$A$ magnifying lens has a focal length of $10 \, cm$. If the image is formed at a distance of $30 \, cm$ from the lens,what is the magnification?

If the focal lengths of a lens for red and violet light rays are $f_{R}$ and $f_{V}$ respectively,then which of the following is the true relationship?

$A$ 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:

An object is placed at a distance of $f/2$ from a convex lens. The image will be

$A$ convex lens is used to form a real image of an object on a screen. It is observed that even when the positions of the object and the screen are fixed,there are two positions of the lens that form real images. If the heights of the images are $4 \ cm$ and $9 \ cm$ respectively,the height of the object is.....$cm$.

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: