Refraction of light at plane surfaces

Refraction of light at plane surfaces
When light ( or any wave) passes from one medium to another its direction changes at the boundary. This phenomenon of changing of direction at the boundary of two medium is called refraction. The angle of incidence is the angle made by the incident ray with the normal at the point of incidence. The angle of refraction is the angle made by the refracted ray with the normal at the point of incidence.
When a ray passes from a medium to a more optically dense medium, the refracted ray bends toward the normal. Conversely, a ray passing from glass to water or water to air bends away from the normal.















Laws of Refraction
The laws of refraction are stated as follows:
Law (1) The incident and the refracted fays are on the opposite sides of the normal at the point of incidence and all three are in the same plane.
Law(2) ( Snell’s law) The ratio of the sine of the angle of the incidence to the sine of the angle of refraction is a constant for a given pair of media and a particular colour of light.

Refractive index
The value of the constant for a ray passing from one medium to another is called the refractive index of the second medium with respect to the first; and is denoted by n.
i.e. n =

If air is the first medium then n is simply referred to as the refractive index of the second medium. In strict sense absolute refractive index is defined with respect to vacuum.

Total internal reflection
We know light is partially reflected and partially transmitted through the interface between two medium. However all of the light can be reflected back from the interface with none being transmitted even the second medium is transparent. This total reflection occurs when light travels from a material of lower refractive index on to a material of higher refractive index (a>b). Let us consider a point light source immersed in water.
From Snell’s law



As a>b b should be greater than a in the above equation. Thus there must be an angel of incidence in the water for which the angle of refraction in air should be equal to 900. This angle of incidence in the water is called the critical angle. Beyond the critical angle the ray cannot pass into the upper material and is completely reflected back in the lower material. This situation is called total internal reflection.
At critical angle of incidence a= crit and the angle of refraction in the second material b= 900.

or,
When air is the second material b = 1. then



Working of an optical fibre
An optical fiber is a glass or plastic fiber designed to guide light along its length by total internal reflection. Optical fibers are widely used in fiber-optic communication, which permits digital data transmission over longer distances and at higher data rates than electronic communication. The fiber consists of a core surrounded by a cladding layer. To confine the optical signal in the core, the refractive index of the core must be greater than that of the cladding. When ever any optical fall on the core cladding boundary at an angle greater than the critical angle of the boundary it is totally internally reflected and is transmitted along the length of the fibre.

Some effect of refraction
Apparent bending of a stick obliquely placed in water as shown in the figure below. The light ray from the tip B of the stick bends away from the normal after refraction and seems to come from point C. similar are the cases for the rays coming out of all the other immersed portions of the stick. The observer sees the stick apparently at position AC.



Air
Water



Real and apparent depth
A thick slab of glass appears to be about two-thirds of its real thickness when viewed from vertically above. Similarly, water in a pond appears to be three-quarter of it actual depth.
The figure below shows how light rays from the bottom point O of a denser medium bends and seems to come from an apparent position I.
Now mathematically it can be shown that
The refractive index of the medium is given by
n = =





Dispersion of light and formation of Rainbows.
White light is made of different colours. The different colours travel at different speed through any medium other than vacuum or air. So when a beam of white light falls on a transparent medium like a glass prism the refracted beam deviates form the original direction during the entrance once and again during the exit. As the speed of different colours are different in the medium the deviations are different. As a result when light come out of the prism different colours are separated at different direction. This is called dispersion of light.
Dispersion of light due to refraction is the cause of rainbow formation. When sunrays hit raindrop light they are refracted and split into their component colours which we then see as an arc of coloured band in the sky. This arc has red at the outer most band and the other colours like orange, yellow green etc toward the inner bands.














Questions

1. State laws of refraction and define refractive index
2. What is meant by total internal reflection and critical angle?
3. Find critical angle of a glass medium having refractive index 1.65
4. Find the angle of refraction for a ray of light incident at an angle of 550 on the plane surface of a slab of Perspex of refractive index 1.49.
5. A microscope is focused on a mark on a table. When the mark is covered by a plate of glass 2 cm thick the microscope has to be raised 0.67 cm for the mark to be once more in focus. Calculate the refractive index of the glass.



Refraction through spherical surfaces and Lens
Lens
Lens is made of a transparent medium bound by two surfaces of which at least one is curve.
Convex lenses are thicker at the center than the edges and concave lenses are thicker at the edge than the center. Some cross section of spherical lenses are shown below.



Principle axis
Principal axis of lens is a line passing through the centers of curvature of its surfaces.

Principle Focus
Principal focus of a lens is a point on the axis of a lens to which all rays originally parallel to the principal axis converge, or from which they appear to diverge, after refraction through the lens.

Focal length (f)
Focal length is the distance between the center of the lens and its principal focus.




Image formation by a lens
Image of an object placed in front of a lens can be constructed graphically by ray tracing method. Here at least two rays are required to construct the image. These two rays are conveniently chosen. One is a ray parallel to the axis of the lens another is one that passes through the centre of the lens. Image formation by a convex and a concave lens are shown below.













Here
Object distance u is negative
Image distance v is positive
And the image is formed by converging rays and is real.


Here
Object distance u and image distance v both are negative
And the image is formed by diverging rays and is virtual.

The relation between object distance u image distance v and the focal length f is


Power of a lens (P)
The power of a lens is its ability to converge or diverge a beam of light. It is measured by the reciprocal of its focal length in meter. The unit of power is Diopter.
P =

Magnification:
The size of the image is different from the size of the object. The linear magnification is the ratio of the height of the image to the height of the object.
i.e. magnification m =
However from geometry it follows that

Image formation by converging lens
The size and position of the image depends on the position of the object. The nature and magnification of the image can be discussed conveniently by taking five possible object locations into five general areas or points:
Case 1: the object is located beyond the 2F point
Case 2: the object is located at the 2F point
Case 3: the object is located between the 2F point and the focal point (F)
Case 4: the object is located at the focal point (F)
Case 5: the object is located in front of the focal point (F)







Case 1: The object is located beyond 2F

When the object is located at a location beyond the 2F point, the image will always be located somewhere in between the 2F point and the focal point (F) on the other side of the lens. In this case, the image will be an inverted image (upside down), reduced in size (magnification number less than 1) . Finally, the image is a real image. Light rays actually converge at the image location. If a sheet of paper was placed at the image the actual replica of the object would appear projected upon the sheet of paper.

Case 2: The object is located at 2F



When the object is located at the 2F point, the image will also be located at the 2F point on the other side of the lens. In this case, the image will be inverted .The image dimensions are equal to the object dimensions.( the magnification is exactly 1) . Finally, the image is a real image

Case 3: The object is located between 2F and F

When the object is located in front of the 2F point, the image will be located beyond the 2F point on the other side of the lens. In this case, the image will be inverted. The image dimensions are larger than the object dimensions.(the magnification is greater than 1). Finally, the image is a real image.

Case 4: The object is located at F

When the object is located at the focal point, no image is formed. The refracted rays neither converge or diverge. After refracting, the light rays are traveling parallel to each other and cannot produce an image.

Case 5: The object is located in front of F

When the object is located at a location beyond the focal point, the image will always be located somewhere on the same side of the lens as the object. In this case, the image will be an upright image, enlarged and a virtual image. (Light rays diverge upon refraction; for this reason, the image location can only be found by extending the refracted rays backwards beyond the lens. The point of their intersection is the virtual image location. It would appear to any observer as though light from the object were diverging from this location. Any attempt to project such an image upon a sheet of paper would fail since light does not actually pass through the image location.

Real and virtual image
A real image is formed by a group of converging rays whereas a virtual image is formed by diverging rays. A real image can be projected on a screen that is, if a screen is placed at the position of the real image it will be seen to be formed on that screen. However a virtual image cannot be projected on a screen. The image seen on the cinema screen or the image projected on the screen of OHP or multimedia projectors are all real images. The image that we see in mirror is virtual image.

Common defects in vision in eye

Farsightedness. If the eyeball is too short or the lens too flat or inflexible, the light rays entering the eye — particularly those from nearby objects — will not be brought to a focus by the time they strike the retina. Eyeglasses with convex lenses can correct the problem. Farsightedness is called hypermetropia.











Nearsightedness. If the eyeball is too long or the lens too spherical, the image of distant objects is brought to a focus in front of the retina and is out of focus again before the light strikes the retina. Nearby objects can be seen more easily. Eyeglasses with concave lenses correct this problem by diverging the light rays before they enter the eye. Nearsightedness is called myopia.










Questions
1. Draw the ray diagram and find position of the image when an object is situated at a distance of 2f from a concave mirror.
2. A small object is placed 25 cm away from a converging lens of focal length 30 cm. What is the position nature and magnification of the image?
3. A concave lens has a power of -2.5D. What is its focal length?
4. The critical angle of light in a glass slab is 38.50. What is the refractive index of its material?
5. Draw the ray diagram and find position of the image when an object is situated at a distance greater than 2f from a convex mirror.
6. Draw the ray diagram and find position of the image when an object is situated at a distance greater than 2f from a concave mirror.
7. An object 1.5 cm tall is placed 25 cm away from a concave mirror of focal length 30 cm. What are the position, nature, magnification and size of the image?
8. An object 1.5 cm tall is placed 25 cm away from a concave lens of focal length 30 cm. What are the position, nature, magnification and size of the image?
9. Draw and name three types of converging lenses.
10. Define the principal focus and focal length of a converging lens.
11. What is meaning of real and virtual image.
12. Draw ray diagram to show the position, nature and size of images formed by a convex lens
13. Draw a ray diagram showing how a thin converging lens of focal length 10 cm forms a real image twice as large as the object.
14. A converging lens has a focal length of 5 cm. What is its power?
15. A small object is placed 6 cm away from a converging lens of focal length 10. What is the position nature and magnification of the image?