Question

An object $2.4\, m$ in front of a lens forms a sharp image on a film $12\, cm$ behind the lens. A glass plate $1\, cm$ thick, of refractive index $1.50$ is interposed between lens and film with its plane faces parallel to film. At what distance (from lens) should object shifted to be in sharp focus on film ?

• A. $7.2\,m$
• B. $4.4\,m$
• C. $3.2\,m$
• D. $5.6\,m$

Answer 1

Answer: (D)

$\frac{1}{f}=\frac{1}{12}+\frac{1}{240}=\frac{20+1}{240}$
$f=\frac{240}{21}m$
shift $=1\left(1-\frac{2}{3}\right)=\frac{1}{3}$
Now $v' =12-\frac{1}{3}=\frac{35}{3}\,cm$
$\therefore \frac{21}{240}=\frac{3}{25}-\frac{1}{u}$
$\frac{1}{u}=\frac{3}{35}-\frac{21}{240}=\frac{1}{5}\left(\frac{3}{7}-\frac{21}{48}\right)$
$\frac{5}{u}=\left|\frac{144-147}{48\times7}\right|$
$u = 560\, cm = 5.6 \,m$