## To Find Focal Length of Convex Lens

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

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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.’

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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.

**1. What are thin lenses? **

A thin lens is a lens bearing a negligible thickness. The thickness is the distance along the optical axis between the two surfaces of the concave/convex lens that can be negligible when compared to the radii of curvature of the lens surfaces, i.e., the thickness of the lens, d, is appreciably lesser than the radii of curvature of its surfaces (R1 and R2), i.e., d ≪ |R1| and d ≪ |R2|. Here, |R1| or |R2| denotes the absolute values of the radius of curvature of the lenses.

**2. Do you think a double-convex lens has a more focal length if the radii of curvature increase for the same index of refraction?” **

In the case of a double-convex lens, the focal length, f is related with the index of refraction, n, and the radii of curvature of both the surfaces, R1 and R2 with the following equation: 1/f = (n-1) *{(1/R1) + (1/R2)}. If the radii of curvature, R1, R2 increases, 1/R1 or 1/R2 will decrease and the overall inverse of the expression {(1/R1) + (1/R2)} will increase, hence the focal length, f, will be more. This equation is also called the Lens-maker's equation.

**3. What is a concave lens and how do you find its focal length? **

A concave lens forms an image that is virtual, erect, and diminished.

When light rays pass through the lens, they diverge. The diverged beam is then traced back which produces a virtual, erect image on the same side of the incident beam. The focal length of a concave lens can be found out using a convex lens with the help of the following two methods – (a) A Lens in contact method, and (b) Lens Out of Contact method. In case of the method, (b), we must conduct a series of trials and average out the focal length of the concave lens.

**4. What is focal length? **

For a convex or concave lens, the focus is a point where the majority of light rays passing through the lens would meet or appear to meet to form a real and inverted or virtual and erect image of the object, respectively. This focus is located on an imaginary line called the principal axis that passes through the center of the lens. The distance between the focus and the optical center of a lens is called the focal length.

**5. How many foci are there in a biconvex/biconcave lens? **

A biconvex/biconcave lens always has two foci on each side of the principal axis. Each of the curved surfaces of the biconvex/biconcave lenses allows light to pass through them. Therefore, each curved surface of the lenses will have a focus on either side. The case of a lens, which has only one focus on one side is called a plano-convex or plano-concave lens.

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