$A$ thin equiconvex glass lens of refractive index $1.5$ has a power of $5 \,D$. When the lens is immersed in a liquid of refractive index $\mu$, it acts as a divergent lens of focal length $100 \,cm$. The value of $\mu$ of the liquid is:

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:

If sunlight is focused on a paper using a convex lens, it starts burning the paper in the shortest time when the lens is kept at $30 \text{ cm}$ above the paper. If the radius of curvature of the lens is $60 \text{ cm}$, then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is . . . . . . .

$A$ lamp is placed $6.0\; m$ from a wall. On putting a lens between the lamp and the wall at a distance of $1.2\; m$ from the lamp,a real image of the lamp is formed on the wall. The magnification of the image is

In the displacement method,a convex lens forms a real image of an object for its two different positions. If the heights of the images in the two cases are $24 \,cm$ and $6 \,cm$,then the height of the object is ........ $cm$.

$A$ thin double-concave lens is made of a very thin transparent material. It can be filled with air or two liquids $L_1$ and $L_2$ having refractive indices $n_1$ and $n_2$ respectively. The lens will converge a parallel beam of light if it is filled with ........