Question

A rod of length $10\, cm$ lies along the principal axis of a concave mirror of focal length $10\, cm$ in such a way that its end closer to the pole is $20\, cm$ away from the mirror. The length of the image is

• A. 10 cm
• B. 15 cm
• C. 2.5 cm
• D. 5 cm

Answer 1

Answer: (D)

The position of image of nearer end to mirror can be found out using mirror equation,
$\frac{1}{ v }+\frac{1}{ u }=\frac{1}{ f } $
$\Rightarrow \frac{1}{ v _{1}}=\frac{1}{-20}-\frac{1}{-10}$
$\Rightarrow v _{2}=-20$
Similarly position of image of farther end to mirror can be found out as
$=\frac{1}{ v _{2}}=\frac{1}{-(10+20)}-\frac{1}{-10} $
$\Rightarrow v _{2}=-15$
Hence the length of the image
$=20 \,cm -15\, cm =5 \,cm$