$A$ lens is made of flint glass (refractive index $= 1.5$). When the lens is immersed in a liquid of refractive index $1.25$,the focal length

$A$ 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:

$A$ thin converging lens of focal length $f=25 \,cm$ forms the image of an object on a screen placed at a distance of $75 \,cm$ from the lens. The screen is moved closer to the lens by a distance of $25 \,cm$. The distance through which the object has to be shifted, so that its image on the screen is sharp again, is (in $\,cm$)

$A$ 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:

The radius of the convex surface of a plano-convex lens is $20 \ cm$ and the refractive index of the material of the lens is $1.5$. The focal length of the lens is......$cm$.

When monochromatic red light is used instead of blue light in a convex lens,its focal length will .....