The focal length of the Convex lens, using the parallax method

Introduction

Lenses came into use in the late 1500s in the making of magnifying glasses for microscopes or telescopes. For this purpose, it was important to know the focal length of the lenses to combine their powers. Before starting with the main topic, here are a few terms that must be understood first.

• Concave lens: It is also referred to as a “diverging lens” because it diverges the light that falls on the lens. It is designed as thick from the edges and thin from the center. It is used by nearsighted people. It always produces a virtual and upright image of the object in front of it. Example – used in telescopes.
• Convex lens: It is also referred to as “converging lens” as it converges/focuses the rays of light to a particular point. It is designed thin from the edges and thick from the middle. It is used by the person suffering from farsightedness. Nonetheless, both real and virtual images can be formed by convex lenses. Example – used in the compound microscope as an eyepiece.

• Focal length: It is defined as the distance between the focus and the surface of a lens. It is represented by “f”. SI Unit is the meter.
• Principle axis: It can be defined as an imaginary line passing through the center of curvature and pole.
• Principal focus: A point where all reflected rays meet.

Body

1. Determination of focal length of lenses: 

• Types of lenses – 

There are two types of lenses, one is the concave lens and the other is the convex lens. The concave lenses are designed thick from their edges and thin from the center whereas the Focal length of a convex lens using an illuminated object is designed to thin from the edges and thick from the middle to converge the lights to a particular point. Concave and Convex lenses are further classified into different types i.e. plano-convex lens and bi-convex lens and Plano concave and bi-concave lens.

• Aim: To determine the focal length of the convex lens

Requirements: convex lens, lens holder, wooden bench, screen bounded to a stand, measuring scale.

Procedure:

1. Align the lens and screen on a wooden bench.
2. Put the convex lens on the lens holder in such a way that it faces a distant object.
3. place the holder on the wooden bench.
4. Arrange the screen in such a way that a sharp image of the object is formed.
5. Now, the distance observed between the screen and position of the lens is the focal length of the convex lens
6. Similarly repeat the experiment to determine the focus of the lens for other distant objects.
7. Record the observations in the observation table.

Observation Table:

Calculations:

The formula for calculating focal length ‘f’ is 

f = position of the lens(L) – position of Screen (S)

and

for the mean calculation of focal length if convex lens,

f = (f1+ f2 + f3 )/ 3

 f = 10 cm

Results: The focal length of the convex lens is 10cm.

• Aim: To measure the focal length of a concave lens.

Requirements: concave lens, measuring scale, mirror holder and screen holder.

Procedure:

1. Select an object which is at least 50ft distant.
2. Place the concave mirror and object in a position facing each other.
3. Adjust the screen in front of the reflecting surface to obtain a clear and sharp image.
4. Now carefully measure the distance between the mirror and screen.
5. Repeat the experiment to determine the average focal length of the mirror.
6. Record the observations in a tabular form.

Observation Table: 

Calculations: The average focal length of the concave mirror is 

f = (f1+ f2 + f3 )/ 3

f = 10+10+10 / 3

f = 10 cm

Results: The focal length of the concave mirror is 10cm. 

2. The no-parallax method:

The focal length of a convex lens by the no-parallax method can be determined by the following steps:

1. Place a plane mirror in such a way that it is perpendicular to its principal axis.
2. Place an inverted pin on the cork pointing towards the principal axis.
3. Move the pin in to and fro motion.
4. Continue to move the pin until its tip coincides with the point of the inverted image.
5. Measure the distance between the lens and pin.
6. This distance observed now is the focal length of the convex lens.

3. Focal length of a convex lens using an illuminated object:

The focal length of the convex lens using an illuminated object is determined as follows:

1. Firstly, by approximate method, determine the average focal length of the lens.
2. place the object in such a way that the distance is greater than the focal length of the mirror.
3. Adjust the screen to obtain a sharp image of the illuminating object.
4. Measure the distance with a meter scale.
5. Repeat the experiment at least thrice.
6. Record the observations.

4. Determination of focal length of the convex lens using parallax method: 

Principle- A plane mirror is put behind a lens in such a way that light from the principal focus passes out of the lens and falls parallel to the mirror.

Procedure-

1. Mount the pin in front of the lens with a plane mirror behind it.
2. Make sure that the lens is parallel to the plane mirror.
3. Adjust the pin until a real image is formed on the lens.
4. Adjust the pin by moving to and fro until the tip of the pin and the image coincides.
5. Measure the distance between the lens and pin.
6. This distance observed now is the focal length of the convex lens.

Conclusion:

The focal length of a lens can be defined as the distance between the lens and its principal focus. The focal length helps in the determination of how sharply the apparatus converges or diverges the light. A concave mirror can be defined as a surface that is curved to the inside whereas a convex lens is defined as the lens which is thicker at the middle and thinner at the edge. A convex lens forms a real and inverted image whereas a concave lens forms an image that is real, inverted and small in size. The reflection mirror follows the law of reflection which are as follows:

• The incident reflected and normal rays lie in the same plane.
• The angle of reflection(r) is always equal to the angle of (i) incidence