The Double$-$Reflected Light Ray

Two mirrors make an angle of $125$ with each other as illustrated in the figure. A ray is incident on mirror $M_1$ at an angle of $62$ to the normal. Find the direction of the ray after it is reflected from mirror $M_2.$

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$(1)$

SOLUTION mirror. In the figure, which mirror is horizontal?

Mirror $M_1$ is horizontal.

Mirror $M_2$ is horizontal.

Categorize Because the interactions with both mirrors are simple reflections, we apply the wave under $-$ Select $-$hat$(**)$ model and some geometry.

Analyze from the law of reflection, the first reflected ray makes an angle $($in degrees$)$ of $-$ with the normal.

Find the angle $($in degrees$)$ the first reflected ray makes with the horizontal:

$=$

From the triangle made by the first reflected ray and the two mirrors, find the angle $($in degrees$)$ the reflected ray makes with $M_2$ :

$y=$

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Find the angle $($in degrees$)$ the first reflected ray makes with $M_2$ :

${}_{M2}=$

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From the law of reflection, find the angle $($in degrees$)$ the second reflected ray makes with the normal to $M_2$ :

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EXERCISE mirrors is $52,$ what is ${}_{\text{i}\text{n}\text{c}}($in degrees$)?$

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