Question

An object is kept at a distance of 100cm from concave lens of focal length 20cm .calculate the image distance and magnification​

Answer 1

Answer:

(a) Given Object distance (u) = -100cm

Focal length (f) = 20cm

Image distance = v

By lens formula; 1 v − 1 u = 1 f

1v−1u=1f ⇒ 1 v − 1 − 100 = 1 50

1v−1−100=150 ⇒ 1 v = 1 50 − 1 100

1v=150−1100 ⇒ 1 v = 2 − 1 100 − 1 100 1v=2−1100−1100

v =100cm

Hence the image is formed at 100 cm behind the lens.

Object distance (u) = -100cm

Focal length (f) = -20c

Image distance = v

By lens formula; 1 v − 1 u = 1 f 1v−1u=1f

1 v − 1 − 100 = − 1 25 1v−1−100=−125 1 v − − 1 25 = 1 100 1v−−125=1100 1 v − − 4 − 1 − 100 = − 5 100 1v−−4−1−100=−5100 ⇒ v = − 100 5 −1005 ⇒ v= -20cm Hence the image is formed at 20cm in front of the lens. (b) For 1st case Object distance (u) = -100cm Image distance (v) = 100cm. By Magnification Formula Magnification (m) = v u vu ⇒ Magnification = 100 − 100 100−100 Therefore, Magnification for the 1st case is -1. The negative sign means the image is real and inverted. For 2nd case Object distance (u) = -100cm Image distance (v) = -20cm. By Magnification Formula Magnification (m) = v u vu ⇒ Magnification = − 20 − 100 = 1 5 −20−100=15 = 0.5 Therefore, Magnification for 2nd case is 0.2.