# To Find Focal Length of Concave Lens Using Convex lens

## To Find Focal Length of Convex Lens

The focal length of convex lens is the distance between the centre 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 focal length of 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:

1. A lens in contact method, and

2. A lens out of contact method.

### Theory Part:

A concave lens is thinner than at its centre 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 concave lens using a convex lens. Also, there are two methods of finding the focal length of concave lens:

1. 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

1. 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.’

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 focal length of 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 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:

 S.No. Distance Between the Combination of Lenses Focal length Object ‘u’ cm Image ‘v’ cm (uv)/(u + v) cm 1. 2. 3. 4. 5.

### Calculations:

1. The focal length of the combination lens  ‘F’ is:.......cm.

2. To obtain the focal length of a convex lens fb, we get the values as …..cm.

3. Now, we get the focal length of the given concave lens as;

fa = (F X fb)/ (fb - F) cm = …….cm.

Q1: What are Thin Lenses?

Ans: A thin lens is a lens bearing a thickness. The thickness is the distance along the optical axis between the two surfaces of the concave/convex lens that remains negligible (zero) when compared to the radii of curvature of the lens surfaces, i.e,  the thickness of the lens is very less than the radii of curvature of its surfaces, i.e., d ≪ |R 1| and d ≪ |R 2|.

Q2: Do You Think a Convex Lens Has More Focal Length?

Ans: The incident ray makes small angles with the surface of the lens on the principal axis. One must note that a convex lens has a less focal length, a concave lens has more focal length.

A convex lens is thick in the middle and thinner at its edges.

A convex lens has a fixed point inside the lens on its principal axis through which light rays pass undiverted.

Q3: What is a Concave Lens and How Do You Find its Focal Length?

Ans: A concave lens forms an image of nature: virtual, erect, and diminished. An image formed by a convex lens is real and inverted and on bringing the object near the convex lens, the size of the image increases subsequently.

For finding the focal length of a concave lens using a convex lens. We use an optical bench with four uprights, and they are as follows:

1. Two uprights fixed in the middle.

2. Two outer uprights with a lateral movement.