$A$ convex lens of refractive index $1.5$ has power $3D$. It is placed in a liquid of refractive index $2$. The new power of the lens is (in $D$)

An illuminated object and a screen are placed $90 \, cm$ apart. What is the focal length of the lens required to produce an image on the screen,twice the size of the object?.......$cm$

In an experiment to measure the focal length $(f)$ of a convex lens,the magnitude of object distance $(x)$ and the image distance $(y)$ are measured with reference to the focal point of the lens. The $y-x$ plot is shown in the figure. The focal length of the lens is . . . . . . $cm$.

If sunlight is focused on a paper using a convex lens, it starts burning the paper in the shortest time when the lens is kept at $30 \text{ cm}$ above the paper. If the radius of curvature of the lens is $60 \text{ cm}$, then the refractive index of the lens material is $\frac{\alpha}{10}$. The value of $\alpha$ is . . . . . . .

An achromatic telescope objective is to be made by combining the lenses of flint and crown glasses. This proper choice is

$A$ diminished image of an object is to be obtained on a large screen $1\, m$ from it. This can be achieved by