two plane mirrors inclined at 65 degree.a ray of light incident on one mirror at angle alpha,is rendered parallel to the first mirror after two reflections.then alpha is?

Asked by gokul | 22nd Jun, 2014, 01:58: PM

Expert Answer:

Given that the two plane mirrors are inclined at angle 65°.
The ray of light is incidenting the first mirror at angle α ,and gets reflected by angle α , hence we can get that the angle B is 90-α .
This ray on striking the secong mirror undergoes a second reflection at an angle 45 - (α/2) [ i. e. (90- α) / 2 ].
From this we get that the angle C = 90 -[45 - (α/2) ]
Angle C = 45 + (α/2)
We know that the sum of the angles of a triangle = 180 °
angle A + angle B +angle C = 180 °
65° + (90- α ) + (45 + (α/2) ) =180 °
130 + 180 - 2α +90 +α =360
400 - α = 360
α = 40°

Answered by Jyothi Nair | 23rd Jun, 2014, 05:54: PM