A paperweight in the form of a hemisphere of radius 3.0 cm is used to hold down a printed page. An observer looks at the page vertically through the paperweight. At what height above the page will the printed letters near the center appear to the observer?

Radius of the paper weight = R= 3.0 cm

Refractive index of paper weight =

Refractive index of air=

• Refraction at point A

Object distance = u= 0

Radius R

By lens equation

⇒

⇒

Therefore, image of the printed letters will be formed at the point.

• Refraction at point B

Object distance u=-3 cm

Radius R= -3 cm

By lens equation

⇒

⇒

⇒

⇒

Hence, there will be no shift in the final image.