Question

An object is placed beyond the centre of curvature $C$ of the given concave mirror. If the distance of the object is $d_{1}$ from $C$ and the distance of the image formed is $d _{2}$ from $C$, the radius of curvature of this mirror is :

• A. $\frac{2 d _{1} \,d _{2}}{ d _{1}- d _{2}}$
• B. $\frac{2 d _{1} d _{2}}{ d _{1}+ d _{2}}$
• C. $\frac{ d _{1} d _{2}}{ d _{1}+ d _{2}}$
• D. $\frac{ d _{1} d _{2}}{ d _{1}- d _{2}}$

Answer 1

Answer: (A)

Using Newton"s formula
$\left( f + d _{1}\right)\left( f - d _{2}\right)= f ^{2} $
$f ^{2}+ fd _{1}- fd _{2}- d _{1} \,d _{2}= f ^{2} $
$f =\frac{ d _{1} d _{2}}{ d _{1}- d _{2}} $
$\therefore R =\frac{2 d _{1} \,d _{2}}{ d _{1}- d _{2}}$