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a convex lens of power 4D is placed at a distance of 40cm from the wall . at what distance from the lens should a candle be placed so that is's imsge is formed on the wall , solve and explain why we have not taken image distance negative in this ques. also explain when we take image distance positive or negative 
Asked by Sanchit Sharma | 02 Mar, 2015, 07:20: PM
answered-by-expert Expert Answer
Given that the power of the lens, P= 4D
Therefore the focal length of the lens, f = 1/ 4 =0.25 m = 25 cm
Given that the image distance, v = 40 cm
According to lens formula:
 
begin mathsize 14px style 1 over straight f equals 1 over straight v minus 1 over straight u straight f space equals space 25 space cm straight v space equals 40 space cm straight u equals space ? 1 over straight u equals 1 over straight v minus 1 over straight f 1 over straight u equals 1 over 40 minus 1 over 25 1 over straight u equals fraction numerator 5 minus 8 over denominator 200 end fraction 1 over straight u equals fraction numerator negative 3 over denominator 200 end fraction straight u space equals negative 200 over 3 straight u equals negative 66.67 space cm end style
 
So the candle should be placed at a distance of 66.67 cm from the lens so as to form an image on the wall. 
 
According to sign convention:
The distance measured from the optical centre to the left side are taken as negative, hence the object distance, u will be negative.
On the other hand the distance measured from optical centre of the lens to the right side are taken as positive.As the image is formed to the right side of the lens on the wall, the image distance,v is taken positive.
Answered by Jyothi Nair | 03 Mar, 2015, 11:06: AM

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