The sun subtends an angle of $0.5^{\circ}$ at the earth's surface. Its image is formed by a convex lens of focal length $50 \ \text{cm}$. The diameter of the image will be (in $\text{mm}$)

$A$ double convex lens,made of a material of refractive index $\mu_1$,is placed inside two liquids of refractive indices $\mu_2$ and $\mu_3$ as shown,where $\mu_2 > \mu_1 > \mu_3$. $A$ wide,parallel beam of light is incident on the lens from the left. The lens will give rise to:

The focal length of an equi-convex lens is greater than the radius of curvature of any of the surfaces. Then the refractive index of the material of the lens is

The distance between an object and its two times magnified real image produced by a convex lens is $45 \,cm$. The focal length of the lens used is . . . . . . $cm$.

$A$ lens having focal length $f$ and aperture of diameter $d$ forms an image of intensity $I.$ If an aperture of diameter $\frac{d}{2}$ in the central region of the lens is covered by a black paper,the focal length of the lens and the intensity of the image will be,respectively:

$A$ plane wave passes through a convex lens. The geometrical shape of the wavefront that emerges is