Refraction of lens

Refraction of lens

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.

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 = =



Principle of reversibility of light
The paths of light rays are reversible.
The refractive indices for rays of light passing from air to glass and from glass to air may be represented by ang and gna respectively

ang =
by principle of reversibility
gna =

Total internal reflection and critical angle
When light passes from medium to a less optically dense medium the ray moves away from the normal, i.e. the angle of refraction is greater than the angle of incidence. And this angle of refraction goes on increasing with the increase of angle of incidence in the denser medium. Finally at a certain critical angle of incidence c the angle of refraction becomes 900. At a greater angle of incidence light is totally internally reflected within the denser medium. This particular property of light enables it to be transmitted through a bent transparent fiber which is called optical fiber




State laws of refraction and define refractive index
What is meant by total internal reflection and critical angle?
Find critical angle of a glass medium having refractive index 1.65
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.
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.



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

Principal 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


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.

Some Optical instruments:
1. Telescope
2. Binocular
3. Microscope
4. Camera
Some Important Definitions:
1. Centre of curvature: A lens is usually bounded by two surfaces which are the parts of two spheres. Each of these two centres of the spheres is known as the centre of curvature of a lens.
2. Principal axis: It is the line passing through the centre of the curvature of the lens.
3. Principal focus: When a beam of parallel rays is incident on a lens in a direction parallel to its principal axis, after refraction through the lens the rays actually converge at a point F on the principal axis or appears to diverge from a point F on the principal axis. This point F is known as the Principal focus of the lens.
4. Focal length: The distance between the principal focus and the optical centre of a lens is called the focal length of the lens.
5. Optical centre: Optical centre of a lens or simply the centre of a lens may be defined as fixed point lying on the principal axis of the lens such that all rays passing through this point within the material of the lens will have their refracted rays parallel to their corresponding incident direction.
6. Power of a lens: When rays parallel to the principal axis pass through the lens the ability of the lens to converge or diverge the rays is called Power of the lens. Power is the reciprocal of the focal length.

Unit of Power of the lens is Dioptre.










Draw and name three types of converging lenses.
Define the principal focus and focal length of a cong\verging lens.
What is meaning of real and virtual image.

Draw ray diagram to show the position, nature and size of images formed by a convex lens
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.
A converging lens has a focal length of 5 cm. What is its power?
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.