$A$ convex lens is made of glass $(\mu_g = 1.5)$ and has a focal length of $4 \, cm$ in air. If it is immersed in water $(\mu_w = 1.33)$,what will be its new focal length in $cm$?

$A$ card sheet divided into squares each of size $1 \, mm^2$ is being viewed at a distance of $9 \, cm$ through a magnifying glass (a converging lens of focal length $10 \, cm$) held close to the eye. What is the magnification produced by the lens?

$A$ double convex thin lens made of glass of refractive index $1.6$ has radii of curvature $15 \ cm$ each. The focal length of this lens when immersed in a liquid of refractive index $1.63$ is.......$cm$.

The thickness at the centre of a plano-convex lens is $3 \, mm$ and the diameter is $6 \, cm$. If the speed of light in the material of the lens is $2 \times 10^{8} \, m/s$,the focal length of the lens is ............ $cm$.

The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)

$A$ convex lens of focal length $f$ produces an image $\frac{1}{n}$ times the size of the object. The distance of the object from the lens is: