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Q.

Two plane mirrors are inclined at 70°. A ray incident on one mirror at angle θ,, after reflection falls on the second mirror and is reflected from there parallel to the first mirror. The value of θ.



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a

 45°

b

 30°

c

 55°

d

 50° 

answer is D.

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Detailed Solution

Concept: Let M1and M2 be the mirror inclined at an angle θ with the plane AM.Now a ray of light PQ is incident at an angle θθ on the plane mirror M. We know Snell’s law states that when a light is incident on a plane mirror at an angle θthen the light will be reflected by making an angle θθ. Hence, we can say QR the reflected ray will also make an angle θθ as shown in the following figure.
Now let’s draw a line XY normal to the mirror AB, therefore we can say
∠PQX=∠RQX
Question Image
From the above figure, since the angle ∠RQM2 is 70° , then the angle ∠RQx=90-70=20°
. Since the angle ∠RQx=20° 
The angle ∠PQx
 is also 20°
. Therefore, the angle ∠AQP=90−20=70°
As we well know the total internal angle of a triangle is equal to 180° . Therefore, the total angle inΔAQP
 is,
70°+70°+90°-θ=180°
By simplifying, we get,
θ=50∘
Hence, option 4 is correct.
 
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