Step-by-Step Method to Determine Concave Lens Focal Length
The focal length of a convex lens is the distance between the center of a lens and its focus. The focal length of an optical instrument/object is a measure of how strongly/sharply the system converges/diverges light and it is just the inverse of the optical power of the system.
The focal length of convex lens formula is object distance multiplied by the image distance divided by the difference of the object distance and the image distance.
Here, we will discuss how to find the focal length of a convex lens, perform the convex lens experiment Class 12 to obtain the focal length of a convex lens.
To find the Focal Length of a Concave Lens using Convex Lens
Now, we will understand the procedure to find the focal length of a concave lens using convex lens:
Aim:
To determine or To find the focal length of a concave lens using convex lens by using the following two methods:
A lens in contact method, and
A lens out of contact method.
Theory Part:
A concave lens is thinner at its center than its edges as compared to a convex lens. So, when the white light passes through the concave lens, it spreads in all directions and this is the reason we call the concave lens a diverging lens.
The nature of the image formation in the concave lens is virtual and diminished.
Now, we know that the image formation is diminished so it becomes difficult to find its focal length. That’s why we are performing an experiment to find the focal length of a concave lens using a convex lens. Also, there are two methods of finding the focal length of concave lens:
A Lens in Contact Method
When a concave lens of focal length fb is placed on the common axis (coaxially) in contact with the convex lens of focal length fa, then the focal length ‘F’ of the combination is:
1/F = 1/fa + 1/fa
Therefore, a formula for focal length of concave lens is:
fa = (F X fa)/ (fa - F) cm
(Image will be uploaded soon)
A Lens Out of Contact Method
Materials required:
Shining wire gauge
Lens stand
Meter scale
Screen
A convex lens of shorter focal length
A concave lens
Theory Part
The real image ( i1) formed by the convex lens works as a virtual object for the concave lens. When a concave lens is interposed/affixed between the convex lens and the real image i1, a new real image forms which is ‘i2.’
(Image will be uploaded soon)
If ‘u’ is the distance of the concave lens from the real image i1, and v is the distance from the real image i2, then the focal length of the concave lens is:
1/f = 1/v - 1/u (We call this the focal length of convex lens formula)
And,
f = (uv)/(u-v)
This is the formula for focal length of concave lens which states that the focal length is the product of the image distance and the object distance divided by the difference in the object and the image distance.
Convex Lens Experiment Class 12
Keep the given concave lens of focal length in contact with the convex lens of focal length f. This forms a combination of two thin lenses in contact.
Make sure that the arrangement of lenses is between the shining wire gauge and the screen at a fixed distance from the gauze, which is ‘u’ cm.
The screen is adjusted in a manner to obtain a clear image of the wire gauge on it.
Measure the distance of the combination of lenses in contact from the screen, which is ‘v’ distance.
Now, to obtain the focal length of the combination lens, we have the following:
F = (uv)/(u + v) cm
From this formula, we get the way to find the focal length of a convex lens/find focal length of a convex lens.
Keep on repeating the above experiment by positioning the combination of thin lenses at various distances from the shining wire gauge.
Now, we will calculate the mean value of F, as we have done so many Convex Lens Experiment Class 12.
By using the value of the focal length of concave lens, fa, and the focal length of the combination, i.e., F, we can obtain the formula for focal length of concave lens and then find the focal length of concave lens:
fa = (F X fb)/ (fb - F) cm
Now, let’s record our observations for future reference:
Calculations
The focal length of the combination lens ‘F’ is:.......cm.
To obtain the focal length of a convex lens fb, we get the values as …..cm.
Now, we get the focal length of the given concave lens as;
fa = (F X fb)/ (fb - F) cm = …….cm.
Why study this Topic?
This topic is an essential experiment that is asked in a practical exam. This experiment in ray optics enables a student to identify how to focus lenses for better image and also informs best practices in the study of lenses. This experiment also enables a student to draw a graphical representation of the observations made.
How to Prepare for this Topic ?
To prepare for this topic, one would need to login to vedantu or download vedantu app. In Vedantu the student will find study material for practical exam preparation and revision questions needed to ace all kinds of viva questions.
FAQs on How to Find the Focal Length of a Concave Lens Using a Convex Lens
1. What is the primary purpose of using a convex lens to find the focal length of a concave lens?
A concave lens is a diverging lens, meaning it spreads out light rays and forms a virtual image that cannot be captured on a screen. The primary purpose of using a convex lens, which is a converging lens, is to first form a real image. This real image can then act as a virtual object for the concave lens, allowing us to calculate its focal length indirectly by measuring the final image position.
2. What are the two main methods used in the experiment to find the focal length of a concave lens with a convex lens?
The two principal methods taught in the CBSE syllabus for this experiment are:
- Lens in Contact Method: The concave lens is placed in direct contact with the convex lens, and they are treated as a single combination lens system. The focal length of the combination is found first, which is then used to calculate the focal length of the concave lens.
- Lens Out of Contact Method: The convex lens forms a real image of an object. The concave lens is then placed between the convex lens and this image. The final image position is shifted, and this shift is used to determine the concave lens's focal length.
3. What is the formula for the effective focal length (F) when a convex lens (f₁) and a concave lens (f₂) are placed in contact?
When two thin lenses are placed in contact, their combined power is the sum of their individual powers. This translates to the following formula for the combination's focal length (F):
1/F = 1/f₁ + 1/f₂
Here, f₁ is the focal length of the convex lens (positive) and f₂ is the focal length of the concave lens (negative). By first measuring the focal length of the convex lens (f₁) and then the combination (F), we can rearrange the formula to find the focal length of the concave lens (f₂).
4. Why is it not possible to find the focal length of a concave lens directly by forming an image on a screen?
It is not possible because a concave lens always forms a virtual, erect, and diminished image of a real object. Virtual images are formed where light rays appear to diverge from; they cannot be projected or focused onto a physical screen. To measure focal length, we need to form a real image, which is why a converging (convex) lens is required as an auxiliary lens in this experiment.
5. In this experiment, what role does the real image formed by the convex lens play for the concave lens in the 'lens out of contact' method?
In the 'lens out of contact' method, the real image formed by the convex lens acts as a virtual object for the concave lens. When the concave lens is placed in the path of the converging rays before they form the image, it intercepts them. For the concave lens, these converging rays are treated as if they are coming from a virtual object located at the point where the convex lens would have formed its image.
6. According to standard sign conventions, is the focal length for a concave lens considered positive or negative?
According to the Cartesian sign convention used in optics, the focal length of a concave lens is always negative. This is because its principal focus is on the same side of the lens from which light is incident, and distances measured against the direction of incident light are taken as negative. Conversely, the focal length of a convex lens is positive.
7. What are some common sources of error in this experiment, and what precautions should a student take to minimise them?
Common sources of error include:
- Parallax Error: Incorrectly judging when the image and the object needle are at the same position. This can be minimised by ensuring the tip of the image and the object needle move together without any relative shift when the eye is moved side-to-side.
- Measurement Errors: Inaccuracies in reading the positions on the optical bench. Taking multiple readings and calculating the mean helps reduce this.
- Lens Alignment: The principal axes of the lenses and the object/image needles may not be perfectly aligned. Ensure all components are at the same height and centred on the optical bench.
- Thick Lens: The formulas used are for thin lenses. Using a lens that is too thick can introduce errors.
8. What do the points 'F' and '2F' signify for a lens, and why are they important in ray optics experiments?
For a lens, these points are crucial references:
- F (Principal Focus): This is the point on the principal axis where parallel rays of light converge (for a convex lens) or appear to diverge from (for a concave lens) after passing through the lens. Its distance from the optical centre is the focal length.
- 2F (Centre of Curvature for spherical mirrors, but for lenses, it's twice the focal length): For a thin lens, 2F represents the point that is at a distance of twice the focal length from the optical centre. It is significant because placing an object at 2F of a convex lens results in a real, inverted image of the same size formed at 2F on the other side. These points are essential for predicting image characteristics and setting up optics experiments accurately.
