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 `alpha=12 times 10^-60 C^-1`)

Options

A. 186.3 cm
B. 153.6 cm
C. 150.036 cm
D. 150.36 cm

Explanation

Given,
focal length of spherical mirror, f=150 cm
coefficient of linear expansion of steel
`a=12 times 10^-6 C^-1`
As we know that
coefficient of linear expansion, `a=(Delta R)/( R times Delta T)`
`(DeltaR)/R=a Delta T`
`(Deltaf)/f=a Delta T` ( `because f=R/2)`
`Delta f= f a Delta T`
`f.-f=f a Delta T`
where f= intial length of the mirror and
f.= final focal length of mirror
`f.=f+f a Delta T`
`f.=f(1+ alpha Delta T)`
`f.=150(1+12 times 10^-6 times 200) ( because Delta T=200 K) `
f.= 150.36 cm