Question

Figure shows the variation of $\frac{1}{\left|v\right|}$ versus $\frac{1}{\left|u\right|}$ for a concave mirror. The line y=3x cuts the graphs at an ordinate ${1.5m}^{-1}$. The curvature radius of the mirror is

• A. 75 cm
• B. 50 cm
• C. 100 cm
• D. 200 cm

Answer 1

The correct option is C 100 cm

$y=\frac{1}{\left|v\right|}=1.5m^{-1}$

As the line $y=3x$ cuts the graph,

$y=3x$

$1.5=3x$

$x=\frac{1}{\left|u\right|}=0.5m^{-1}$

Substituting the values in mirror formula,

$\frac{1}{f}=\frac{1}{u}+\frac{1}{v}$

$\frac{1}{f}=1.5+0.5=2m^{-1}$

$f=0.5m=50cm$

$R=2f=2\times 50=100cm$

The curvature radius of the mirror is 100 cm.