Question

The mirror in FIGURE EX$34.6$ deflects a horizontal laser beam by ${60}^{\circ }$. What is the angle $\varphi$?

Short answer

Angle of the laser beam,$\varphi =30°$

Step-by-step solution

The Law of Reflection

The incident and reflected rays are parallel to the surface and within the same plane.

${\theta }_i={\theta }_r$

Estimate the values

In FIGURE $34.6$, a horizontal beam strikes the mirror and deflects it by $60$degrees.

When we are asked to calculate the angle supported the geometry of the figure, we notice that

${\theta }_i+\varphi =90°⟶{\theta }_i=90°-\varphi$

${\theta }_r+\left(60°-\varphi \right)=90°⟶{\theta }_r=90°-\left(60°-\varphi \right)$

Find the Angle

${\theta }_i={\theta }_r$, In keeping with the rule of reflection. so,

$90°-\varphi =90°-\left(60°-\varphi \right)$

$\varphi =60°-\varphi$

$2\varphi =60°$

$\varphi =30°$