Spherical refracting surfaces. An object O stands on the central axis of a spher

Question

Spherical refracting surfaces. An object O stands on the central axis of a spherical refracting surface. For this situation, the data in the table below refers to the index of refraction n1 where the object is located, the index of refraction n2 on the other side of the refracting surface, the object distance p, the radius of curvature r of the surface, and the image distance i. (All distances are in centimeters.) Fill in the missing information, including whether the image is real or virtual, and on the same side of the surface as object O or on the opposite side.

Explanation / Answer

We know that

The equation for the spherical refracting surface is given by

n1/p+n2/i =n1-n2/r

The refractive index n1, where the object is placed is =1.0

The refractive index n2 is image formed =1.5

The image distance is given by i = +750cm

The object distance is given by p =?

Now from the above formula

n1/p+n2/i =n1-n2/r

1/p+1.5/750 =1-1.5/36

1/p =-0.5/36-1.5/750 =-0.0138 -0.002=-0.0158

Then the object distance P =-63.29cm

So the image is virtual and it must be on the same side

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