Calculate the distance at which an object should be placed in front of a convex lens of focal length 100 cm to obtain an error image of double its size.
Answers
Given: f = +10 cm (Convex lens)
m = +2 (as image is virtual)
begin mathsize 12px style straight m space equals space straight v over straight u space equals space 2 space rightwards double arrow straight v space equals space 2 straight u
because 1 over straight v space minus space 1 over straight u space equals space 1 over straight f
rightwards double arrow fraction numerator 1 over denominator 2 straight u end fraction space minus space 1 over straight u equals space 1 over 10
rightwards double arrow fraction numerator negative 1 over denominator 2 straight u end fraction space equals space 1 over 10
rightwards double arrow space straight u space equals space minus 5 space cm end style
The object should be placed at a distance of 5 cm in front of convex lens.
Answer:
GIVEN,
f= 100 cm
v= 2u
Therefore,
=1/v-1/u=1/f
=1/2u-1/u=1/100
=1-2/2u=1/100
=-100/2u=1
=50=u
=u=50cm
Therefore,v=2*50
=100cm