Question

A 10 cm tall object is placed perpendicular to the principal axis of a convex lens of a focal length 30 cm the distance of the object from the lens is 20 cm find the position nature size of the image from ed

Answer 1

$\textit{\large{\underline{\underline{EXPLANATION:}}}}$

$\textbf{\underline{Given,,}}</p><p>$

Distance of the object from the lens,,u=-20cm

Height of the object,h=+10cm

Focal length,f=+30cm

$\textbf{\underline{To find,,}}</p><p>$

1. Position of image
2. nature of image
3. size of image(h')

$\textbf{\underline{Using lens formula,,}}</p><p>$

$\mathtt{\boxed{\blue{\frac{1}{v}-\frac{1}{u}=\frac{1}{f}}}}$

$\mathtt{\implies{\frac{1}{v}-\frac{1}{(-20)}=\frac{1}{30}}}$

$\mathtt{\implies{\frac{1}{v}=\frac{1}{(30)}-\frac{1}{20}}}$

$\mathtt{\implies{\frac{1}{v}=\frac{2-3}{60}}}$

$\mathtt{\implies{\frac{1}{v}=\frac{-1}{60}}}$

$\mathtt{\implies{v=-60cm}}$

$\textbf{\underline{Now,,}}</p><p>$

Magnification,,

$\mathtt{\boxed{\blue{m=\frac{v}{u}=\frac{h'}{h}}}}$

$\mathtt{\implies{\frac{-60}{-20}=\frac{h'}{10}}}$

$\mathtt{\implies{3\times{10}=h'}}$

$\mathtt{\implies{h'=30cm}}$

$\textbf{\underline{Hence,,}}</p><p>$

1. Position of image=60 cm on the front side of the lens.
2. Nature of the image=Real and Magnified
3. Size of the image=30 cm(i.e.,bigger than the object)

❣️❣️❣️Hope it helps ❣️❣️❣️