Question

A $5cm$ long needle lies along the principal axis axis of a concave mirror of focal length $20cm$ in such a way that the end closer to the pole is $40cm$ from it. Find the length of the image of the needle formed by the mirror.

Answer 1

Given,

Length of needle, $l=5cm$

Focal length, $f=20cm$

(i) distance of near end of needle from pole of th emirror, $u_1=40cm$

(ii) distance of far end of needle from pole of the needle from pole of the mirror, ${\mu }_2=40+5$

$=45cm$

for (i) , th eobject is at $2f$, so its image will be at $2f$

$v_1=-2f=-2\times 20=-40cm$

for (ii),

$\frac{1}{f}=\frac{1}{v_2}-\frac{1}{u_2}$

$-\frac{1}{20}=\frac{1}{45}-\frac{1}{20}$

$v_2=-36cm$

length of the needle's image, $l^{\prime }=|v_2-v_1|=|40-36|$

$l^{\prime }=4cm$