CBSE Class 12 · 2017 · Delhi · Geometrical OpticsShort Answer

(i) A ray of light incident on face

A B

of an equilateral glass prism shows a minimum deviation of

3 0^{\circ}

. Calculate the speed of light through the prism.
(ii) Find the angle of incidence at face

A B

so that the emergent ray grazes along the face

A C

Solution

(i) Equilateral prism

A = 6 0^{\circ}

δ_{m} = 3 0^{\circ}

μ = \frac{sin ( \frac{A + δ _{m}}{2} )}{sin ( \frac{A}{2} )} = \frac{sin 4 5 ^{\circ}}{sin 3 0 ^{\circ}} = 2, v = \frac{c}{μ} = \frac{3 \times 1 0 ^{8}}{2} = 2.12 \times 1 0^{8} m s^{- 1}

(ii) For the emergent ray to graze

A C

e = 9 0^{\circ}

, so

r_{2} = θ_{c} = sin^{- 1} \frac{1}{2} = 4 5^{\circ}

. Then

r_{1} = A - r_{2} = 6 0^{\circ} - 4 5^{\circ} = 1 5^{\circ}

, and

sin i = μ sin r_{1} = 2 sin 1 5^{\circ} \Rightarrow i = sin^{- 1} (2 sin 1 5^{\circ}) \approx 21. 5^{\circ}

CBSE Class 12 Board · 2017 · Delhi · Subjective