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Prism

A prism is a polyhedron with two identical polygonal bases and flat sides, categorized into right, oblique, and regular types. The volume and surface area of prisms can be calculated using specific formulas, and prisms also play a significant role in optics, such as in cameras and binoculars. Key properties include faces, edges, vertices, and the ability to create identical cross-sections when sliced parallel to the base.

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78 views12 pages

Prism

A prism is a polyhedron with two identical polygonal bases and flat sides, categorized into right, oblique, and regular types. The volume and surface area of prisms can be calculated using specific formulas, and prisms also play a significant role in optics, such as in cameras and binoculars. Key properties include faces, edges, vertices, and the ability to create identical cross-sections when sliced parallel to the base.

Uploaded by

athrvakaranjikar
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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INTRODUCTION

Introduction to Prisms

Triangular prism

Rectangular prism
Hexagonal prism

What is a prism?

A prism is a polyhedron with two identical bases and


flat sides. The bases are polygons (triangles, squares,
pentagons, etc.), and the sides are parallelograms.
Prisms are named after the shape of their base (e.g.,
triangular prism, square prism).
Types of prisms:

* Right prisms: Sides perpendicular to bases.

* Oblique prisms: Sides not perpendicular to bases.


* Regular prisms: Bases are regular polygons

* Real-world examples: Optical prisms (cameras,


binoculars), decorative crystal prisms, some building
designs.
Properties of Prisms

* Faces: Two bases + rectangular sides (number of


sides = number of base sides).

* Edges: Lines where faces meet.

* Vertices: Points where edges meet.

* Cross-sections: Slicing parallel to the base creates


an identical cross-section
Volume of Prisms

* Formula: Volume = Area of base × Height

* Explanation: Find the base's area, multiply by the


prism's height (perpendicular distance between bases).

* Examples:

* Triangular prism: Base area 10 cm², height 5 cm.


Volume = 10 cm² × 5 cm = 50 cm³

* Cube: Side 4 cm. Volume = 4 cm × 4 cm × 4 cm =


64 cm³
Surface Area of Prisms

* Formula: Surface Area = Lateral Area + 2 × Base


Area

* Explanation:
* Lateral Area: Sum of rectangular side areas.

* Base Area: Area of one base.

* Example:

* Rectangular prism: 3 cm, 4 cm, 5 cm. Surface Area =


2(3×4 + 3×5 + 4×5) = 94 cm²
Prisms and Light

Refraction

* Refraction: Light bends as it passes from one


medium to another (e.g., air to glass). The angle of
bending depends on the angle of incidence and the
refractive indices of the materials.

* Dispersion: White light separates into colors


because each color bends slightly differently.
Types of Optical Prisms

* Triangular prisms:

Dispersion and reflection

* Right-angle prisms:

Total internal reflection (used in binoculars,


cameras).

* Dispersion prisms:

Maximize color separation


Applications in Technology

* Cameras: Direct light to the image sensor.

* Binoculars: Invert and magnify the image.


* Spectrometers: Separate light into wavelengths
for analysis.

* Fiber optics: Internal reflection within optical


fibers.

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