An object is placed in front of a concave lens at a distance of 45 cm from it. If its image is formed at a distance of 30 cm from the lens, calculate the focal length of the lens.
(a) Given,
Object distance (u) = -45 cm
Image distance (v) = -30 cm
From lens formula,
1f=1v−1u1f=1−30−1(−45)1f=−130+1451f=−3+2901f=−190f=−901f=−90 cm\dfrac{1}{\text f} = \dfrac{1}{\text v} - \dfrac{1}{\text u} \\[1em] \dfrac{1}{\text f} = \dfrac{1}{-30}-\dfrac{1}{(-45)}\\[1em] \dfrac{1}{\text f}=-\dfrac{1}{30}+\dfrac{1}{45}\\[1em] \dfrac{1}{\text f} = \dfrac{-3+2}{90}\\[1em] \dfrac{1}{\text f} = -\dfrac{1}{90} \\[1 em] \text f = -\dfrac{90}{1}\\[1 em] \text f= - 90 \text { cm}f1=v1−u1f1=−301−(−45)1f1=−301+451f1=90−3+2f1=−901f=−190f=−90 cm
