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The Human Eye and Optical Phenomena - REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF LIGHT THROUGH A PRISM

Grade 10CBSE

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

🔑Concepts

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A glass prism is a transparent object with two triangular bases and three rectangular lateral surfaces inclined at an angle.

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The Angle of Prism (AA) is the angle between the two lateral faces of the prism.

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When a ray of light enters the prism from air (rarer medium) to glass (denser medium), it bends towards the normal. When it exits from glass to air, it bends away from the normal.

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The Angle of Deviation (DD) is the angle formed between the direction of the incident ray and the direction of the emergent ray.

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Unlike a rectangular glass slab where the emergent ray is parallel to the incident ray, in a prism, the emergent ray is deviated by a certain angle due to the non-parallel faces.

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The unique shape of the prism makes the emergent ray bend towards the base of the prism.

📐Formulae

i+e=A+Di + e = A + D

Where: i=Angle of Incidence\text{Where: } i = \text{Angle of Incidence}

e=Angle of Emergencee = \text{Angle of Emergence}

A=Angle of PrismA = \text{Angle of Prism}

D=Angle of DeviationD = \text{Angle of Deviation}

n=sin⁡isin⁡rn = \frac{\sin i}{\sin r}

💡Examples

Problem 1:

A ray of light is incident on one face of an equilateral glass prism at an angle of 48∘48^\circ. If the angle of emergence is 44∘44^\circ, calculate the angle of deviation.

Solution:

A=60∘ (for an equilateral prism)A = 60^\circ \text{ (for an equilateral prism)} i=48∘i = 48^\circ e=44∘e = 44^\circ Using the formula: A+D=i+e\text{Using the formula: } A + D = i + e 60∘+D=48∘+44∘60^\circ + D = 48^\circ + 44^\circ 60∘+D=92∘60^\circ + D = 92^\circ D=92∘−60∘D = 92^\circ - 60^\circ D=32∘D = 32^\circ

Explanation:

For an equilateral prism, all internal angles are 60∘60^\circ, so A=60∘A = 60^\circ. By substituting the given values of incidence and emergence into the prism relationship formula, we find the angle of deviation to be 32∘32^\circ.

Problem 2:

In a laboratory experiment, the angle of prism is 60∘60^\circ and the angle of deviation is measured to be 38∘38^\circ. If the angle of incidence is 42∘42^\circ, find the angle of emergence.

Solution:

A=60∘A = 60^\circ D=38∘D = 38^\circ i=42∘i = 42^\circ Since i+e=A+D:\text{Since } i + e = A + D: 42∘+e=60∘+38∘42^\circ + e = 60^\circ + 38^\circ 60+3898\begin{array}{r} 60 \\ + 38 \\ \hline 98 \end{array} 42∘+e=98∘42^\circ + e = 98^\circ e=98∘−42∘e = 98^\circ - 42^\circ e=56∘e = 56^\circ

Explanation:

The relationship between the four angles (i,e,A,Di, e, A, D) allows us to find any one missing value. Here, the light emerges at an angle of 56∘56^\circ relative to the normal at the second face.

REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF LIGHT THROUGH A PRISM10.3 REFRACTION OF…