A small object is placed in the air, at a distance 45 cm from a convex refracting surface of radius of curvature 15 cm . If the surface separates air from glass of refractive index 1.5, then the position of image is

A prism is made of a glass having refractive index $\sqrt{2}$. If the angle of minimum deviation is equal to angle of the prism, then the angle of prism is

A thin glass prism of angle $9^{\circ}$ with refractive index 1.4 is combined with another glass prism of refractive index 1.6 as shown in the figure. The combination of the prism provides dispersion without deviation. Determine the angle $(A)$ of the second prism.

The magnifications produced by a convex lens for two position of an object are 4 and 3, respectively. If the distance of separation between the two positions of the object is 2 cm , then the focal length of the lens is