For an equilateral prism $∠ A + ∠ i = ∠ e + ∠ D$ .

True

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False

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Solution

The correct option is B False
$∠ A + ∠ D = ∠ i + ∠ e$
The total angle of deviation is the sum of the angles it is bent by at the two surfaces i.e. $θ_{1} = i - r_{1}$ and $θ_{2} = e - r_{2}$ Thus,
$δ = (i - r_{1}) + (e - r_{2}) = i + e - (r_{1} + r_{2})$
The triangle made by top of the prism and the light ray must have a total internal angle of $180^{o}$ . Thus,
$A + (90 - r_{1}) + (90 - r_{2}) = 180$ i.e. $A = r_{1} + r_{2}$
Substituting in the equation for angle of deviation $δ = i + e - A$
Therefore, $δ + A = i + e$

Suggest Corrections

Similar questions

δ = i + e - A

∠ i = a n g l e o f I n c i d e n c e

∠ e = a n g l e o f E m e r g e n c e

∠ P = a n g l e o f P r i s m

∠ D = a n g l e o f D e v i a t i o n

23^{\circ}

23^{\circ}

μ

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