Optical Centre: Terms, Image Formation, Magnification

What is an Optical Centre?

The optical centre of a lens is a point inside the lens on the principal axis. A ray of light passes through without any change in its direction. In simple words, it is a point that is at the geometrical centre of the lens.

Important Terms Related to Optics

There are some important terms we need to know to understand the way images are formed by optical systems.

Lens
It is an object made of glass, plastic, or any transparent material, which can form real and virtual image of an object. The lenses which we study are considered thin lenses due to the comparison between their thickness and the diameter of their spheres. There are two types of lenses – Concave lens and Convex lens.

a. Concave Lens: It is a transparent object whose one or both sides are curved as if from inside of a sphere; that is, it curves inwards or “caves” in.
b. Convex Lens: It is the opposite of a concave lens. It is one or both sides bulge out as if like the outer surface of a sphere. We see the outside world because of a convex lens inside each of our eyes.

Refraction
It is the phenomenon in which light rays bend after touching the surface of an optical medium. When light rays pass from air into glass, they bend with a smaller angle towards the normal. The same happens when light passes into water. When light passes from a dense medium like water or glass into a rare medium like air, it bends away from the normal with a bigger angle.

Principal Axis- It is the line passing through the geometrical centre of a lens. It is normal to the surface. Another name for this is the optical axis. The optical centre of a lens is on the principal axis.

Focal Point
It is also called the focus. When a ray of light parallel to the principal axis passes –
i. through a convex lens, it bends and passes through a point on the principal axis. All rays of light focus or converge on this point
ii. through a concave lens; it bends away and appears to emerge out of a point on the principal axis. All rays of light appear to diverge out of this point

This point, in a concave or convex lens, is called the focal point or principal focus. The distance between the optical centre and focal point is called the focal length.

Centre of Curvature- A lens is made with one or both sides as a part of a sphere. The centre of this sphere is the centre of curvature. The radius of this sphere is the radius of curvature.

Image Formation in a Convex Lens

A convex lens converges light rays onto a single point. The type of image formed depends on the position of the object it is refracting.

Real image: It can be focused on a screen and captured on a film or sensor. The object and the image will be on the opposite sides of the lens.
Virtual image: We can only see this. It cannot be focused on a screen. In a lens, it will be on the same side as the object.

Position of Object	Position, Size and Nature of Image
At infinity	The image on the focal point \(\left( {{F_2}} \right),\) point size, real, and inverted.
Near lens, but beyond centre (\({C_1},\) or \(2{F_1}\))	Image between \({F_2}\) and \({C_2},\) diminished, real, and inverted.
At the centre of curvature \(\left( {{C_2}} \right)\)	Image at \({C_2},\) the same size as object, real, and inverted.
Between \({C_1}\) and \({F_1}\)	Image beyond \({C_2},\) enlarged, real, and inverted.
At focal point \(\left( {{F_1}} \right)\)	Image at infinity, highly enlarged, real, and inverted.
Between \({F_1}\) and optical centre \(\left( O \right)\)	Image on the same side of the object, enlarged, virtual, and erect.

Image Formation in a Concave Lens

A concave lens diverges light rays out from a single point.

Lens Equation

This equation relates the distances between the object and the image with focal length.
\(\frac{1}{v} – \frac{1}{u} = \frac{1}{f}\)
\(u\) is the distance of the object from the lens.
\(v\) is the distance of the image from the lens. \(f\) is the focal length.

Sign Convention
a. Object is always placed left of lens
b. Distance of object or image always measured from optical centre, \(O\)

The lens equation is the same for both convex and concave lenses. However, in concave lenses, the focal point, image, and object are all on the same side of the lens. So, the focal length \(f\) is considered negative.

Magnification Factor

We have heard and used the term magnifying glass for a lens. The lens referred to here is always a convex lens that we use to read very fine print or tiny objects. As we have seen from the table and line diagrams above, an object closer to the lens gives an enlarged, virtual image.
Magnification is defined as the ratio of the height of the image to the height of the object.
\({\rm{Magnification}},\;M = \frac{{{h_i}}}{{{h_o}}}\)

Magnification for Real Images:

Using the rule of similar triangles,
\(\frac{{{h_i}}}{v} = \frac{{{h_o}}}{u}\)
This means that,
\(\frac{{{h_i}}}{{{h_o}}} = \frac{v}{u} = M\)

Magnification for Virtual Images:

Using the rule of similar triangles,
\(\frac{{{h_o}}}{u} = \frac{{{h_i}}}{v}\)
This means that,
\(\frac{{{h_i}}}{{{h_o}}} = \frac{v}{u} = M\)
The equation for magnification is the same for both real and virtual images.

Summary

Lens and Optical Centre: Sample Problems

1. The focal length of a convex lens is \({\rm{20\;cm}}{\rm{.}}\) If the object is placed behind it at \({\rm{12\;cm}}\) from the optical centre, where is the image located, and what type of image is it?
Sol:
Given,
focal length, \(f = 20\;{\rm{cm}}\)
object distance, \(u = 12\;{\rm{cm}}\)
Lens formula is,
\(\frac{1}{v} – \frac{1}{u} = \frac{1}{f}\)
Therefore,
\(\frac{1}{v} – \frac{1}{{12}} = \frac{1}{{20}}\)
Solving for \(v,\)
\(v = 7.5\;{\rm{cm}}\) The image is \(7.5\;{\rm{cm}}\) from the optical centre.

FAQs on Optical Centre

1. Are optical centre and centre of curvature the same?
Ans: No. The optical centre is within the lens. It is the geometrical centre of the lens. The Centre of curvature is the centre of the sphere whose surface the lens is a part of. The centre of curvature is always outside the lens.

2. What lens do we use when observing a tiny seed?
Ans: We use a convex lens to magnify the image of small objects. When held close to the object, it gives an enlarged, erect image. A concave lens always reduces the size of the image.

3. What is the difference between real and virtual images?
Ans: A real image is inverted and can be projected on a screen. It can be captured on a light-sensitive film or sensor. A virtual image is erect but cannot be projected on a screen. Likewise, it cannot be captured on a photographic film or sensor.

4. What kind of lens do our eyes have?
Ans: Convex lens. Our eyes need to focus the light rays that enter it onto a screen at the back of the eyeball called the retina. Creating a real image is possible only in a convex lens.

5. If concave lenses do not magnify or give a real image, why do we need them?
Ans: Concave lenses diverge out the light. This property is used in spectacles for short sight, in-vehicle headlights, and door peepholes. They are also used in optical instruments like cameras, microscopes, telescopes in combination with convex lenses.