In the figure,an air lens of radii of curvature $10 \ cm$ ($R_1 = 10 \ cm$,$R_2 = -10 \ cm$) is cut in a cylinder of glass $(\mu = 1.5)$. The focal length and the nature of the lens is:

$A$ convex lens makes a real image $4 \, cm$ long on a screen. When the lens is shifted to a new position without disturbing the object,we again get a real image on the screen which is $16 \, cm$ tall. The length of the object must be.......$cm$

An object is placed at a distance $m$ times the focal length of a divergent lens. The size of the image is shorter than that of the object by what factor?

$A$ thin converging lens of focal length $f=25 \,cm$ forms the image of an object on a screen placed at a distance of $75 \,cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object has to be shifted,so that its image on the screen is sharp again,is (in $\,cm$)

The objective glass of a telescope is an achromat of focal length $90\,cm$. The magnitudes of dispersive powers of the two lenses are $0.024$ and $0.036$. The focal lengths of the two lenses are:

The sun subtends an angle of $0.5^o$ at the earth's surface. Its image is formed by a convex lens of focal length $50 cm$. The diameter of the image will be......$mm$.