5.4 Understanding Lenses

~Lenses are divided into
a)convex lens@converging lens@positive lens

 b)concave lens@diverging lens@negative lens

-Optical centre, O : A point which all rays traveling through this point pass through the lens in a straight line.
-Principal axis : A straight line which passes through the optical centre , O at a right angles to the plane of the lenses
-Principal focus,F : i) F is a point on the principal axis to which incident rays of light travelling parallel to the principal axis, converge after refraction through a convex lens.
ii) F is a point on the principal axis from which incident rays of light travelling parallel to the principal axis appear to diverge after refraction through a concave lens.
-Object distance, u : Distance of the object from the optical centre,O.
-Image distance, v : Distance of the image from the optical centre,O.
-Focal plane : A plane through the principal focus and parallel to the plane of the lens.
-Focal length, f : Distance between the principal focus, F and the optical centre, O.Focal length = OF.
 The focal length of a convex lens is positive whereas the focal length of a concave lens is negative.

Power of Lenses

a)Power of lenses,P = 1/f(m) or 100/f(cm)

b)The unit of power of a lens is dioptre,P.

c)The power of a convex lens is taken to be positive.

d)The power of a concave lens is taken to be negative.

Images formed by Convex Lenses

★Distant object : u = infinity

★Image distance : v =f

★Real

★Inverted

★Diminished in size
★On the opposite side of the object 

★Object distance is more than 2f : u>2f

★Image distance : f<v<2f

★Real

★Inverted
★Diminished in size
★On the opposite of the object

★Object distance is equal to 2f : u=2f

★Image distance : v = 2f

★Real 

★Inverted
★Same size as object

★On the opposite side of the object

★Object distance is between f and 2f : f<u<2f

★Image distance : v>2f

★Real 

★Inverted

★Magnified

★On the opposite side of the object

★Object distance is equal to f : u = f

★Images is at infinity

★Virtual 

★Upright

★Magnified

★On the same side as the object

★Object distance is less than f : u<f

★Object distance : v>u

★Virtual 

★Upright

★Magnified

★On the same side as the object

Images Formed by Concave Lenses

a)Images formed by concave lenses do not depend on the position of the object with respect to the lens.

b)An image formed by a concave lenses is always

i) virtual

ii) upright

iii) diminished

iv) located between the lens and the object

v)the image distance is less than the focal length

★When the object is at infinity
★The image formed is:
-formed at F1
-upright
-diminished
-virtual

★When the object is placed at any position between O and infinity 

★The image formed is :

-formed between O and F1
-upright
-diminished
-virtual

Linear Magnification

Linear magnification ,

m = Image height / Object height = h_I / h_o

OR

m= Image distance / Object distance = v / u

Lens Equation

The relationship between distance of the object (u), distance of the image (v) and focal length (f) of the lens is called lens formula or lens equation.

  Microscope

Compound Microscope

 A Laboratory Model of Compound Microscope
The essential parts of a compound microscope are two convex lenses of short focal length. These lenses are referred to as:

• the objective lens or objective

• the eye piece or lens

~Working
The ray diagram given below gives the principle of a compound microscope. The object is mounted on the stand below the microscope tube. The objective lens forms a real, inverted and magnified image (I₁) of the object. The image I₁ acts as an object for the eye piece. The position of the eyepiece is so adjusted that the image lies within the focus of the eyepiece (F_e). The eyepiece acts like a magnifying glass and forms a virtual erect and magnified image of the object. 

Image Formation in a Compound Microscope

• The object (O) is placed just outside F_o, the principal focus of the objective lens.

• F_e is the principal focus of the eye lens.

• A real, inverted magnified image I₁ is formed. The magnified image I₁ acts as an object for the eye lens.

• The final image I₂ is virtual and is magnified still further. It is inverted compared with the object. I₂ may appear 1000 times larger than the object. 

 Telescope

This type of telescope is used to view heavenly bodies like stars, planets and satellites.

 

It consists of two convex lenses called objective and eyepiece. The objective is of large focal length whereas the eyepiece is of short focal length. The distance between the two lenses can be adjusted by adjusting the tube which holds the lens.
The ray diagram showing the principle of the astronomical telescope is given below.

 The Differences between Microscope and Telescope

Compound microscope	Astronomical telescope
Objective lens has smaller focal length, than the eyepiece	Objective lens has larger focal length than the eyepiece
Distance between the objective lens and the eyepiece is greater than f0+fe	Distance between the objective lens and the eyepiece is equal to f0+fe
It is used to see very small objects	It is used to see distant astronomical objects