The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors a → , b → a n d c → respectively. Then choose the correct relation for these vectors.

r ^ − i ^ = 2 c o s θ n ^ . . . . . . ( 1 ) ⇒ r ^ = i ^ − 2 ( i ^ . n ^ ) n ^ ⇒ b → = a → − 2 ( a → . c → ) c →

The incident ray, reflected ray and the outward drawn normal are denoted by the unit vectors $\vec{a}, \vec{b} a n d \vec{c}$ respectively. Then choose the correct relation for these vectors.

Option 1 - <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>−</mo> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> </mrow> </math>

Option 2 - <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>+</mo> <mn>2</mn> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> </mrow> </math>

Option 3 - <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mn>2</mn> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>+</mo> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> </mrow> </math>

Option 4 - <math> <mrow> <mover accent="true"> <mi>b</mi> <mo>→</mo> </mover> <mo>=</mo> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mo>−</mo> <mn>2</mn> <mrow> <mo>(</mo> <mrow> <mover accent="true"> <mi>a</mi> <mo>→</mo> </mover> <mtext> </mtext> <mo>.</mo> <mtext> </mtext> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> </mrow> <mo>)</mo> </mrow> <mover accent="true"> <mi>c</mi> <mo>→</mo> </mover> </mrow> </math>

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Alok Kumar Singh | Contributor-Level 10

4 months ago

Correct Option - 4

Detailed Solution:

$\hat{r} - \hat{i} = 2 c o s θ \hat{n} . . . . . . (1)$