In school labs, we may always be presented with a lenses whose focal length we don’t know. We can always determine the focal length of the given lenses by applying various methods of estimating focal length of a lens.
This methods may includes:
- Focusing on a distance object
- Using lens formula experiments
- Using non-parallax method
- Using an illuminated object
- Displacement method
Focusing a distance object
A white screen, convex lens on a lens holder and ruler are arranged such that rays of light from a distance object are incident on a lens that is close to the white screen.
See the diagram below
We adjust the lens position to and fro until a sharp image of a distance object is obtained on the screen.
Distance object means an object that is at large distance relative to the focal length of the lens. For instance an object 30 metre from a lens whose focal length is 21cm. We note that, object position is many times longer compared to the focal length of the lens.
Distance between the lens and screen where the sharp image of a distance object is formed is the focal length. The area occupied by the image is the focal plane of the lens.
The estimated focal length is not exact but can be 2 cm plus or minus the real focal length.
This method of estimating focal length depends on the fact that parallel rays from infinity converges at the focal point on the screen.
Non-parallax method
Parallax is a displacement or difference in the apparent position of an object viewed along two different lines of sight and is measured by the angle of inclination between those two lines.
Non-parallax is therefore when there is no difference in apparent position when an object is viewed along two different lines of sight.
An optical pin fixed on a cork that is supported by a clamp is placed above a lens that is on the mirror as shown below. The cork is such that it slides up and down the glass rod.
Adjust height of the pin until it’s image is seen on the mirror.
The position of the pin is adjusted until the image from the mirror and the object pin seems to be moving together when you move your eyes.
Distance between lens and the pin when there is no parallax between image and object is the focal length of the lens.
Non-parallax: Using an illuminated object
A bulb is placed behind a hole with a cross wire on a cardboard so as shown in figure below. A lens on a lens holder is placed between a mirror and the cardboard.
The cardboard together with the source of light is moved along the metre rule until a sharp image of the cross wire is formed along the cross wire object as shown. The figure shows two rays emerging from the point source towards the mirror through the lens
The lengths f gives the focal length of the lens.
Explanation
The ray striking the mirror are reflected back along the same paths of the incidence so that the image of the source coincides with the source itself. This image can be received on a screen placed at the same position as the source as shown.
If both lens and the mirror are perfectly vertical or parallel , image coincides perfectly with the illuminated crosswire. This makes it hard to see when Estimating focal length.
It is therefore necessary to tilt either the lens or the mirror a little so that the image can be mapped besides the hole.
some equivalent arrangement is as shown.
In the above arrangement, the object pin is moved towards the lens or away until it coincides with it’s inverted image. This occurs when the pinhead is vertically above the center of the lens.
At a point where the object and the image perfectly coincides, there is no relative motion between them. As the eye is moved perpendicular to them, they all move together as one.
The distance between the pin and the lens is then measured as the focal length of the lense.
NB: Focal length increases as thickness of the lens decreases. This is because thick lenses refracts and deviates light more sharply than a thin lenses. Therefore, rays emerging from thick lens tends to converge earlier because because of the sharp bending in the lens.
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