$A$ thin glass (refractive index $1.5$) lens has an optical power of $-5 D$ in air. Its optical power in a liquid medium with a refractive index of $1.6$ will be:

In the displacement method,the distance between the object and the screen is $70 \; cm$ and the focal length of the lens is $16 \; cm$. Find the separation between the magnified and diminished image positions of the lens. (in $; cm$)

The magnifications produced by a convex lens for two positions of an object are $4$ and $3$, respectively. If the distance of separation between the two positions of the object is $2 \,cm$, then the focal length of the lens is (in $\,cm$)

Parallel rays are incident on a thick plano-convex lens having radius of curvature $R$,refractive index $\mu$ and thickness $t$. When rays are incident on the plane surface,they converge at a distance $x$ from the plane surface. When rays are incident on the curved surface,they converge at a distance $y$ from the curved surface. Then:

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......$mm$.

$A$ glass convex lens $(\mu_{g}=1.5)$ has a focal length of $8 \ cm$ when placed in air. What would be the focal length of the lens in $cm$ when it is immersed in water $(\mu_{w}=\frac{4}{3})$?