The distance between the convex lens or a concave mirror and the focal point of a lens or mirror is called the focal length. Focal length can be positive or negative. A lens is a piece of transparent glass which concentrates or disperses light rays when passing through them by refraction. In this article, let us know how to find the focal length of a concave lens using a convex lens.
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Aim
To find the focal length of a concave lens using a convex lens.
Materials Required
- An optical bench with four upright
- A convex lens with a lens focal length
- A concave lens with a more focal length
- Two lens holders
- One thick and one thin optical needle
- A knitting needle
- A half-metre scale
Theory
We use the lens formula in this experiment to calculate the focal length of the concave lens:
Where,
- f is the focal length of the concave lens L1
- u is the distance of I from the optical centre of the lens L2
- v is the distance of I’ from the optical centre of the lens L2.
From sign convention, the f obtained from the above formula will be negative as v > u and u – v is negative.
Ray Diagram
Procedure
To determine the rough focal length of the convex lens
- Place the convex lens on the lens holder.
- Now face the lens towards a distant tree or building.
- Obtain the image either on the white wall or on a screen and keep moving the lens either forward or backwards till a sharp image is formed.
- To determine the rough focal length of the lens, measure the distance between the lens and the screen.
To set the convex lens
- Place the lens on the holder with fixed upright such that the upright is kept at 50 cm mark.
- The lens should be placed in such a way that its surface is vertical and perpendicular to the length of the optical bench.
- The upright should be kept in this position throughout.
To set the object needle
- Place the thin optical needle which is the object needle O near-zero end of the upright which is moveable.
- Place the object needle upright at a distance nearly 1.5 times the focal length of the lens.
- The tip of the needle should be horizontal to the optical centre of the lens.
- Note the position of the index mark below the object needle upright.
- To see an inverted and enlarged image of the object needle which is in the middle of the lens, close the left eye and see with a right eye open.
- On the other end of the optical bench, place the image needle on the fourth upright.
- The tip of the image needle should be in line with the image that is seen with the right eye.
- To see the parallax, move the eye towards the right. The image needle and object needle are no longer in line.
- Remove the parallax tip to tip.
- Note the position of the index mark at the base of the image needle upright.
- Record the position of the index marks.
- Now place the concave lens holder on the I side of the convex lens.
- The upright and convex lens should be placed at a distance from each other.
- The concave lens should be placed such that it coincides with the principal axes.
To set the image needle at I’
- Repeat steps 4 and 5.
To get more observations
- Repeat the experiment by moving the object needle towards the lens by 2cm.
- Repeat the experiment by moving the object needle away from the lens by 2cm.
- Record all the observations.
Observations
The rough focal length of a convex lens = ……….
The actual length of the knitting needle, x = ………
Observed distance between the concave lens and image = ……..
Needle when knitting needle is placed between them, y = ……..
Index correction for u as well as v, x – y = ……..
Table for u, v and f
| Sl. no | Position of | Observed | Corrected | \(\begin{array}{l}f=\frac{uv}{u-v}\end{array} \) in cm |
||||||
| O in cm | L1 at O1 in cm | I in cm | L2 at O2 in cm | I’ in cm | u = IO2 in cm | v = I’O2 in cm | u in cm | v in cm | ||
| 1. | f1= | |||||||||
| 2. | f2= | |||||||||
| 3. | f3= | |||||||||
Calculations
- To find observed u by finding the difference of position of L2 and I.
- To find observed v by finding the difference of position of L2 and I’.
- Corrected values of u and v are obtained by applying index correction.
- Calculate \(\begin{array}{l}f=\frac{uv}{u-v}\end{array} \).
- Finding the mean of f
Result
The focal length of the given concave lens = …….. cm.
Precautions
- The lens must be clean.
- The focal length of the convex lens should be lesser than the concave lens.
- For u and v index correction should be applied.
- To obtain a real and inverted image, the needle should be kept at a certain distance.
- To avoid parallax, a distance of at least 30 cm should be maintained between the tip of the needle and eye.
Sources of Error
- Vertical uprights might not be used.
- The removal of parallax might not be perfect.
Viva Questions
Q1. What is a spherical lens?
Ans: Spherical lens is defined as a lens that is part of a sphere and has a surface that is spherical.
Q2. What type of lens is present in the human eye?
Ans: Convex lens is present in human eye.
Q3. What are the factors affecting the power of lens?
Ans: Following are the factors affecting the power of lens:
- Refractive index of the material used in the lens.
- The change in medium.
- The radius of curvature.
- The wavelength of the light.
- The thickness of the lens.
Q4. What is the focal length of a lens?
Ans: The focal length of a lens is defined as the distance between the optical centre and the principal focus of the lens.
Q5. What are the use of lens?
Ans: Lenses are used in spectacles, microscopes, in optical instruments, and in telescopes.
Stay tuned with BYJU’S to learn more about other Physics-related experiments.
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