The size of the image of an object at infinity, formed by a convex lens of focal length $30 \,cm$, is $2 \,cm$. If a concave lens of focal length $20 \,cm$ is placed between the convex lens and the image at a distance of $26 \,cm$ from the convex lens, what is the new size of the image (in $\,cm$)?

$A$ parallel beam of light is incident on a system of two convex lenses of focal lengths $f_1 = 20\, cm$ and $f_2 = 10\, cm$. What should be the distance between the two lenses so that the rays after refraction from both the lenses emerge as a parallel beam (in $, cm$)? (Note: The condition for the final rays to emerge parallel is that the focal point of the first lens must coincide with the focal point of the second lens).

$A$ thin convex lens of focal length $5 \ cm$ and a thin concave lens of focal length $4 \ cm$ are combined together (without any gap) and this combination has magnification $m_1$, when an object is placed $10 \ cm$ before the convex lens. Keeping the positions of the convex lens and object undisturbed, a gap of $1 \ cm$ is introduced between the lenses by moving the concave lens away, which leads to a change in the magnification of the total lens system to $m_2$. The value of $\left|\frac{m_1}{m_2}\right|$ is . . . . . . .

Three lenses of focal lengths $+10 \ cm, -10 \ cm$ and $+30 \ cm$ are placed at distances of $30 \ cm, 35 \ cm$ and $45 \ cm$ respectively from an object. The distance between the object and the final image formed is: (in $cm$)

Two thin convex lenses of focal lengths $20 \; cm$ and $25 \; cm$ are placed in contact. The effective power of the combination is:

Two lenses of power $6D$ and $-2D$ are combined to form a single lens. The focal length of this lens will be (in $m$)