The optical power of a thin glass lens (refractive index $1.5$) in air is $-5 \ D$. What will be its optical power in a liquid with a refractive index of $1.6$ (in $D$)?

The radius of curvature of the convex surface of a thin plano-convex lens is $15 \ cm$ and the refractive index of its material is $1.6$. The power of the lens is

An object approaches a convergent lens from the left of the lens with a uniform speed $5 \ m/s$ and stops at the focus. The image :-

$A$ rod of length $2 \text{ cm}$ makes an angle of $\frac{2 \pi}{3} \text{ rad}$ with the principal axis of a thin convex lens. The lens has a focal length of $10 \text{ cm}$ and is placed at a distance of $\frac{40}{3} \text{ cm}$ from the object as shown in the figure. The height of the image is $\frac{30 \sqrt{3}}{13} \text{ cm}$ and the angle made by it with respect to the principal axis is $\alpha \text{ rad}$. The value of $\alpha$ is $\frac{\pi}{n} \text{ rad}$,where $n$ is:

$A$ convex lens of focal length $0.15 \,m$ is made of a material of refractive index $\frac{3}{2}$. When it is placed in a liquid, its focal length is increased by $0.225 \,m$. The refractive index of the liquid is

The diameter of the Sun is $1.4 \times 10^9 \, m$ and its distance from the Earth is $10^{11} \, m$. What is the diameter of the image (in $cm$) formed by a convex lens of focal length $2 \, m$?