referred to as the normal to the surface. It therefore follows that the angle between the incoming ray and the surface equals 90° − $\theta$, and the angle between the reflected ray and the surface equals 90° − $\theta'$ .