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Light: Shadows and Reflections - Kaleidoscope

Grade 7CBSE

Review the key concepts, formulae, and examples before starting your quiz.

πŸ”‘Concepts

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A kaleidoscope is an optical instrument that uses the principle of multiple reflections to create beautiful, symmetrical patterns.

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The primary principle behind a kaleidoscope is the reflection of light by multiple plane mirrors inclined at an angle to each other.

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In a standard kaleidoscope, three rectangular plane mirror strips are joined together at an angle of 60∘60^\circ to each other, forming an equilateral triangular prism.

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When objects like colored glass pieces or beads are placed inside, they undergo multiple reflections, resulting in a variety of symmetrical patterns.

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A unique feature of a kaleidoscope is that you can never see the same pattern twice, as the arrangement of glass pieces changes upon rotating the device.

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The number of images (nn) formed by two mirrors depends on the angle (ΞΈ\theta) between them.

πŸ“Formulae

n=360βˆ˜ΞΈβˆ’1n = \frac{360^\circ}{\theta} - 1

ForΒ aΒ KaleidoscopeΒ whereΒ ΞΈ=60∘:n=360∘60βˆ˜βˆ’1=5\text{For a Kaleidoscope where } \theta = 60^\circ: n = \frac{360^\circ}{60^\circ} - 1 = 5

πŸ’‘Examples

Problem 1:

Calculate the number of images formed if two plane mirrors are placed at an angle of 90∘90^\circ to each other.

Solution:

Given: Angle ΞΈ=90∘\theta = 90^\circ. Using the formula: n=360∘90βˆ˜βˆ’1n = \frac{360^\circ}{90^\circ} - 1 n=4βˆ’1=3n = 4 - 1 = 3

Explanation:

When two mirrors are kept perpendicular, the multiple reflection of light creates 33 distinct images.

Problem 2:

In a standard triangular kaleidoscope, the mirrors are arranged at 60∘60^\circ. How many images of a single bead will be formed by any two mirrors?

Solution:

Given: Angle ΞΈ=60∘\theta = 60^\circ. Using the formula: n=360∘60βˆ˜βˆ’1n = \frac{360^\circ}{60^\circ} - 1 n=6βˆ’1=5n = 6 - 1 = 5

Explanation:

Because the mirrors are inclined at 60∘60^\circ, light bounces between them to form 55 images of the object, which creates the hexagonal symmetrical pattern observed in the kaleidoscope.

Problem 3:

Calculate the difference in the number of images formed when the angle between two mirrors is changed from 120∘120^\circ to 40∘40^\circ.

Solution:

  1. For ΞΈ=120∘\theta = 120^\circ: n1=360∘120βˆ˜βˆ’1=3βˆ’1=2n_1 = \frac{360^\circ}{120^\circ} - 1 = 3 - 1 = 2 2. For ΞΈ=40∘\theta = 40^\circ: n2=360∘40βˆ˜βˆ’1=9βˆ’1=8n_2 = \frac{360^\circ}{40^\circ} - 1 = 9 - 1 = 8 Calculation of difference: 8βˆ’26\begin{array}{r} 8 \\ - 2 \\ \hline 6 \end{array}

Explanation:

As the angle between the mirrors decreases, the number of images formed increases significantly.