Question

(Marking scheme for all questions will be: correct answer +3 and wrong answer -1)

The focal length of a spherical mirror is given by $f=\frac{R}{2}$, where $R$ is the radius of curvature of the mirror. For a given spherical mirror made of steel, the focal length is f$=24.0\text{cm}$. Find its new focal length if temperature increases by ${50}^{\circ }C$.
Given, ${\alpha }_{steel}=1.2\times {10}^{-5}{}^{\circ }{C}^{-1}$.

• A. $24.0144\text{cm}$
• B. $28.0012\text{cm}$
• C. $30.0008\text{cm}$
• D. $22.002\text{cm}$

Answer 1

The correct option is A $24.0144\text{cm}$

$R_0=2f=48.0\text{cm}$
$R=R_0(1+\alpha \Delta \theta )=48.0[1+1.2\times {10}^{-5}\times 50]$
$=48.0\left[1.0006\right]=48.0288\text{cm}$
$\therefore$ New focal length is $f=\frac{48.0288}{2}=24.0144\text{cm}$