To find the Focal Length of a Concave Lens using a Convex Lens

Focal length of a concave lens can be found using a convex lens by following a simple experimental procedure. Lenses are optical tools that have the ability to converge or diverge a beam of light through the process of refraction. A concave lens is a lens that is thicker around the edges while the convex lens is the one with thick centers. A convex lens is also called a converging lens while a concave lens is known as a diverging lens due to its ability to converge and diverge light respectively. The bending of light involves the concept of refraction. To find the Focal Length of a Concave Lens using a Convex Lens, we use the focal length formula.

Key Takeaways: Focus, Focal length, Lens, Convex lens, Concave lens, Image formation, Refraction, Light

What is focus and focal length?

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Focus: The focus of a lens is the point or plane at which the beam of light coming from infinity converges when it passes from the given lens.

Focal Length: The distance of the focus from the center of the length is called the focal length of the lens. 

Aim of the Experiment

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The aim of the experiment conducted is to find the focal length of a concave lens using a convex lens. 

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Material Required 

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The materials required to find the focal length of a concave lens using a convex lens are as follows:

1. Optical bench with 4 uprights
2. Convex lens
3. 2 lens holders
4. A concave lens with a higher focal length
5. Thick and thin optical needle
6. Knitting needle
7. Half-meter scale

Theory 

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To calculate the focal length of the concave lens in the experiment, we use the following formula:

The formula for focal length: f = \( {uv\over u - v}\)

Where:

f: focal length of the concave lens L1

u: distance between I and optical center of the lens L2

v: distance between I’ and the optical center of the lens L2

From sign convention, the focal length (f) we obtain from the above formula will be negative as we know that v > u and therefore u – v is negative.

Ray Diagram

The ray diagram for the calculation of the focal length of the concave lens using a convex lens experimental procedure is given below.

Procedure

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The following steps can be followed – 

For determining the rough focal length of the convex lens

1. Put the convex lens in the lens folder.
2. Face it towards any distant object like a tree or a building.
3. Obtain a clear image on the white wall or on a screen by moving the lens forward or backward until the image formed is sharp.
4. Measure the distance between the lens and screen to determine the rough focal length of the convex lens.

For setting the convex lens

1. Put the lens on the folder using the fixed upright in a way that the upright is placed at a 50 cm mark.
2. See that the surface of the lens is vertical and perpendicular to the length of the optical bench.
3. The upright should be placed in this position all throughout the experiment.

For setting the object needle

1. Put the thin object needle (object needle) near the zero-end of the upright.
2. It should be kept at a distance of about 1.5 times that of the focal length of the lens.
3. The tip of the needle should be kept horizontal to the optical center.
4. Mark the position of the index below the object needle upright.
5. With your right eye open and left eye closed, see an enlarged and inverted image of the needle that is in the middle of the lens.
6. Place the image needle on the fourth upright at the other end of the optical bench.
7. See that the tip of the needle is in line with the image seen with the right eye.
8. Remove parallax if required by moving your eye towards the right side.
9. Note the positions of index marks at the base of the upright image needle.
10. Place the concave lens holder at the I side of the convex lens used.
11. Place the concave lens in a way that it coincides with the principal axis.

To see the image needle at I’

1. Repeat steps 3 and 4 for setting up the image needle at I’.

For getting more observations

1. Repeat the same experiment as you move the object needle towards the lens by 2 cm.
2. Repeat the same experiment as you move the object needle away from the lens by 2 cm.
3. Record all the observations.

Observations

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The rough focal length of the convex lens used: ____

The true length of the knitting needle x: ____

Observed distance between concave lens and image: ____

Needle when knitting needle is placed between them, y: ____

Index correction for u and v, i.e. x – y: ____

To find the focal length of a concave lens using a convex lens observation table is as given below:

Calculations 

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Fill the table with all the necessary information.

Calculate f = \( {uv\over u - v}\)

Mean f = \( {f1 + f2 + f3\over 3}\)

Result of the Experiment

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The focal length of the concave lens is found to be: ___ cm.

Precautions

• The lenses of the mirror must be clean.
• The focal length of the concave lens must be more than that of the convex lens.
• There must be an application of the correction of u and v index
• The needle should be placed at such a distance so that the resulting image can be obtained as real and inverted
• There should be a minimum distance of 30 cm between the needle’s tip and eye in order to avoid parallax.

Things to Remember

1. To find the focal length of a concave lens using a convex lens we can use the focal length formula.
2. There might be an absence in the use of vertical uprights.
3. The removal of parallax might be imperfect. 
4. The focal length of the convex lens that is taken should be less than that of the concave lens.
5. A concave lens always forms a virtual image.
6. This is why the focal length of this lens cannot be found directly.

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