An object is placed 45 cm in front of a crystal ball. the crystal ball has a radius of 14 cm, and is made from a glass with an index of refraction of n = 1.5.
find the position of the final image once the rays have gone through the two faces, as measured from the second face. is a virtual object formed anywhere in the analysis? yes or no

Explanation:

 Using the formula for refraction at curved surface

For refraction at first surface

μ₂ /v -μ₁ /u = ( μ₂ - μ₁ )/R

1.5/v -1/-45 =.5/14

v = 111 cm

For refraction at opposite surface ,

u ( object distance ) = 111 - 28 =83 cm

It will act as virtual object for surface 2 so it will be positive in sign

again using the above equation for 2 nd surface we have

1/v - 1.5/83.17 = -.5-=/-14 = 1/28

v = 18.62 cm from second face.

yes, virtual image will be formed.

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