Question

Find the distance at which an object should be Placed in front of a convax lens of focal length 10cm to obtain an image of double in its size

Answer 1

GiveN :-

• An object should be Placed in front of a convex lens of focal length 10cm.
• The Image is obtained .

To FinD :-

• The distance at which the object should be placed to obtain a image of double size.

SolutioN :-

Here let us take the height of the object be x . Then the Height of the image will be 2x.

And the convex lens has the focal length of 10cm . Here we can use the formula of magnification in terms of focal length and object distance .

$\sf:\implies \pink{ Magnification =\dfrac{f}{f+u}}\\\\\sf:\implies m = \dfrac{10cm}{10cm+u}\\\\\sf:\implies \dfrac{2x}{x}=\dfrac{10cm}{10cm+u}\\\\\sf\implies 2 = \dfrac{10cm}{10cm+u} \\\\\sf:\implies 2(10cm + u)= 10cm \\\\\sf:\implies 20cm + u =10cm \\\\\sf:\implies u = 10cm -20cm \\\\\sf:\implies\boxed{\pink{\frak{ Object\ Distance = (-10 \ cm )}}}$

$\underline{\underline{\blue{\textsf{ Hence the object should be placed at \textbf{ 10cm from optical centre }.}}}}$