The focal length of a spherical mirror made of steel is (150 ~cm ). If the temperature of the mirror increases by (200 ~K ), its focal length become (coefficient of linear expansion of steel ( =12 10⁻⁶⁰ C ⁻¹ ).)

Step-by-step solution

Given, focal length of spherical mirror, (f=150 ~cm ) coefficient of linear expansion of steel, ( =12 10^ -6 C ⁻¹ ) As we know that, coefficient of linear expansion, ( = R R T ) ( aligned R R & = T f f & = T ( f= R 2 ) f & =f T f^ -f & =f T aligned ) where, (f= ) initial focal length of the mirror and (f^ = ) final focal length of mirror (f^ =f+f T ) (f^ =f(1+ T) ) (f^ =150 (1+12 10⁻⁶ 200 ) ( T=200 ~K ) ) (f^ =150.36 ~cm )