As given:

u = -2.4m = −240cm ;

v = 12cm

Accoring to the lens formula:

\(\frac{1}{f} = \frac{1}{v} – \frac{1}{u} \)

= \( \frac{1}{f} = \frac{1}{12} – \frac{1}{-240} \)

= \(\frac{1}{f} = \frac{1}{12} + \frac{1}{240} \) \(\frac{1}{f} = \frac{21}{240}cm \)

When a glass plate is interposed between lens and film, so shift produced by it will be

Shift t = \( (1 – \frac{1}{\mu}) = 1 \)

= \((1 – \frac{1}{1.5}) =1 \)

= \( (1 – \frac{2}{3}) \)

= \(\frac{1}{3}cm \)

Inorder to get image at film, the lens should form image at a distance:

\({v}’ = 12 – \frac{1}{3} \)

= \( \frac{35}{3}cm \)

Now, by using the lens formula:

\(\Rightarrow \frac{21}{240}cm = \frac{3}{35}cm – \frac{1}{{u}’} \) \(\Rightarrow \frac{1}{{u}’} = \frac{3}{35}cm – \frac{21}{240}cm \) \(\Rightarrow \frac{1}{5} = [\frac{3}{7}cm – \frac{21}{48}cm] \) \(\Rightarrow \frac{1}{{u}’} = \frac{1}{5} [\frac{144 – 147}{336}] \) \(\Rightarrow {u}’ = -560 cm = -5.6m \)

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