Refraction Through a Lens
Lens
A lens is a transparent refracting medium bounded by two curved surfaces which are generally spherical.
Convex lens or converging lens converges light rays as shown in figure 1.
Concave lens or diverging lens diverges light rays as shown in figure 2.
Type of Lens:
A convex lens bends the ray of light towards its middle i.e. it converges the light.
A concave lens bends the ray of light towards its edges i.e. it diverges the light.
Important terms
The centre of curvature of a lens is usually represented by the letter C. Since there are two centres of curvature, we may represent them as C1 and C2.
The radius of the sphere, of which the part is the lens surface is called the radius of curvature of that surface of the lens.
An imaginary straight line passing through the two centres of curvature of the lens is called its principal axis.
The central point of a lens is its optical centre. It is usually represented by the letter O.
A ray of light through the optical centre of a lens passes without suffering any deviation.
The effective diameter of the circular outline of a spherical lens is called its aperture.
A lens has two principal foci F1 and F2.
F1 is the first focal point and F2 is the second focal point.
The distance of the principal focus from the optical centre of a lens is called its focal length. The letter f is used to represent the focal length.
f1 is the first focal length (the distance of O from F1).
Difference between a convex and a concave lens:
Convex lens Concave lens
It is thick in the middle and thin at its periphery.
It is thin in the middle and thick at its periphery.
It converges the incident rays towards the principle axis.
It diverges the incident rays away from the principle axis.
It has a real focus. It has a virtual focus.
Distinction between real and virtual image:
Real image Virtual image
A real image is formed due to the actual intersection of the refracted (or reflected) rays.
A virtual image is formed when the refracted (or reflected) rays appear to meet if they are produced backwards.
A real image can be obtained on the screen.
A virtual image cannot be obtained on the screen.
A real image is inverted with respect to the object.
A virtual image is erect with respect to the object.
Example: the image of a distant object formed by a convex lens.
Example: the image of an object formed by a concave lens.
A virtual image is erect with respect to the object.
Image Formation by Convex Lenses:
Case 1
Position of object At infinity
Position of image At the focus 𝐹2
Relative size of the image Highly diminished, point-sized
Nature of image Real and inverted
Application Burning glass
Case 2
Position of object Beyond 2𝐹1
Position of image Between 𝐹2 and 2𝐹2
Relative size of the image Diminished
Nature of the image Real and inverted
Case 3
Position of object At 2𝐹1
Position of image At 2𝐹2
Relative size of the image Same size
Nature of image Real & inverted
Application To get inverted image
Case 4
Position of object Between 𝐹1 & 2𝐹1
Position of image Beyond 2𝐹2
Relative size of the image Magnified
Nature of the image Real & inverted
Case 5
Position of object At 𝐹1
Position of image At infinity
Relative size of the image Very much magnified
Nature of the image Real & inverted
Application Collimator
Case 6
Position of object Between 𝐹1 & O
Position of image Same side as object
Relative size of the image Magnified
Nature of the image Virtual & erect
Application Magnifying glass
Case 1
Position of object Btw infinity & O
Position of image Btw 𝐹1 & O
Relative size of image Diminished
Nature of image Virtual & erect
Case 2
Position of object At infinity
Position of image At focus 𝐹1
Relative size image Highly diminished point-sized
Nature of image Virtual & erect
The power of a lens is a measure of deviation produced by it in the path of rays refracted through it.
1. P = 1 𝑓
2. The SI unit of power of a lens is ‘dioptre’, denoted by the letter D. 3. Power of a convex lens is positive and that of a concave lens is negative. Ray diagram of simple microscope
Magnifying power = m = 1 + 𝐷 𝑓
The magnifying power of the microscope can be increased by using the lens of short focal length, but it cannot be increased indefinitely.
Experiments for determination of focal length of a convex lens
Estimation of focal length by the distant object method
Estimation of focal length by auxiliary plane mirror method. Application of lenses
Uses of a convex lens
It is used in a number of optical instruments such as camera, telescope, microscope and so on.
It is used as a reading lens and as a magnifying glass.
It is used in spectacles for the correction of long-sightedness of the eyes.
Uses of a concave lens
· It is used in telescopes to see far off places.
