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# Concave|Definition & Meaning

## Definition

Concave is defined as a shape that has an **inward curve**. Any shape with an **internal angle** greater than **180°** has a concave surface. It has the word “**cave**” that tells that a** concave** shape will be like the entrance of a cave.

For example, in a **hexagon**, if any two sides are **curved inwards**, then it is called a **concave** hexagon. **Figure 1** shows a regular hexagon and a concave hexagon.

## Lens

A lens is defined as a** transparent** optical device that is used to **refract** light rays. They focus at a point to form an image of an object.

There are two types of lenses; **simple** and **compound** lenses.

A **concave** lens is a **simple** lens as it only consists of a **single** lens whereas a compound lens consists of more than one lens in its geometry.

## Concave Lens

A concave lens has a **thin** **middle** area and is **thicker** in the **outer** edges. **Figure** **2** shows a concave lens.

It refracts light rays to **disperse** them in all directions. It has a variety of **uses** including the treatment of **myopia** that is shortsightedness.

## A Diverging Lens

The **concave lens** is also known as the diverging lens. This is because it **diverges** the light rays that are **refracted** through it.

**Figure 3** shows light rays passing through the concave lens.

In **figure 3**, **F** is the concave lens’s **focal point** or focus. It is the point where all the light rays **coincide** when **traced** backward. Thus, the concave lens **focuses** the light rays at point **F**.

The **principle axis** is the axis that passes through the focal point and the **optical center** of the concave lens.

## Image Formed by a Concave Lens

The **image** of the object formed by the concave lens is **real** or **virtual**(diminished) and **erect**(upright). **Figure 4** shows a virtual image formed by a **concave** lens.

The image is formed between the **focal point F** and the **optical center C** of the concave lens.

The image is **upright** and inward. It is also virtual or **diminished**, meaning the image appears** smaller** than the object’s size.

## Focal Length of a Concave Lens

The **distance** from the **center** to the **focal point F** of a lens is called the focal length denoted by “**f**”.

It can be calculated by using the **formula** given below:

\[ \frac{1}{f} = \frac{1}{i} \ – \ \frac{1}{o} \]

Where **i** and **o **are the distances of the **image** and **object **respectively from the **center** of the lens.

**Figure 5** shows the **focal length**, object distance, and image distance when light rays are **refracted** through the concave lens.

The concave lens’s focal length is always **negative** by sign convention. It is because the concave lens **diverges** the light rays. It is on the lens’s** left** side, which also makes it negative.

That is why it is also called a **negative lens**.

## Magnification

Magnification is the ability to **enlarge** the object’s **apparent size** from its original size. It is calculated by using a **ratio** thus magnification has** no units**.

A magnification of **one** means that the object’s size and the image size are the **same**.

A magnification number **greater** than **one** means that the image is **enlarged** and a magnification **less** than **one** means that the image is diminished or **de-magnified**.

A **concave** lens always has a magnification of **less than one**. This is because the image formed is always **smaller** than the object’s size.

Magnification can be calculated by using the **formula** given below:

\[ m = \frac{ h_{i} }{ h_{o} } \]

Where,

$h_i$ = height of the **image**

$h_o$ = height of the **object**.

Height is the **vertical** distance. Another **formula** for magnification is:

\[ m = \frac{i}{o} \]

Where **i** is the **image** distance and** o** is the **object** distance.

## Applications

There are many applications of concave lenses one of which the most common are **eyeglasses** for **myopia** correction.

The eyeball with myopia is **elongated** which can’t **focus** light from far away objects. The **concave** lens diverges the light rays coming to the **eyeball** which helps it make a **clearer** image of **distant** objects.

**Concave** lenses are also **used** in binoculars, compound microscopes, cameras, spy holes, mobile phones, telescopes, and flashlights.

## Types of Concave Lens

Different **variations** and additions to concave lenses produce the following types.

### Plano-concave Lens

A Plano-concave lens has a **plane** surface on one side and a **concave** surface on the other. It has a **negative** focal length like the concave lens.

### Biconcave Lens

A biconcave lens is a **compound** lens and has **two** concave lenses joined together. Both lenses have the **same** optical center.

### Convexo-concave Lens

A Convexo-concave lens has one **concave** surface and one **convex** surface. The concave side is more **curved** as compared to the convex side.

**Figure 6** shows these three lenses.

## A Solved Problem Involving a Concave Lens

A **concave** lens forms an image at **7 cm** from the optical center. It has a focal length of **14 cm**. Find the distance of the **object** from the lens. Also, calculate the magnification.

### Solution

The formula for** focal length** is:

\[ \frac{1}{f} = \frac{1}{i} \ – \ \frac{1}{o} \]

The **focal length **and the **image distance** of a concave lens will be **negative** as it is on the **left** of the lens. So, the given values are:

**f = -14 cm , i = -7 cm**

Calculating the **object distance** **o**, the formula becomes:

\[ \frac{1}{o} = \frac{1}{i} \ – \ \frac{1}{f} \]

Putting the values gives:

\[ \frac{1}{o} = \frac{1}{-7} \ – \ \frac{1}{-14} \]

\[ \frac{1}{o} = – \frac{1}{7} + \frac{1}{14} \]

\[ \frac{1}{o} = \frac{ – 2 + 1 }{14} \]

\[ \frac{1}{o} = \frac{ -1 }{14} \]

\[ o = – \ 14 \]

So, the object distance is **14 cm**. The negative sign indicates that the **image** formed was **virtual**.

The **magnification** is calculated as follows:

\[ m = \frac{i}{o} \]

\[ m = \frac{-7}{-14} \]

\[ m = \frac{1}{2} \]

So, the magnification is **0.5**.

*All the images are created using GeoGebra.*