Magnifying glasses are made of two convex lenses. It is known that the picture of an image will be smaller than the related object when the object is positioned farther than twice the focal length.

$$
begin{align}
{d_o}>2cdot {f}
end{align}
$$

$$
{d_o}>2cdot {f}
$$

Since we know $f=6times10^{-2}text{ m}$ and $d_{o}=2times10^{-2}text{ m}$ will calculate, by using the definition of the thin lens equation, that the distance of image.

Also, we need to find the high of an image with knowing $h_{o}=3times10^{-2}text{ m}$ and present this situation on a ray diagram.

$$
begin{align}
frac{1}{f}&=frac{1}{d_i}+frac{1}{d_o} \
{d_i}&=frac{d_ocdot f}{d_o -f} \
{d_i}&=frac{2times10^{-2}mcdot 6times10^{-2}m}{2times10^{-2}m- 6times10^{-2}m}{} \
{d_i}&=-3times10^{-2}m
end{align}
$$

Minus in solution means that the image is on the same side of a lens as the object.

Now, we use the magnification equation.

$$
begin{align}
frac{h_i}{h_o}&=frac{-d_i}{d_o} \
{h_i}&=frac{-d_i cdot h_o}{d_o} \
{h_i}&=frac{-(-3)times10^{-2}m cdot 3}{2times10^{-2}m} \
{h_i}&=4.5times10^{-2}m
end{align}
$$

${d_o}=-3times10^{-2}m$

$$
{h_i}=4.5times10^{-2}m
$$

Chromatic aberration is an effect that appears in every lens because lenses have defect that mirrors do not have. A lens refracts different wavelengths of light at slightly different angles, so an object viewed through a lens appears to be ringed with rainbow colors. To manage the precision in focusing the picture when looking through a microscope, we use $textbf{achromatic lens}$ which is a system of two or more lenses.