Two plane mirrors are inclined at 70^{circ}. | vedclass

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Question

(A) Let the two mirrors be $AC$ and $AB$ inclined at an angle of $70^{\circ}$.Let the ray be incident on mirror $AC$ at point $C$ at an angle $	heta$

Vedclass · Accepted Answer

$50$

Vedclass · Answer

(A) Let the two mirrors be $AC$ and $AB$ inclined at an angle of $70^{\circ}$.Let the ray be incident on mirror $AC$ at point $C$ at an angle $	heta$ with the mirror surface.The angle of incidence with the normal is $(90^{\circ} - 	heta)$.By the law of reflection,the angle of reflection is also $(90^{\circ} - 	heta)$.Thus,the angle the reflected ray makes with the mirror $AC$ is $	heta$.In the triangle formed by the two mirrors and the reflected ray,the angle at $C$ is $	heta$.The angle at $A$ is $70^{\circ}$.The angle at $B$ (where the ray hits the second mirror) is $180^{\circ} - (70^{\circ} + 	heta) = 110^{\circ} - 	heta$.The ray is reflected from mirror $AB$ parallel to mirror $AC$. This means the angle between the reflected ray and mirror $AB$ must be equal to the angle between mirror $AC$ and mirror $AB$,which is $70^{\circ}$.Therefore,the angle of reflection at $B$ is $70^{\circ}$.The angle of incidence at $B$ is also $70^{\circ}$.In the triangle at $B$,the angle between the incident ray and the mirror $AB$ is $90^{\circ} - 70^{\circ} = 20^{\circ}$.From the geometry of the triangle $ABC$,the sum of angles is $180^{\circ}$.In triangle $ABC$,the angle at $C$ is $	heta$,the angle at $A$ is $70^{\circ}$,and the angle at $B$ is $180^{\circ} - (70^{\circ} + 	heta) = 110^{\circ} - 	heta$.Since the reflected ray is parallel to $AC$,the angle between the ray and $AB$ is $70^{\circ}$.Thus,$110^{\circ} - 	heta = 70^{\circ} + 20^{\circ} \implies 	heta = 110^{\circ} - 90^{\circ} = 20^{\circ}$ is incorrect based on the provided figure.Looking at the figure: The angle of incidence with the normal is $	heta$. The angle with the surface is $90^{\circ} - 	heta$. From the figure,the angle with the surface at $C$ is $40^{\circ}$.Thus,$	heta + 40^{\circ} = 90^{\circ} \implies 	heta = 50^{\circ}$.

Two plane mirrors are inclined at $70^{\circ}$. $A$ ray incident on one mirror at an angle $\theta$ with the surface,after reflection,falls on the second mirror and is reflected from there parallel to the first mirror. The value of $\theta$ is ......$^{\circ}$.

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