Question

A ray of light impinges on a mirror as shown in the figure. A second mirror is fastened at 90? to the first.

Part A

After striking both mirrors, at what angle relative to the incoming ray does the outgoing ray emerge? (Figure 1)

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Part B

What is the answer if the incoming angle is 30??

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Answer 1

Concepts and reason

The concept used to solve this problem is the law of reflection.

Use the law of reflection to find the angle of the outgoing ray after striking both mirrors. Then, find at what angle relative to the incoming ray the outgoing ray emerges.

Fundamentals

The reflection of light ray from the smooth surface like mirror is governed by the law of reflection.

The law of reflection states that

• The incident ray, reflected ray, and the normal line on the surface of the mirror lie in the same plane.

• The angle of reflection and angle of incidence are equal.

The incident angle and refracted angle are measured with respect to the normal line on the mirror.

(A)

The figure below shows the path traced by the ray after reflection from the first and second mirrors when the incoming ray is $35\,^\circ$ to the plane of the mirror.

From the diagram, the light ray is incident on the mirror at an angle of $35\,^\circ$ to the plane of the mirror.

The angle of incidence is,

${\theta _i} = \left( {90\,^\circ - \theta } \right)$

Here, ${\theta _i}$ is the angle of incidence.

Substitute $35\,^\circ$ for $\theta$ in the above equation.

$\begin{array}{c}\\{\theta _i} = \left( {90\,^\circ - 35^\circ } \right)\\\\ = 55^\circ \\\end{array}$

Therefore, the angle of reflection is $55\,^\circ$ .

The angle of reflection from the second mirror is $35\,^\circ$ .

Therefore, the angle of emergent ray relative to the incoming ray is $180\,^\circ$ .

(B)

The figure below shows the path traced by the ray after reflection from the first and second mirrors when the incoming ray is $30\,^\circ$ to the plane of the mirror.

From the diagram, the light ray falls incident on the mirror at an angle of $30\,^\circ$ with the plane of the mirror.

The angle of incidence is

${\theta _i} = \left( {90\,^\circ - \theta } \right)$

Here, ${\theta _i}$ is the angle of incidence.

Substitute $35\,^\circ$ for $\theta$ in the above equation.

$\begin{array}{c}\\{\theta _i} = \left( {90\,^\circ - 35^\circ } \right)\\\\ = 55^\circ \\\end{array}$

The angle of incidence is

$\left( {90\,^\circ - 30\,^\circ } \right) = 60\,^\circ$

Therefore, the angle of reflection is $60\,^\circ$ .

The angle of reflection from the second mirror is $30\,^\circ$ .

Therefore, both the angles would be at $180\,^\circ$ relative to the incoming ray.

Ans: Part A

The angle of emergent ray relative to the incoming ray is ${\bf{180}}\,{\bf{^\circ }}$ .

Part B

The angle relative to incoming ray and outgoing ray is ${\bf{180}}\,{\bf{^\circ }}$ .