Lenses are fascinating tools that can bend and manipulate light. They are transparent materials with two surfaces and they have a principal axis, a principal focus, a centre of curvature, an aperture, and an optical centre. There are two main types of lenses - convex and concave. The images produced by these lenses can either be real or virtual. In this article, we will be focusing on a particular experiment that explores how the image distance varies with different object distances when using a convex lens. We will illustrate this with the help of ray diagrams.
The aim of this experiment is to determine the image distance for varying object distances using a convex lens. We will also be drawing the corresponding ray diagrams to illustrate the nature of the image formed.
Theory
What is a convex lens?
A convex lens is a lens that is thicker in the middle and thinner at the edges. It is often referred to as a converging lens because it converges the light rays that fall on it. There are three types of convex lenses:
Double convex lens
Plano-convex lens
Concavo-convex lens
What is the lens formula?
The lens formula is a mathematical relationship that connects the object distance (u), the image-distance (v), and the focal length (f). The lens formula is expressed as follows:
Where,
f is the focal length of the lens
v is the distance of the image from the optical centre of the lens
u is the distance of the object from the optical centre of the lens
Place the convex lens on a lens holder, and place the screen on the other side of the lens.
Adjust the lens and screen until you get a clear, sharp, and inverted image on the screen. The distance at which this happens is the approximate focal length, which can be measured using a meter scale.
Mark the position where the lens is fixed as O.
Once you have determined the focal length, mark point F on both sides of the lens.
Mark a point 2F, which is twice the focal length of the lens from the lens.
Place the candle beyond point 2F and adjust the height of the lens so that it is level with the flame.
Adjust the screen position to get a sharp image of the candle flame through the convex lens and record your observations.
Repeat the above step, but this time place the needle or candle at 2F.
Repeat the above step, but this time place the object between F and 2F.
Repeat the above step, but this time place the object at F.
Repeat the above step, but this time place the object between O and F.
For each position of the object, draw the corresponding ray diagram.
Ray Diagrams
Observation Table
Sl. no
Position of the optical centre O of the lens l (cm)
Position of candle a (cm)
Position of screen s (cm)
Distance between lens and candle (object distance) u=a-l (cm)
Distance between lens and screen (image distance) v=s-l (cm)
Focal length ( l )
1
50
30
70
-20
20
10 cm
2
50
35
80
-15
30
10 cm
3
50
20
65
-30
15
10 cm
4
50
40
No image obtained on screen
-10
Infinity
5
50
45
No image obtained on screen
-5
Virtual image obtained and cannot be taken on screen
Here are the calculations for determining the focal length (f) for the different cases. All these calculations confirm that the focal length of the given lens is 10cm:
Case 1:
Case 2:
Case 3:
Result
S.no
Position of the object
Position of the image
Relative size of the image
Nature of the image
1
At 2F 1
At 2F 2
Same size
Real and inverted
2
Between F 1 and 2F 1
Beyond 2F 2
Enlarged
Real and inverted
3
Beyond 2F 1
Between F 2 and 2F 2
Diminished
Real and inverted
4
At focus F 1
At infinity
Infinitely large or highly enlarged
Real and inverted
5
Between focus F 1 and optical center O
On the same side of the lens as the object
Enlarged
Virtual and erect
6
At infinity
At focus F 2
Highly diminished, point-sized
Real and inverted
The focal length of the lens used in this experiment is 10cm.
Precautions
The convex lens used should have a focal length between 15 to 20 cm.
The convex lens should have a small aperture.
Conduct the experiment in calm air to prevent the candle flame from flickering.
Perform the experiment in a dark room for a clear and distinct image of the candle flame.
Ensure the image screen is stable and not shaking.
Viva Questions
Q1. What is a lens? Ans: A lens is a transparent material that has either two curved surfaces or one curved and one flat surface.
Q2. What is the power of a lens? Ans: The power of a lens is the reciprocal of its focal length. It is represented mathematically as:
Where,
P is the power of the lens
f is the focal length
Q3. What is one dioptre? Ans: One dioptre is the unit of measurement for the optical power of a lens or a curved mirror. It is defined as follows:
1 dioptre = 1m -1
Q4. What is the principal axis? Ans: The principal axis is the line that passes through the centre of the lens or a spherical mirror.
Q5. What is the focal length of a lens? Ans: The focal length of a lens is the distance between the principal focus and the optical centre of the lens.