Question

Two plane mirrors are inclined at an angle θ. A ray of light is incident on one mirror and is then reflected from the other mirror. Then the angle between the first ray and the final ray will be

Answer 1

Answer:

Kindly refer the attachment..

Hope it helps..

Answer 2

The angle made by first ray and the final ray is ($180-2$θ).

Explanation:

From the figure below:

• AO and BO are two plane mirrors inclined at an angle θ.

• Let the incident ray from point meet the plane mirror AO first at the point A.

• MN is the normal at the point A i.e. incident point.

• Let the final reflection be from point B on the mirror BO.

• Let the two normal meet at point L.

• Law of reflection is obeyed during both the reflections and so the reflection angle and incident angle are same.

• At point A, angle made by reflected and incident ray is $x$.

• And at point B, angle made by reflected and incident ray is $y$.

• In OMLB: ∠$LMO=$∠$LBO$$=90$, because LM and LB are normal to the surface. So, ∠$MLB=180-$θ

• Now, in Δ$ABL$: $d=180-(x+180-$θ$)=$θ$-x$

• So, in Δ$MBZ$:

∠$MZB=180-2x-2($θ$-x)=180-2$θ

• So, the angle made by first ray and the final ray is ($180-2$θ).