Showing posts with label Reflection of Light. Show all posts
Showing posts with label Reflection of Light. Show all posts

Working of Human Eye and Simple Microscope

Human eye

Human eye is a natural optical instrument. The human eye is shaped like double convex lens having a refractive index close to 1.437. It is fixed in its place with the help of the muscles. It has the ability to change the focal length while seeing near and distant objects. The unique feature of automatic adjustment of focusing is called power of accommodation.

The nearest a distance for a human eye is 25 cm and it is called least distance of distant vision. The far point is infinity.

The angle that an object subtends at the eye is called visual angle. Microscope and telescopes are designed to increase the visual angle and hence increase the apparent size of the image.

With respect to the increase of the age, the near point gradually increases.

Myopia means near point is fine for a human eye but the Far Point turns finite instead of infinite. It is also called the short sight.

Long sight  means the far distant objects appears fine but near distant object is unable to be seen properly. It is simply because the near point for the particular eye is more than 25 cm. It happens because the final images formed behind the retina.

The long sight and the short sight can be corrected with the help of the proper lenses.



Simple microscope

It is a simple convex lens which is used to see the magnified image of an object. With the help of this is simple microscope we can increase the visual angle as well as the size of the image. This process is called magnification and the simple instrument is called simple microscope. This is also called as magnifying glass or reading glass.

The object is placed before the convex lens and the corresponding image also shall be seen in the same direction. This is possible only when the object is placed at between the principal focus of the convex lens. If the object is placed at the principal focus of the lens, the final images formed at infinity. This kind of adjustment is called relaxed eye adjustment and in this case the magnification is going to be less.

If the object is placed within the principal focus and the final images formed at a finite point and we will be getting a better magnification. Anyway as the image is at a finite point to observe that image, our eyes will be strained a little bit more and that’s why this position is called strained position.



If the light of higher wavelength is used, its focal length is more and hence its magnification will be less.

The simple microscope is having a limitation of producing a better magnification up to only four times the size of the object. If we try to get better magnification above that four times, the image consists of aberrations. That is why, we prefer to use it only to produce a magnification that is less than the four times the size of the object.

If we are in need of the magnification more than this, we shall use a device called compound microscope.

Problem and solution

The image attached below is having two problems. Solving the first problem is a simple task. We need to calculate the power of the lens and we know that the power is nothing but the reciprocal of the focal length of the lens. We can also calculate the magnification of the lens as the ratio of image distance of distant vision to the focal length of the lens. Similarly using the formula we can also calculate the focal length for the strained eye as shown in the diagram.

The second problem needs a little bit of analysis. Let us try to first give the problem and then give you the analysis.

Problem

A man with the normal near point reads a book with the small print using a magnifying glass of focal length 5 cm. What are the closest and the farthest distance at which he can read the book when viewing through the glass?

What are the maximum and minimum magnifying powers for this gas?

Solution

We have to use the lens formula with proper sign convention to solve this problem. For the object distance to be minimum, the corresponding image also shall be minimum location. For the object distance to be maximum, the corresponding image can be at infinity. Taking these points into consideration, we can solve the problem as shown below.





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Ray Optics Introduction and Reflection of Light 
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Ray Optics Complete Lesson

Light is a form of energy. It exhibits a wide variety of properties. If the size of the object is much larger than the wavelength of the light, light appears like travelling in straight lines. It exhibits certain properties under these conditions and that properties are studied and rename called Ray optics.

In Ray optics we study about reflection, refraction, dispersion and the deviation. 

Reflection is the phenomena of light bouncing back into the same medium after striking a boundary that is separating the two media.

Refraction is the phenomenon of light due to which light travels into the other medium after striking a boundary that is separating the two media.

Dispersion is the phenomenon of splitting up of a white light into multiple colors when it is passed through a prism. 

Deviation is the phenomena of changing its path when the light is passing through a different media.

In this chapter we are also going to study regarding mirrors, lenses, prisms, critical angle, total internal reflection, microscopes and telescopes.


This post is a list of all the topics in Ray optics which includes problems and solutions.

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Refraction of Light Through Prism

The prism is an optical medium which has at least two nonparallel surfaces. Light incidents on one of the surfaces of the prism and emerges out from the other surface. These two surfaces are always nonparallel to each other. The plane surfaces on which light incidents and emerges are called refracting surfaces.

The angle between the two surfaces on which light is incident and emerges is called refracting angle. This is also called angle of prism or apex angle.

The incident light ray, in the absence of the prism can continue in its path without any change in its path. But after passing through the prism it takes a different path. Angle of deviation is the angle between the incident light ray and the emerging light ray.

At any particular point of incidence we can allow the light ray to strikes the surface of the prism. The angle between the normal and the incident light ray is called angle of incidence. As there is a change of media, the light ray will deviate from its path. As the light ray is moving from rarer medium to denser medium, it moves towards the normal inside the prism. The ratio of angle of incidence to angle of refraction at the first surface is equal to refractive index of glass prism with respect to medium.

Inside the prism, the light ray strikes the surface with a particular angle of incidence once again. Again it emerges out from the other surface by moving from denser medium to rarer medium. As a result the light ray moves away from the normal and this light ray is called emerging light ray. The angle between the normal and the emerging light ray is called angle of emergence. Again on the second surface refractive index of the prism with respect to the medium is equal to the ratio of angle of incidence in the second surface to the angle of emergence.




For different angles of incidence, angle of deviation is different. It is practically observed that with the increase of angle of incidence, angle of deviation decreases and reaches to a minimum value. This minimum value of deviation is called angle of minimum deviation. After this minimum deviation, with the increase in angle of incidence angle of deviation further increases as shown in the graph.

When the angle of deviation is minimum, the light ray inside the prism travels parallel to the base of the prism. At this angle , we can derive the equation for the refractive index of a prism with respect to the medium basing on angle of the prism and the angle of minimum deviation is shown below.



For a small angled prism, we can derive the equation for the angle of minimum deviation in terms of angle of prism and refractive index without involving the trignometircal functions like SIN.

Anyway this formula has to be used only when the angle of the prism is small. When the angle of the prism is constant we can write that the angle of minimum deviation is directly proportional to refractive index of the prism as shown below.

As per Cauchy’s formula, we can identify that the refractive index of the present material is inversely proportional to the wavelength of the light approximately. Thus among all the visible colors being the readies having the highest wavelength, its refractive index is lowest.

We shall also understand that among all the visible colors, red deviates least because of its highest wavelength.




Normal incidence and grazing emergence

If a light ray incident the face of a prism with zero angle, that is along the normal drawn, the incidence is called normal incidence. When the light ray emerges, if it emerges along the surface of a prism then it is called the grazing emergence.

For normal incidence, angle of incidence and angle of refraction at the first surface are equal to zero.

The grazing emergence is possible only when the angle of incidence inside the prism is equal to critical angle. As the light ray is emerging at the second surface in a grazing manner, damaging angle is equal to 90°.

By writing the basic conditions of these things in the appropriate equations, we can derive some conditions as shown below.



Grazing incidence and grazing emergence

If the light ray strikes the first surface of the prism along the surface and emerges out of the second surface of the prism again along the surface, it is called grazing incident and grazing emergence. In this case the angle of refraction at the first surface and the angle of incidence at the second surface inside the prism are equal to critical angle.

The angle of incidence as well as the angle of emergence at both the surfaces is equal to 90°. We can derive the equations for critical angle on the minimum deviation is shown in the above diagram.


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Problems and Solutions on Refraction of Light

Problem and solution

A 2 cm high object is placed on the principal axis of a concave mirror at a distance of 12 cm from the pole. If the image is inverted, real and 5 cm in height, find the location of the image and the focal length of the mirror?

We can solve this problem basing on the very definition of magnification and the mirror formula. Magnification is defined as the ratio of height of the image to the height of the object. The other way of defining the magnification is as the ratio of distance of the image to the distance of the object. The sign of the magnification is negative which means that object and image are in the different directions. The problem is solved as shown below.



An object is placed in the principal axis of a concave mirror at a distance X  from a principal focus. The images formed at a distance Y the focus. What is the focal length of the mirror ?

This problem also has to be solved basing on the mirror formula. Being both object and the major place to before the mirror they shall be treated as negative and a concave mirror focal length is also negative.The solution is shown in the above diagram.

Problem and solution

An object is placed in front of a concave mirror at a distance of 50 cm. A plain mirror is introduced covering the lower half of a convex mirror. The distance between the object and the plain mirror is 30 cm. It is found that there is no gap between the image formed by the two mirror. Then what is the radius of curvature of the convex mirror?

In the problem object is placed at a distance of 50 cm from a concave mirror. Between the object and the mirror at a distance 30 cm from the object a plain mirror is placed. That means the plain mirror is a distance of 20 cm from the convex mirror. The image of the object due to the plain mirror will be farmed again at the 30 cm as a virtual image in the backward direction as shown. And hence it is going to be 10 cm behind the convex mirror.

The same shall be the image of the convex mirror also as it is given in the problem that both the images are coinciding with each other.

Therefore we know that the object is in front of the mirror at a distance of 50 cm and the image is behind the concave mirror at a distance of 10 cm and using the mirror formula we can calculate the focal as shown below.



Problem and solution

Two blocks each of mass m lies on a smooth table. They are attracted to the two other masses as shown. The pullies are straight and light. An object to is kept on the table as shown. The surfaces of the two blocks are made are reflecting surfaces. Find the acceleration of the two images by the two reflecting surfaces with respect to each other?

We shall try equations of motion using Newton’s laws. We shall draw  free body diagram and identify the direction of motion. The forces along the direction of motion shall be treated as positive and vice versa. As shown in the below diagram, we can write the equations of motion and derive acceleration of the individual images.

As per the law of optics, the acceleration of the image is twice the acceleration of the mirror.

As the two images are moving in the opposite direction, we can calculate the relative acceleration is the sum of the two accelerations.




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Sign Convention and Image Tracing of Light in Ray Optics

Sign convention

We shall follow certain sign convention in measuring the distances while we are solving the problems are dealing the concepts in Ray optics.

For the sign convention, pole is taken as the origin and the principal axis as the x-axis.
We shall assume that light is always coming from left to right in the given diagram.

All the distances are measured from the pole.

If the distance of the object is measured along the direction of the incident light, it shall be treated like a positive.

If the distance of the object is measured against the direction of incident light, then it is treated as negative.

The same rules are valid even when we are measuring the distance of the image.

The heights measured upward normal to the principal axis are treated as positive and the height measured in the downward direction is treated as negative.

Focal length and the radius of curvature for a convex mirror are treated as positive and for a concave mirror they are treated as negative. It is simply because these values, when measured from the pole appear along the same direction of the incident light as shown in the diagram below.



Image tracing

When a point object is placed before a spherical mirror, a point images formed. The point of intersection of the incident rays is called object and the point of intersection of reflected light rays is called image.

To measure object distance, image distance, focal length and radius of curvature we need to follow certain sign convention. If the reflected light rays intersect with each other, then at the point of intersection is the place a real images formed. If the reflected light rays diverged from the surface of the reflection, the image is a virtual image. It is going to form at the point from where these light rays are appearing like diverging.
Basing on the sign convention we can take their values as positive or negative as shown in the diagram below.



Problem and solution

A rod of length 10 cm lies along the principal axis of a concave mirror of focal length 10 cm in such a way that its one end close to the pole is 20 cm away from the mirror. What is the length of the image formed in this case?

We have to solve this problem in  two different parts. Let us consider the rod as combination of two points where one is the starting point and other one is the ending point.

We can apply mirror formula for both the points with appropriate sign convention as shown below.



Radius of curvature is numerically double to the value of the focal length. Basing on the values of object distance, image distance and the focal length of a mirror, we can derive a relation for magnification. Magnification is simply defined as the ratio of heat of the image to the height of the object. It can be also defined as the ratio of image distance to the object distance.

Relation between them can be shown as



Problem and solution

An object is placed on the principal axis of a concave mirror of focal length 10 cm at a distance 8 cm from the pole. Find the position and the nature of the image?

While solving this problem, we shall apply the proper sign convention. Being the mirror is a concave mirror; its focal length is negative.

Object is placed before the concave mirror as shown. As the object distance is measured from the pole which is against the direction of the incident light Ray, it shall be treated as negative. We don’t know the value of the image location therefore we are not going to assign any specific sign to it. We will take it as it there in the formula and basing an answer will conclude that what is the location and the nature of the image is.
As for the formula it can be identified that the image distances +40 cm. It means that it is developed at the other end of the mirror and then only can be treated as positive. It means the image is a virtual image.



Problem and solution

The above diagram is having another problem with the solution.

At what distance from the concave mirror of focal and 25 cm boy shall stand so that his image as a high equal to half of its original height?


The magnification of the concave mirror is negative which means to say that object and image will never be along the same direction. If object distances positive image distances negative and vice versa. By applying the basic formula of magnification as ratio of image distance to the object distance and the mirror formula with can solve the problem as shown above.


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Ray Optics Introduction and Reflection of Light

Light is a form of energy and it satisfies law of conservation of energy. Light travels like a electromagnetic wave. Human eye has a sensitivity to detect the electromagnetic waves of certain wavelength ranging from 4000 Å to 8000 Å.

Light travels with a very high velocity that is equal to 3 into 10 power 8 m/s in vacuum. The velocity of the light is maximum in vacuum and in any other medium it is less than that value. When the light falls on the objects whose size is much larger than that of the wavelength of the light, it appears like a straight line. Further properties of this and its applications are called ray optics.

Optics is a known subject for us for many years and it is a part of classical physics. We are able to see any objects because sunlight falls on the body and the body absorbs some particular colors, and reflects the other colors. What is the color that the body reflects is the color we see as the color of the body.

Light is a form of energy and it exhibits a wide variety of properties. To understand all these properties of the light we shall follow different theories of light that are evolved over the time.

Initially we have Newton’s corpuscular theory according to which light consists of  tiny particles called carpuscules. The size of the particle decides the color of the light. They travel in straight lines with high velocities.

Further we have different theories like Huygen’s wave theory, Maxwell’s electromagnetic theory and Plank’s quantum theory. Each theory is successful in explaining some properties of light and failed to explain to some other properties.

Finally we have a concept of dual nature. Here we assume that light travels like a wave and interacts with objects like a particle.

A ray of light gives the direction of propagation of light. In the absence of the obstacle, light advancing straight line without changing its direction.

 Reflection of light

The phenomena of the light coming back to the same medium after striking an obstacle is called as reflection. A light ray is reflected by the smooth surface in accordance to the rules of reflection. There are two laws of reflection.

The first law is that the angle of incidence is equal to angle of reflection. Here the angle of incidence is the angle between the incident ray and the normal. The point at which the light ray strikes the surface is called point of incidence. A line drawn through the point of incidence perpendicular to the surface is called normal.

The angle between the reflected and the normal is called angle of reflection. As per the first law angle of incidence is equal to angle of reflection.

As per the second law the incident ray, the reflected ray and the normal lies in the same plane.

The angle of deviation is the angle between the original path of the light and the path taken by of the light. We can derive the equations for the as shown below.

From the diagram it is clear that the reflected ray moves away from a plain surface. It is very clear from the diagram that the reflected ray is diverging from the obstacle and it is not going to form a real image. By extending these two light rays we can identify the location of the image and this kind of the images is called virtual image. From the obstacle the distance of the object in this case is equal to the distance of the virtual image.



Spherical mirror

A spherical mirror is a part that is cut from a hollow sphere and in general made up of the glass. One surface of the glass is silvered therefore it can behave like a mirror. The reflection of the light takes place on the other surface. If the reflection takes place at the convex surface then the mirror is called a convex mirror. If the reflection of the tile light takes place at the concave surface then the mirror is called as concave mirror. There were as shown in the diagram below.


Definitions

The Centre of the sphere from which the mirror is drawn is called Centre of curvature of the mirror.

The radius of the sphere is called radius of curvature of the mirror.

The point of the mirror at the middle of the surface is called as pole.

The line joining the pole and the Centre of the curvature is called principal axis.

The point where all the reflected light rays converge or from where the reflected light rays appears like diverging is called principal focus.

The distance between the principal focus and the pole of the mirror is called focal length.

The light rays that are close to the principal axis are called paraxial light rays.

The area of the spherical surface which is available for the reflection of the light is called Aperture.




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