A small object is embedded inside a glass sphere ( = 1.5 ) of radius 5.0 cm , located at a distance of 1.5 cm left to the centre. Determine the position of the image of the object as seen by an observer standing to the right of the sphere.

Step-by-step solution

The observer is to the right of the sphere, so refraction occurs at the right surface. Light travels from left to right, which is taken as the positive direction. Let the pole P be the rightmost point of the sphere. Radius of curvature of the right surface is R = -5.0 cm . The object is 1.5 cm to the left of the centre, so its distance from the pole P is u = -(5.0 + 1.5) = -6.5 cm . Refractive index of the glass sphere is ₁ = 1.5 and for air is ₂ = 1 . Using the spherical refraction formula: ₂ v - ₁ u = ₂ - ₁ R 1 v