Refraction through spherical surface-part-2-optics

Parallel rays of light are falling on convex sphere surface of radius of curvature R = 20 cm as show. Refractive index of the medium is mu = 1.5 . A refraction from the spherical surface parallel rays

Show that for refraction at a concave spherical surface (separating glass-air medium), the distance of the object should be greater than three times the radius of curvature of the refracting surface for the image to be real.

Starting with an expression for refraction at a single spherical surface, obtain Lens Maker.s formula.

Electric flux through a spherical surface shown in the figure is _______

A parallel narrow beam of light is incident on the surface of a transparent hemisphere of radius R and refractive index mu=1.5 as shown. The position of the image formed by refraction at the image formed by refraction at the spherical surface only as

In Figure, a point object O is placed in air. A spherical boundary separates two media. Ab is the principall axis. The refractive index above AB is 1.6 and below AB is 2.0. The separation between the images formed due to refraction at a the spherical surface is (assume the radius of curvature (R) to be 1 unit)

Find the fluz f the electric field through a spherical surface of radius R due to a charge of 10^(-7) C at the centre and another equal charge at a point 2R away from the centre (figure ).

The image for the converging beam after refraction through the curved surface is formed at

The image for the converging beam after refraction through the curved surface is formed at

In the figure, a point object O is placed in air. A spherical boundry separates two media of radius of curvature 1.0 m. AB is principal axis. The separation between the images formed due to refraction at spherical surface is