Finding Image Distance for Varying Object Distances using a Convex Lens with Ray Diagrams

Lens can be defined as a piece of transparent glass, which is used to produce an image of an object either by concentrating or diverging the rays from a specific point. Lenses in physics are categorized broadly into the convex lens, also called converging lens and a concave lens, also called a diverging lens. 

These lenses are used to form images of an object. But the images formed are greatly dependent on the type of lens being used and the position of the object with respect to the lens.In this article, we have discussed an experiment to find the image distance for different object distances using a convex lens with ray diagrams.

Read Also: Lens and its types

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Theory

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Convex lens, also referred to as a converging lens is the type of lens in which the rays of light travel parallel to its principal axis, wherein the rays of light come together or converge. According to their shape, this lens can be identified by its thickness in the middle and how it tapers towards the edges. A plane or convex mirror could generate a real image if the object is found to be virtual.

The most common example of a convex lens is the magnifying glass as it converges rays to one point. Hence, the distance between the lens and object will happen to be less than the focal length, due to which the image of the object will be magnified.

Types of Convex Lens

There are 3 types of convex lens namely plano-convex lens, double convex lens and concave-convex lens.

Plano-convex lens

In this type of lens, one side is spherical or curved and the other side is plane or flat. 

Double convex lens

In this type of lens, both sides of the lens are spherical or curved outwards. These types of lenses are also known as biconvex lenses. 

Concave-convex lens

In this type of lens, one of the sides is curved outwards(convex) and the other side is curved inwards(concave).

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Aim

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The aim of our study is “Finding Image Distances with varying Object Distances in case of a Convex Lens”. There are a total of five cases with respect to the images formed of the objects at respective positions. These cases are:

Case 1 – Position of Object at 2F₁.

Case 2 – Position of Object between F₁ and 2F₁.

Case 3 – Position of Object beyond 2F₁.

Case 4 – Position of Object at Focus F₁.

Case 5 – Position of Object at infinity.

The setup is as follows:

Check More: Uses of Concave Mirror

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Discussion

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Here, we will be considering the right-side convention of the lens as positive and the left side of the convention as negative.

Case 1 – Position of Object at 2F₁.

When the Object is positioned at 2F₁, the image is formed at 2F₂. The size of the image remains the same and the nature of the image is real and inverted.

Case 2 – Position of Object between F₁ and 2F₁.

When the object is positioned between F₁ and 2F₁, the image is formed beyond 2F₂. The size of the image will appear to be enlarged and the nature of the image will remain real and inverted. 

Read Also: Magnification

Case 3 – Position of Object beyond 2F₁.

When the Object is positioned beyond 2F1, the image is formed between F₂ and 2F₂. The size of the image will appear to be small or diminished. However, the nature of the image will be real and inverted. 

Case 4 – Position of Object at Focus F₁.

When the Object is positioned at Focus F1, the image is formed at infinity where the size of the image is extremely enlarged. The nature of the image remains real and inverted. 

Case 5 – Position of Object at infinity

When the Object is positioned at infinity, the image will be formed at Focus F₂. The size of the image will be extremely small or diminished to a point and the nature of the image will be real and inverted. 

Read Further: Lens and its formation

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Important Terms & Equations

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Here are some important terms and equations that will be used in Class 10 Science Book Chapter 10- Light: Reflection and Refraction.

• Pole – The point in the middle of the lens is called Pole. It is the point where the principal axis reaches the lens. It is denoted as P.
• Principal Axis – It is an imaginary line that passes through the centre of curvature.
• Centre of Curvature – The centre of the two spherical surfaces of a lens is its centre of curvature. 
• Optical Centre – Optical Centre is the point on the pricipal axis at the centre of the lens.
• Aperture – The diameter of the light transmitting area of a lens is called the aperture of the lens.
• Principal Focus – The point on the principal axis where the rays of light converge and meet. It is denoted as F.
• Focal Length – The distance between the principal focus and the optical centre. It is usually denoted as f.
• Power – The reciprocal of focal length is power. Dioptre is the SI Unit of Power.

Important Formulas

Four equations are important for solving basic to complex level questions of Light chapter of class 10^th science book. These are as follows: 

1. Lens formula:

The lens formula is given as: 1/f = 1/v – 1/u

Where v is the distance from the image to the optic center and u is the distance from the object to the optic center.

2. Magnification:

Magnification is given as: m = Height of Image/Height of Object

or

m = v/u

where, m is magnification, v is image distance incase of lens and u is object distance in case of lens.

3. Image Distance: 

​Image Distance is given as: 1/d_i = 1/f – 1/d_o

Where, di is the image distance, f is focal length and do is the object distance.

4. Image Height:

Image height is given as: m = hi/ho, hence

h_i = m*h_o

Where, m is magnification, hi is height of the image and ho is the height of the object.

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Uses of Convex Lens

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Convex lenses are used in:

• Magnifying glass
• Eyeglasses to correct hypermetropia
• Magnifying cameras
• Microscopes
• Projectors
• Plano-convex lens is used in telescopes

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Things to Remember

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• A convex lens is also known as a converging lens since it converges the light rays that are passing through it.
• There are three types of convex lenses: plano-convex, biconvex, and concave-convex lenses.
• The important terms to keep in mind regarding lenses are: pole, principal focus, principal axis, center of curvature, optical center, aperture, focal length and power. 
• Convex lenses are used in magnifiers, cameras, to treat hypermetropia, etc.