# Lenses

Edited by Sim, Jen Moreau

## Lenses

A lens is a piece of glass or a transparent substance having two opposite regular surfaces. Either both surfaces are curved or only one is curved. The lenses are commonly used in optical instruments.

### Types of Lenses

- 1The lens which is thicker at the center and thinner at the edges is called a convex lens. It converges a parallel beam of light at a point and hence is called a converging lens. It has three subtypes.Convex Lens:Advertisement
- Bi convex Lens: It is also called a double convex lens where both sides are convex.
- Plano Convex: Whose one side is a plane and the other is convex.
- Concave Convex: Whose one surface is concave and the other is convex.

- 2A lens which is thinner at the center and thicker at the edges. It diverges a parallel beam of light. It is also called a diverging lens. It has the following subtypes.Concave Lens:
- Bi Concave Lens: Whose both sides are concave. Also called a double concave lens.
- Plano Concave Lens: Whose one side is a plane and the other is concave.
- Convexo Concave Lens: Whose one side is convex and the other is concave.

### Definitions and Terms

- 1
- 2The line, passing through the principal focus and the pole, is called principal axis.Principal Axis:
- 3The point, where all the parallel beams of light converge or diverge after passing through the lens, is called principal focus. It is generally denoted by 'F'. A lens has two focal points that are at equal distance from the optical center. Each focal point is on the opposite side of the lens. A convex lens has real focus whereas a concave lens has virtual focus.Principal Focus:
- 4The distance between the principal focus and the optical center of the lens is called focal length. It is generally denoted by 'f'.Focal Length:
- 5The center of the sphere from which the lens is cut is called center of curvature.Center of Curvature:
- 6

### Ray Diagram

In order to understand the formation of images by lenses, we make use of the following three ways.

- 1A ray which passes through the optical center of the lens goes un-deviated or undeflected.
- 2A ray coming parallel to the principal axis always passes through the focus after refracting through the convex lens, and in the case of the concave lens, this ray appears to come from the focus.
- 3

### Image Formation by Convex Lens

The size, nature, and position of the image formed by a convex lens depend upon the distance of the object from the lens. The following are the different positions.

- 1
- 2
- 3
- 4
- 5

### Image formation by Concave Lens

In a concave lens, for any object position, the image is always virtual, erect and smaller in size. Moreover, it is always located between F and P i.e. between the optical center and the principal axis.

**Sign Conventions:**
Sign convention is used while using the formula. They are as follows.

- 1All the distances are measured from the optical center of the lens.
- 2Whereas that of virtual objects and images are taken as negative values.The distances of real objects and real images are taken as positive values.
**OR**The distances measured in the same direction as that of incident rays are taken as positive and against the direction of incident rays are taken as negative. - 3The focal length of a convex lens is positive and that of a concave is negative.

**Lens Formula:** The formula which relates the object distance 'p' image distance 'q' and focal length 'f' is called lens formula.

1/f= 1/p+1/q

**Proof:**

Consider an image formed by a convex lens as shown in the figure. Take �" OBO'ß-------à IBI' Since these triangles are similar, so OO'/II'= OB/IB= p/q -------------- (1)

Again we take triangles �" EBF and �" II'F

Since the triangles are similar, so

EB/II' = BI/FI= f/q-f

OO'/II'=f/q-f --------------------- (2)

From eq (1) and (2), we obtain:

P/q= f/q-f > p (q-f) = qf

pq- pf= qf

Dividing both sides by 'pqf', we obtain:

1/f-1/q= 1/p

1/f= 1/p+1/q -------------- (3) which is the required lens formula

### Linear Magnification or Magnifying Power

The ratio of the size of the image to the size of the object is called linear magnification (M).

M= size of image/ size of object= hi/ho

The ratio of the distance of the image from the pole or optical center to the distance of the object is called magnification.

M= Distance of image/ Distance of Object= q/p

**Resolving Power:** Resolving power is the ability of an imaging device to separate (to see as distinct ) points of an object that are located at a small angular distance.

### Power of Lens:

The power of a lens is a measure of the degree of convergence or divergence of light rays falling upon it. It is defined as, "The reciprocal of the focal length (in meters) of a lens*. The unit of Power is "Diopter" and its symbol is 'D'. *

D= 1/ f(m)

The power of a lens is said to be one diopter if its focal length is one meter. The power of a lens can be measured directly by using an instrument called diopter meter. It is used by opticians to test the power of spectacle lenses.

### Simple Microscope

A double convex lens of shorter focal length (f) can be used as a simple microscope or magnifying glass.
The apparent size of an object depends upon the angle made at the eye. This angle is called *visual angle*. The greater is the visual angle, the greater is the apparent size. The smaller the distance of the object is from the eye, the greater will the visual angle be and therefore the larger it will appear.
As we know, a normal person cannot clearly see an object that is closer than the least distance of distinct vision (25 cm). A convex lens helps us see the details of an object by bringing it closer than 25 cm. such a convex lens is known as a simple microscope or magnifying glass.

M= d/f +1

Where 'd' is the least distance of distinct vision=25cm and f=focal length of the convex lens. The smaller the focal length, the greater will its magnification be and vice versa.

**Uses:**
A simple magnifier is used as an eyepiece in many optical instruments.

- 1students use them to examine slides.Biology:
- 2menders of watch use them to see small parts clearly.Watch:
- 3detective departments use them to match fingerprints.Police:
- 4use them to see fine parts of jewelry.Jewelers:

### Compound Microscope

A compound microscope is an optical device used for high magnification.

**Construction:**A compound microscope consists of two convex lenses of short focal lengths fitted at the outer ends of two tubes. These tubes can slide into one another to adjust the distance between the two lenses. The lens which is towards the object is called**objective**and the lens which is towards our eyes is called**eyepiece**.**Working:**the object "AB" to be examined is placed just beyond the focus "Fo" of the objective. The objective lens forms a real, inverted and magnified image A'B'. It acts as an object for eyepiece lens. The eyepiece is moved in such as way that the image A'B' lies within its focus. The eyepiece now acts as a magnifying glass for this image and produces highly magnified and virtual image.

Magnification= size of the final object seen with compound microscope/ size of the object seen without the microscope.

M= A"B"/A'B'/AB/A'B'

M= Mobj* Meye piece

M= Mo * Me ------------ (1)

Where Mo is the magnifying power of the objective and Me is that of the eyepiece.

Mo= image distance/ Object Distance= qo/po

The eyepiece is a simple magnifier, so Me = 1+ d/fe Where 'd' is the least distance of distinct vision and 'fe' is the focal length of the eyepiece. Therefore (1) M= qo/po (1+ d/fe) --------------- (2) When the object AB is situated very near to the principal focus of the objective, and the image A'B' is formed very near to the eye lens, in this case

Po= fo= focal length of objective

Qo= l= length of microscope tube

So eq. (2) M= L/fo (1+ d/fe) ------------- (3)

From equation (3) it is clear that for large magnification, the two lenses used should have small focal lengths. A good microscope has magnification as high as 2000 or even more.

### Astronomical Telescope:

An astronomical telescope is an optical instrument used to see heavenly bodies and distant objects. The image is inverted.

**Construction:**
An astronomical telescope consists of an objective and an eyepiece. The objective is a lens combination of large focal length and large aperture. The eyepiece, a convex lens, is also a combination of short focal length and aperture. The objective is mounted on a wide brass tube while the eyepiece is mounted on a small brass tube.
The distance between the objective and the eyepiece can be changed.

**Function:**
The rays coming from a distant object fall on the objective as parallel beams at some angle. These rays, after being refracted through the objective, converge at the focus and make an inverted real image A1B1 (as shown in the figure). This image acts as an object for the eyepiece, and the image formed is so adjusted, that the image A1B1 lies within the focal length of the eyepiece which forms a magnified image A2B2, that is inverted with respect to the object.

When the distance between the image (A1B1) and the eyepiece is equal to the focal length of the eyepiece, the final image is formed at infinity. In this case, the telescope is said to be in normal adjustment or focused for infinity. Also, in this case, the length of the telescope "L" is represented as;

L= Fo+Fe

**Magnification:**
The magnification of a telescope in normal adjustment is given by the formula

M= Fo/Fe----------- (1)

Where 'fo' is the focal length of objective and 'fe' is the focal length of the eyepiece of the telescope. From eq (1) it is clear that for high magnifying power, the focal length of its objective 'fo' should be large.

### Vision and its Defects

The eyes are responsible for collecting visual stimuli from their surrounding environment and sending their signals to the brain for interpretation. A defective eye can affect vision thus causing problems in seeing clearly. Some eye defects can be corrected with eyeglasses or contact lenses and some others through surgery.

__Defects of Eye__

- 1Is a defect in which the eye is unable to see distant objects but is able to see near objects. The defects occur either when the eyeball is longer than normal or when the maximum focal length of the lens is insufficient to form a clear image at the retina due to its high converging power. In this condition, the image of the distant object is formed in front of the retinaShort Sightedness(Myopia):
**Correction or Treatment:**This defect can be corrected with a diverging lens (Concave lens) of suitable focal length in front of the eye.

- 2The defect in which an eye is unable to see near objects and is able to see distant objects is called long sightedness or hypermetropia. This defect is can be either due to the less converging power of the lens of the eye or due to the shortness of the eyeball. In these defects, the rays from the near objects are focused behind the retina and the objects are not seen clearly.Long Sightedness (Hypermetropia):
**Correction or Treatment:**This defect can be corrected with converging lenses (convex) of some suitable focal lengths in front of the eye.

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Categories : Physics

Recent edits by: Sim