Two vertical plane mirrors are inclined at an angle of $60^{0}$ with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

Question

Two vertical plane mirrors are inclined at an angle of

60^{0}

with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is

Toppr Admin · Accepted Answer

Fromthefigurea-b-900-x21D2-b-900-x2212-aNow-b-60-c-180-x21D2-c-180-x2212-60-x2212-b-180-x2212-90-x2212-a-30-aNow-d-c-90d-90-x2212-c-90-x2212-30-a-60-x2212-aThus-intrianglePQR-x2220-Q-2a-x2220-R-2d-2-60-x2212-a-120-x2212-2aso-angle-x2220-QPTis-x2220-Q-x2220-R-120Now-angleofdeviation-reflex-x2220-QPT-360-x2212-120-240-x2218-Hence-theoptionDisthecorrectanswer-

Two vertical plane mirrors are inclined at an angle of 600 with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is 100024006001800

Fromthefigurea+b=900⇒b=900−aNow,b+60+c=180⇒c=180−60−b=180−(90−a)=30+aNow,d+c=90d=90−c=90−(30+a)=60−aThus,intrianglePQR∠Q=2a∠R=2d=2(60−a)=120−2aso,angle∠QPTis=∠Q+∠R=120Now,angleofdeviation=reflex∠QPT=360−120=240∘Hence,theoptionDisthecorrectanswer.

Two vertical plane mirrors are inclined at an angle of $60^{0}$ with each other. A ray of light travelling horizontally is reflected first from one mirror and then from the other. The resultant deviation is
$100^{0}$
$240^{0}$
$60^{0}$
$180^{0}$