Answer to Question #109644 in Optics for william

Question

a man used a glasses of-1d to see distant object. Where should the object be placed to have an image which is half of the object? Write the answer in 2 decimal after dot and give a space to write the unit exampple 98.52 D or 22.12 kg

Answer 1

As per the given question,

Power of the lens(P)=-1d

We know that $(f)=\dfrac{1}{-d}=\dfrac{-100}{d}cm$

As per the given question,

Let the height of the object $=(h_o)$

So, height of the the image $=\dfrac{h_o}{2}$

We know that $m=\dfrac{v}{u}=\dfrac{h_1}{h_o}=0.5$

Hence, v= x and u = 2x

Now substituting the values,

$\dfrac{1}{v}-\dfrac{1}{u}=\dfrac{1}{f}$

Now, substituting the values,

$\dfrac{1}{x}+\dfrac{1}{2x}=-\dfrac{100}{d}$

Hence$\dfrac{3}{2x}=-\dfrac{100}{d}$

$x=-\dfrac{200}{3}$