question_answer

In the given figure, two mirrors P and Q are situated at an angle of \[{{60}^{o}}\] with each other and a ray of light is incident on mirror P at an angle of \[{{55}^{o}}\]. What is the value of angle A if the ray again reflected by the mirror Q?                

A)          \[{{35}^{o}}\]                                

B)  \[{{55}^{o}}\]                    

C)                     \[{{50}^{o}}\]                    

D)  \[{{70}^{o}}\]

Correct Answer: C

Solution :

A ray of light incident on   mirror P    at an angle \[={{55}^{o}}\] \[\therefore \] \[\angle i=90-{{55}^{o}}={{35}^{o}}\] \[\therefore \] \[\angle r=\angle i={{35}^{o}}\] Hence \[\angle B={{180}^{o}}-({{55}^{o}}+{{35}^{o}}+{{35}^{o}})\] \[={{180}^{o}}-{{125}^{o}}={{55}^{o}}\] \[\therefore \] \[\angle C={{180}^{o}}-({{60}^{o}}+{{55}^{o}})={{180}^{o}}-{{115}^{o}}={{65}^{o}}\] \[\therefore \] \[\angle A=2[{{90}^{o}}-{{65}^{o}}]=2[{{25}^{o}}]={{50}^{o}}\]