Two identical equiconvex thin lenses each of focal lengths \(20\) cm, made of material of refractive index \(1.5\) are placed coaxially in contact as shown. Now, the space between them is filled with a liquid with a refractive index of \(1.5\). The equivalent power of this arrangement will be:

2. \(R\)
3. \(\frac{3}{2}R\)
4. \(R^2\)

Shown in the figure here is a convergent lens placed inside a cell filled with a liquid. The lens has focal length + 20 cm when in air and its material has refractive index 1.50. If the liquid has refractive index 1.60, the focal length of the system is

1. + 80 cm                         

2. – 80 cm

3. – 24 cm                         

4. –160 cm

A plane-convex lens fits exactly into a plano-concave lens. Their plane surfaces are parallel to each other. If lenses are made of different materials of refractive indices \(\mu_1\) and \(\mu_2\) and \(R\) is the radius of curvature of the curved surface of the lenses, then the focal length of the combination is:

Two identical thin plano-convex glass lenses (refractive index = \(1.5\)) each having radius of curvature of \(20\) cm are placed with their convex surfaces in contact at the centre. The intervening space is filled with oil of a refractive index of \(1.7\). The focal length of the combination is:
1. \(-20\) cm
2. \(-25\) cm
3. \(-50\) cm
4. \(50\) cm