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# Prism|Definition & Meaning

**Definition**

A **prism** is a **three-dimensional solid,** closed object **defined by** two **identical polygon-shaped ends** called **bases,** and **flat parallelogram-shaped lateral/side** faces. The **lateral faces** are also **identical** and cannot be curved. A **prism** has a **uniform cross-section** along its **entire length** and is **classified according** to the **shape** of its **bases** (e.g., triangular, rectangular, etc.).

**Conceptual Overview**

Figure 1 – Ray of light coming from square prism

**Prism** is a **term** that is often **used** in **optics** and **geometry** and has a **variety** of **applications** in science, technology, and everyday life. In **optics, prisms** are used to **refract** or **bend light** in a **specific direction.** This **property** is **based on** the **refractive index** of the **material** from which the **prism** is **made. **

The refractive index is a measure of how much a given material will bend light as it passes through it. When **light enters** a **prism,** it is **refracted,** or **bent,** as it passes through the material. This **refraction occurs** because the **light waves** are **slowed down** as they pass through the denser material of the prism.

**Formula for Prism**

There is **no specific formula** for a prism in general, as the formula for a prism depends on the specific type of prism and the information that is known about it. **However,** there are **several formulas** that can be **used** to **calculate** various **properties** of a **prism,** such as its **volume, surface area,** and **lateral** area.

Figure 2 – Volume of Prism

For the volume of a prism, you can use the formula:

**Volume** = Base Area x Height

Where **“base area”** is the **area** of **one of** the **flat, parallelogram-shaped sides** of the prism (also known as the base of the prism), and **“height”** is the **distance between** the **two bases** of the prism. The base area can be calculated using the formula for the area of the specific shape of the base (such as a rectangle for a rectangular prism or a triangle for a triangular prism).

**Properties of Prism**

There are several properties of prisms that are important to understand:

- A
**prism**is a**three-dimensional**shape with**flat, parallelogram-shaped sides**and**triangular ends.** - The
**sides**of a prism are called its**bases,**and the**distance between**the**bases**is called the**height**of the**prism.** - The
**triangular ends**of a prism are called its**lateral faces.** **Prisms**are**made**of a**transparent material,**such as**glass**or**plastic,**which allows light to pass through them.**Prisms have**a**refractive index,**which is a measure of how much they bend light as it passes through them.- Prisms can be
**used**to**refract,**or**bend, light**in a specific direction. - Prisms can
**disperse light**into its**individual colors,**a**phenomenon**known as**dispersion.** - Prisms are
**used in**the**construction**of**lenses,**windows, lasers, and other**optical devices.** - Prisms are also
**used**in**geometry, computer graphics,**and**3D modeling.** - There are several
**types**of**prisms,**including**triangular prisms, rectangular prisms,**and**pentagonal prisms.**

**Types of Prism**

There are **several types** of **prisms** that **differ based on** their **shape** and the way they refract light. Some common types of prisms include:

**Triangular Prism**

Figure 3 – Triangular Prism

This is a **three-sided prism** with **two triangular bases** and **three rectangular faces.** It is used to **refract** **light** at a **specific angle** or to **disperse light** into its **various wavelengths.**

**Rectangular Prism**

Figure 4 – Rectangular Prism

This is a **six-sided** prism with **two rectangular bases** and **four rectangular faces.** It is commonly **used** in **optical instruments** such as binoculars and telescopes.

**Pentagonal Prism**

This is a **five-sided prism** with **two pentagonal bases** and **five rectangular faces.** It is used in various applications, including **laser systems** and fiber optics.

**Hexagonal Prism**

This is a **six-sided prism** with **two hexagonal bases** and **six rectangular faces.** It is commonly used in **optical instruments** such as **telescopes** and **microscopes.**

**Octagonal Prism**

This is an **eight-sided prism** with **two octagonal bases** and **eight rectangular faces.** It is used in a variety of applications, including laser systems and **fiber optics.**

**Conical Prism**

This is a **three-dimensional shape** with a **circular base** and a **pointed top.** It is used to **refract** the **light** at a **specific angle.**

**Spherical Prism**

This is a **three-dimensional** shape with **two spherical bases** and curved faces. It is used to refract **light** in a variety of **applications,** including **telescopes** and **microscopes.**

**Regular Vs. Irregular Prism**

The **main difference** between regular and irregular prisms **is** the **shape** and **size of** their **bases.** A **regular prism** has **bases** that are **congruent,** or **identical** in **shape** and **size,** while an **irregular prism** has **bases** that are **not congruent.**

In addition to the difference in their bases, regular and irregular prisms may also differ in the following ways:

**Sides:**The**sides**of a**regular prism**are**perpendicular**to the**bases**and have**equal angles**between them, while the sides of an**irregular prism**may**not**be**perpendicular**to the bases and may have unequal angles between them.**Number of faces:**A**regular prism**always has the**same number**of**faces**as it has edges. For example, a triangular prism has three faces and three edges, while a hexagonal prism has six faces and six edges. An**irregular prism**may have a**different number**of**faces**and edges.**Symmetry: Regular prisms**have**rotational symmetry,**meaning they look the same when rotated about their axis.**Irregular prisms**may**not have rotational symmetry.****Volume:**The**volume**of a**regular prism**can be calculated using its**base area**and**height.**The volume of an**irregular prism**can be**more difficult**to calculate and may**require more complex mathematical techniques.**

**Numerical Examples**

**Example 1**

We are **given** the **triangular prism** whose **base area** is **50 **cm^{2} and whose **height** is **4cm**. **Calculate** the **volume** of the prism.

**Solution**

Base Area = 50 cm^{2}

Height = 4 cm

Volume = ?

We know that:

Volume = Base Area x Height

Volume = 50 cm^{2} * 4 cm

Volume = 200 cm^{3}

**Example 2**

We are **given** the **prism** whose **base area** is **30 **cm^{2} and the **volume** of the **prism** **120 **cm^{3}. **Calculate** the **height** of the prism.

**Solution**

Base Area = 30 cm^{2}

Volume = 120 cm^{3}

Height = ?

We know that:

Volume = base area x height

Height = $\dfrac{\text{Volume}}{\text{Base Area}}$

Height = $\dfrac{120 \text{ cm}^{3}}{30 \text{ cm}^{2}}$

**Height = 4 cm**

*All mathematical drawings and images were created with GeoGebra.*