$A$ thin lens made of glass of refractive index $\mu_g = 1.5$ has a focal length of $12 \ cm$ in air. If it is immersed in water of refractive index $\mu_w = 4/3$,what will be its new focal length in $cm$?

$A$ bi-convex lens has a radius of curvature for both surfaces equal to $1/6 \ cm$. If this lens is to be replaced by another convex lens having different radii of curvature on both sides $(R_1 \neq R_2)$,without any change in the lens power,then the possible combination of $R_1$ and $R_2$ is:

The sun's diameter is $1.4 \times 10^9 \ m$ and its distance from the earth is $10^{11} \ m$. The diameter of its image,formed by a convex lens of focal length $2 \ m$,will be.......$cm$.

In the displacement method,the distance between the object and the screen is $70 \, cm$. The focal length of the lens is $16 \, cm$. The distance between the positions of the lens for the magnified and diminished images will be ..... $cm$.

$A$ concave lens of focal length $f$ produces an image $(1/x)$ of the size of the object. The distance of the object from the lens is:

$A$ point object $O$ is placed on the principal axis of a convex lens of focal length $20 \, cm$ at a distance of $40 \, cm$ to the left of it. The diameter of the lens is $10 \, cm$. If the eye is placed $60 \, cm$ to the right of the lens at a distance $h$ below the principal axis,then the maximum value of $h$ to see the image will be.......$cm$.