Question

A 2cm tall object is located 40cm in front of a convex lens of focal length 200mm what are the image position and its magnification

Answer 1

Given :

• Height of object (ho) = 2cm
• Distance of Object from Convex Lens (u) = -40cm
• Focal lenght of convex lens (f) = 200mm or 20cm

To Find :

• Image Position
• Magnification

Formula Used :

$\bullet\underline{\boxed{\sf \dfrac{1}{f}=\dfrac{1}{v}-\dfrac{1}{u}}}$

$\bullet\underline{\boxed{\sf Magnification (m)=\dfrac{h_i}{h_o}=\dfrac{-v}{u}}}$

Solution :

$\implies{\sf \dfrac{1}{20}=\dfrac{1}{v}-\left(\dfrac{1}{-40}\right)}$

$\implies{\sf \dfrac{1}{20}=\dfrac{1}{v}+\dfrac{1}{40} }$

$\implies{\sf \dfrac{1}{v}=\dfrac{1}{20}-\dfrac{1}{40} }$

$\implies{\sf \dfrac{1}{v}=\dfrac{40-20}{20 \times 40} }$

$\implies{\sf \dfrac{1}{v}=\dfrac{20}{800} }$

$\implies{\sf v =\dfrac{800}{20} }$

$\implies{\bf v = 40 \: cm}$

Characteristics of image :

• Image formed at 2F
• Image is real and inverted
• Height of image will be same as of object ,but inverted.

➞ Magnification of image

$\implies{\sf m=\dfrac{-v}{u} }$

$\implies{\sf m=\dfrac{-40}{40} }$

$\implies{\bf m = -1\: cm}$

Answer :

Image Position (v) = 40cm

Magnification of image = -1