Prove the following statements.a. If the angle of incidence and angle

1.	Prove the following statements.a. If the angle of incidence and angle ofemergence of a light ray falling on aglass slab are i and e respectively, provethat, i e.
Answer» Assume ABCD to be the glass plate with sides AB parallel to CD. Let the refractive index of air and glass be n1and n2. Consider a ray of light EF incident on surface AB of the glass slab with angle of incidence,∠i.The light ray is refracted into the glass slab along the path FG and towards the normal, NN’ .∠r1is the angle of refraction.The light ray is refracted out of the glass slab at the surface CD along the path GH. The angle of incidence at this surface is∠r2. The light ray emerges out of the slab forming∠e as angle of emergence. The surfaces AB and CD are parallel and FG is the transversal,Therefore,∠r1=∠r1 Applying Snell’s Law at the surface AB,sinisinr1=n2n1.......(1)Similarly, at surface CD, according to Snell’s Lawsinr2sine=n1n2.......(2)Multiplying equation 1 and 2, sinisinr1×sinr2sine=n2n1×n1n2sinisinr1×sinr2sine=1 As AB is parallel to CD, the perpendiculars to the AB and CD, NN’ and MM’ are also parallelTherefore, alternate interior angles, r1and r2are congruent i.e.r1=r2Hence,sinisinr1×sinr1sine=1sinisine=1Therefore,sini=sineor,i=e Hence, angle of incidence equals angle of emergence.

Prove the following statements.a. If the angle of incidence and angle ofemergence of a light ray falling on aglass slab are i and e respectively, provethat, i e.

Answer»

Assume ABCD to be the glass plate with sides AB parallel to CD.

Let the refractive index of air and glass be n1and n2.

Consider a ray of light EF incident on surface AB of the glass slab with angle of incidence,∠i.The light ray is refracted into the glass slab along the path FG and towards the normal, NN’ .∠r1is the angle of refraction.The light ray is refracted out of the glass slab at the surface CD along the path GH. The angle of incidence at this surface is∠r2.

The light ray emerges out of the slab forming∠e as angle of emergence.

The surfaces AB and CD are parallel and FG is the transversal,Therefore,∠r1=∠r1

Applying Snell’s Law at the surface AB,sinisinr1=n2n1.......(1)Similarly, at surface CD, according to Snell’s Lawsinr2sine=n1n2.......(2)Multiplying equation 1 and 2,

sinisinr1×sinr2sine=n2n1×n1n2sinisinr1×sinr2sine=1

As AB is parallel to CD, the perpendiculars to the AB and CD, NN’ and MM’ are also parallelTherefore, alternate interior angles, r1and r2are congruent i.e.r1=r2Hence,sinisinr1×sinr1sine=1sinisine=1Therefore,sini=sineor,i=e

Hence, angle of incidence equals angle of emergence.

Prove the following statements.a. If the angle of incidence and angle ofemergence of a light ray falling on aglass slab are i and e respectively, provethat, i e.

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