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Two plane mirrors make the angle α = 46.0 ° α=46.0° between them. A ray of light incident on one of the mirrors is reflected and it hits the second mirror. Find the angle between the ray incident on the first mirror and the ray reflected off of the second mirror.

Respuesta :

Answer:

β = 88°

Explanation:

Given,

Angle between the mirror, α = 46.0 °

Let 'i' and 'r' be the angle made with mirror by incident and reflected ray respectively.

Now,

α + i + r = 180°

i + r = 180°-46°

i + r = 134°

we know, angle of incidence and angle of reflection are equal.

Let β be the required angle

β + (180°-2i) + (180°-2r) = 180°

β -2(i+r) = -180

β = -180° + 2 x 134°

β = 88°

Hence, the angle between them is equal to 88°.

Ver imagen wagonbelleville

The angle between the ray incident on the first mirror and the ray reflected off of the second mirror is 88°.

Calculation of the angle:

Since The angle between the mirror, α = 46.0 °

Now let us assume the following things:

Here i be the  angle made with mirror by the incident

And, r be the reflected ray.

Now

α + i + r = 180°

i + r = 180°-46°

i + r = 134°

Also, the  angle of incidence and angle of reflection should be equal.

So,

Let β be the required angle

Now

β + (180°-2i) + (180°-2r) = 180°

β -2(i+r) = -180

β = -180° + 2 x 134°

β = 88°

Therefore, The angle between the ray incident on the first mirror and the ray reflected off of the second mirror is 88°.

Learn more about an angle here: https://brainly.com/question/14661707

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