Question

The cross-section of a glass prism has the form of an isosceles triangle. One of the refracting faces is silvered. A ray of light falls normally on the other refracting face. After being reflected twice, it emerges through the base of the prism perpendicular to it. The angles of the prism are

• A. ${54}^0,{54}^0,{72}^0$
• B. ${72}^0,{72}^0,{36}^0$
• C. ${45}^0,{45}^0,{90}^0$
• D. ${57}^0,{57}^0,{76}^0$

Answer 1

The correct option is B ${72}^0,{72}^0,{36}^0$

Given,

The prism is isosceles, hence its two of the angles are the same, therefore

$\theta +2\varphi ={180}^{\circ }$ …… (1)

Now from the figure, it can be observed that

For $\Delta PQR$

$\angle P+\angle Q+\angle R={180}^{\circ }$

${90}^{\circ }+2\theta +{90}^{\circ }-\varphi ={180}^{\circ }$

$\varphi =2\theta$ ……. (2)

Now from equation (1) and (2)

$\theta +2\left(2\theta \right)={180}^{\circ }$

$5\theta ={180}^{\circ }\Rightarrow \theta ={36}^{\circ }$

Hence,

$\varphi =2\times {36}^{\circ }={72}^{\circ }$

Therefore the angles of prim is ${72}^{\circ }$, ${72}^{\circ }$, ${36}^{\circ }$ .