In the previous section we saw the details about refractive index. In this section we will learn about lens.
Lens is a transparent medium having spherical surfaces
From the above definition, we can say that, a lens should satisfy the following two conditions:
(i) It must be transparent
• That is., a lens can be made using glass, plastic or any similar materials. But it must be transparent
(ii) It should have spherical surfaces
• That is., any surface of a lens should be a part of a sphere.
• It is just like saying: An arc is a part of a circle
Let us see the details about those spherical surfaces. We will write them in steps:
1. Consider the two spheres in fig.7.10 (a) below:
• They are identical spheres. That is., both have the same radii
• The centre of the left sphere is C1
• The centre of the right sphere is C2
• The red line joins C1 and C2
2. In fig.7.10(b), the two spheres are brought closer to each other.
• So close that, they intersect each other
• The distance C1C2 is now lesser than the C1C2 in fig.a.
3. The 'portion common to both the spheres' is retained as such
• The rest of the two spheres are erased off
• The result is shown in fig.c
• The retained portion in fig.c forms a convex lens
• Note that, the distance C1C2 is fib.c is the exact same as that in fig.b
4. The surfaces of the lens are thus parts of the surfaces of spheres
Now we will see the concave lens:
1. Consider the two spheres in fig.7.11 (a) below:
• They are identical spheres. That is., both have the same radii
• The centre of the left sphere is C1
• The centre of the right sphere is C2
• The red line joins C1 and C2 .
2. In the fig.a, the spheres are close to each other. But they are not touching each other
• In fig.b, the space between them is filled up with a transparent material
3. In fig.c, the two spheres are removed.
• The newly added transparent material is left behind. This forms a concave lens.
• Note that, the distance C1C2 is fib.c is the exact same as that in fig.b
4. The surfaces of the lens are thus parts of the surfaces of spheres
Let us see the properties of convex and concave lenses:
1. Optic centre
• Optic centre is the midpoint of a lens.
• It is denoted by the letter 'P'. It is shown in fig.7.12 below:
2. Centre of curvature
• We have seen that each lens is associated with two spheres with centres C1 and C2
• Both C1 and C2 are eligible to be called as the 'centre of curvature' of the lens
• So the definition is:
Centre of curvature is the centre of the imaginary spheres of which the surfaces of the lens are parts. It is denoted by the letter 'C'
3. Principal axis
• The definition is:
Principal axis is the imaginary line that passes through the optic centre joining the two centres of curvatures
• So the principal axis should satisfy both the conditions given below:
(i) The principal axis must pass through both C1 and C2
(ii) The principal axis must pass through P
4. Principal focus
(a) Convex lens
• The definition is:
Light rays parallel and close to the principal axis converge at a point on the principal axis of a convex lens. This point is it's principal focus. It is denoted by the letter 'F'
• This will be clear from fig.7.13(a) below
• The red line is the principal axis.
• Note that light rays will be travelling in all directions. In the fig.a above, we are considering only those which satisfies the following two conditions:
(i) Light rays must be parallel to the principal axis
(ii) Light rays must be close to the principal axis
• A ray which travel exactly along the principal axis will also satisfy the two conditions. So it is also included in the diagram
(b) Concave lens
• The definition is:
Light rays parallel and close to the principal axis diverge from one another after refraction. These rays appear to originate from a point on the same side. This point is the principal focus of a concave lens. It is denoted by the letter 'F'
• This will be clear from fig.7.13(b) above.
5. Focal length
It is the distance between the principal focus F and the optic centre P. This distance is denoted by the letter 'f'
■ Why do we say that the principal focus of a concave lens is virtual?
Let us analyse:
• Consider the dashed green lines diverging from F in the fig.7.13(b).
• The lines are dashed from 'F' up to the outer boundary of the lens.
• Why are they 'dashed'?
• The answer can be written in steps:
1. The actual light rays pass through the lens and after refraction, leaves the outer boundary of the lens
• They diverge from each other
2. These rays cannot travel back to give us the position of 'F'
• That is., there are no actual rays along the dashed lines behind an actual concave lens in 'real life'
♦ So they are drawn with dashed lines
• Consequently, there is no actual 'F' behind an actual concave lens in 'real life'
3. We can only draw them on paper.
• So the principal focus of a concave lens is said to be virtual
■ In short, we can write:
It is impossible to converge light at a point using a concave lens. Therefore the principal focus of a concave lens is virtual
Now we will learn about image formation. Consider fig.7.14 below:
1. A convex lens is placed in front of a candle. A screen is placed in front of the lens.
• In this arrangement we have two distances:
(i) Distance between the object (candle) and the lens. This is denoted by the letter 'u'
(ii) Distance between the image (screen) and the lens. This is denoted by the letter 'v'
2. By adjusting the above two distances, we can form a clear image of the candle on the screen
■ How is the image formed on the screen?
We will write the answer in steps:
1. Consider the fig.7.15 below:
• An object (consisting of an yellow pole and a cube at the top) is placed on the left side of a lens
2. We know that rays of light reflect from the object in all directions. When those rays fall on our eyes, we see the object.
• Two such rays are considered here. Those two rays start from the cube and travel in two different directions.
• That is., after starting from the cube, they diverge from each other.
• But after passing through the lens, they converge at a point on the other side of the lens.
3. At that point of convergence, we get an image of the cube.
■ So we can note a point:
To define a single point on the image, we will need at least two rays.
4. In the fig.7.15 above, we defined the cube in the image. In the same way, we can define all other points on the image.
Lens is a transparent medium having spherical surfaces
From the above definition, we can say that, a lens should satisfy the following two conditions:
(i) It must be transparent
• That is., a lens can be made using glass, plastic or any similar materials. But it must be transparent
(ii) It should have spherical surfaces
• That is., any surface of a lens should be a part of a sphere.
• It is just like saying: An arc is a part of a circle
Let us see the details about those spherical surfaces. We will write them in steps:
1. Consider the two spheres in fig.7.10 (a) below:
• They are identical spheres. That is., both have the same radii
 |
| Fig.7.10 |
• The centre of the right sphere is C2
• The red line joins C1 and C2
2. In fig.7.10(b), the two spheres are brought closer to each other.
• So close that, they intersect each other
• The distance C1C2 is now lesser than the C1C2 in fig.a.
3. The 'portion common to both the spheres' is retained as such
• The rest of the two spheres are erased off
• The result is shown in fig.c
• The retained portion in fig.c forms a convex lens
• Note that, the distance C1C2 is fib.c is the exact same as that in fig.b
4. The surfaces of the lens are thus parts of the surfaces of spheres
Now we will see the concave lens:
1. Consider the two spheres in fig.7.11 (a) below:
• They are identical spheres. That is., both have the same radii
 |
| Fig.7.11 |
• The centre of the right sphere is C2
• The red line joins C1 and C2 .
2. In the fig.a, the spheres are close to each other. But they are not touching each other
• In fig.b, the space between them is filled up with a transparent material
3. In fig.c, the two spheres are removed.
• The newly added transparent material is left behind. This forms a concave lens.
• Note that, the distance C1C2 is fib.c is the exact same as that in fig.b
4. The surfaces of the lens are thus parts of the surfaces of spheres
Let us see the properties of convex and concave lenses:
1. Optic centre
• Optic centre is the midpoint of a lens.
• It is denoted by the letter 'P'. It is shown in fig.7.12 below:
 |
| Fig.7.12 |
• We have seen that each lens is associated with two spheres with centres C1 and C2
• Both C1 and C2 are eligible to be called as the 'centre of curvature' of the lens
• So the definition is:
Centre of curvature is the centre of the imaginary spheres of which the surfaces of the lens are parts. It is denoted by the letter 'C'
3. Principal axis
• The definition is:
Principal axis is the imaginary line that passes through the optic centre joining the two centres of curvatures
• So the principal axis should satisfy both the conditions given below:
(i) The principal axis must pass through both C1 and C2
(ii) The principal axis must pass through P
4. Principal focus
(a) Convex lens
• The definition is:
Light rays parallel and close to the principal axis converge at a point on the principal axis of a convex lens. This point is it's principal focus. It is denoted by the letter 'F'
• This will be clear from fig.7.13(a) below
 |
| Fig.7.13 |
• Note that light rays will be travelling in all directions. In the fig.a above, we are considering only those which satisfies the following two conditions:
(i) Light rays must be parallel to the principal axis
(ii) Light rays must be close to the principal axis
• A ray which travel exactly along the principal axis will also satisfy the two conditions. So it is also included in the diagram
(b) Concave lens
• The definition is:
Light rays parallel and close to the principal axis diverge from one another after refraction. These rays appear to originate from a point on the same side. This point is the principal focus of a concave lens. It is denoted by the letter 'F'
• This will be clear from fig.7.13(b) above.
5. Focal length
It is the distance between the principal focus F and the optic centre P. This distance is denoted by the letter 'f'
■ Why do we say that the principal focus of a concave lens is virtual?
Let us analyse:
• Consider the dashed green lines diverging from F in the fig.7.13(b).
• The lines are dashed from 'F' up to the outer boundary of the lens.
• Why are they 'dashed'?
• The answer can be written in steps:
1. The actual light rays pass through the lens and after refraction, leaves the outer boundary of the lens
• They diverge from each other
2. These rays cannot travel back to give us the position of 'F'
• That is., there are no actual rays along the dashed lines behind an actual concave lens in 'real life'
♦ So they are drawn with dashed lines
• Consequently, there is no actual 'F' behind an actual concave lens in 'real life'
3. We can only draw them on paper.
• So the principal focus of a concave lens is said to be virtual
■ In short, we can write:
It is impossible to converge light at a point using a concave lens. Therefore the principal focus of a concave lens is virtual
Now we will learn about image formation. Consider fig.7.14 below:
 |
| Fig.7.14 |
• In this arrangement we have two distances:
(i) Distance between the object (candle) and the lens. This is denoted by the letter 'u'
(ii) Distance between the image (screen) and the lens. This is denoted by the letter 'v'
2. By adjusting the above two distances, we can form a clear image of the candle on the screen
■ How is the image formed on the screen?
We will write the answer in steps:
1. Consider the fig.7.15 below:
 |
| Fig.7.15 |
2. We know that rays of light reflect from the object in all directions. When those rays fall on our eyes, we see the object.
• Two such rays are considered here. Those two rays start from the cube and travel in two different directions.
• That is., after starting from the cube, they diverge from each other.
• But after passing through the lens, they converge at a point on the other side of the lens.
3. At that point of convergence, we get an image of the cube.
■ So we can note a point:
To define a single point on the image, we will need at least two rays.
4. In the fig.7.15 above, we defined the cube in the image. In the same way, we can define all other points on the image.
• The rays emerging from the object, passes through the lens and then converge to give points on the image.
• To draw the exact paths taken by the rays, we must first familiarise ourselves with some rules. We will see those rules in the next section.
• To draw the exact paths taken by the rays, we must first familiarise ourselves with some rules. We will see those rules in the next section.
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