Question

How far should an object be placed from a convex lens of focal length 20 cm to obtain its image at a distance of 30 cm from the lens? What will be the height of the image, if the objects is 6 cm tall?

Answer 1

According to the question;

Object distance = u; 

Image distance (v) = 30cm; 

Focal length = 20cm 

By lens formula; 

\(\frac1v\,-\,\frac1u\,=\,\frac1f\)

⇒\(\frac{1}{30}\,-\,\frac1u\,=\,\frac{1}{20}\) 

⇒\(\frac1u\,=\,\frac{1}{30}\,-\,\frac{1}{20}\)

⇒\(\frac1u\,=\,\frac{20\,-\,30}{600}\,=\,\frac{-10}{600}\)

⇒ \(\frac1u\,=\,\frac{-1}{60}\)

u = -60cm.

Therefore object is placed at 60 cm in front of lens.

Now; 

Height of object h1= 6cm; 

Magnification =\(\frac{h_2}{h_1}\) =\(\frac{v}{u}\) 

Putting values of v and u 

Magnification =\(\frac{h_2}{6}\,=\,\frac{30}{-60}\)

⇒ \(\frac{h_2}{6}\,=\,\frac{-1}{2}\)

⇒ h₂ = - \(\frac62\) = -3

Height of image is 3 cm. 

Negative sign means image is real and inverted.