Question

the magnifying glass is made of lenses of power +20D and -4D. if distance of distinct vision is 25cm. calculate the size of an object 2cm high seen through the magnifying glass

Answer 1

As per the given question,

The power of the lenses are $(P_1)=+20D$ and $(P_2)=-4D$

distance of distinct vision (v) =25cm

The size of the object $(h_o)=2cm$

Let the focal length of the glasses are $f_1$ and $f_2$

We know that,

$f_1=\dfrac{1}{P_1}=\dfrac{100}{20}=5cm$

Similarly,

$f_2=\dfrac{1}{P_2}=\dfrac{-100}{4}=-25cm$

Now, combined focal length $\dfrac{1}{f}=\dfrac{1}{f_1}+\dfrac{1}{f_2}=\dfrac{1}{5}-\dfrac{1}{25}=\dfrac{4}{25}$

$f=\dfrac{25}{4}$

Now, let the distance of object is u

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

$\Rightarrow \dfrac{1}{u}=\dfrac{1}{25}-\dfrac{4}{25}=\dfrac{3}{25}$

So, $u=\dfrac{25}{3}cm$

we know that,

$\dfrac{h_i}{h_o}=\dfrac{-v}{u}$

$h_i=\dfrac{25\times 3\times 2}{25}=-6cm$