Where would an object be placed in a medium of refractive index μ1 , so that its real image is formed at equidistant from sphere (of radius R and refractive index μ2) which is also placed in the medium of refractive index μ1 as shown in figure?
A
(μ2−μ1μ2+μ1)R
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B
(μ2μ2−μ1)R
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C
(μ1μ2−μ1)R
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D
(μ2+μ1μ2−μ1)R
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Solution
The correct option is A(μ1μ2−μ1)R
Since the image is formed equidistant from the sphere as the distance of the object.
In order to form the image at the same distance, the ray should emerge out of the sphere at the same angle as its incident angle. To obtain this, the ray should be parallel to the axis of the sphere as shown in the figure.
Now, applying the formula for refraction at the spherical surface.
μ2v−μ1u=μ2−μ1R
Since the ray becomes parallel, it will form the image at infinite.
μ2+∞−μ1−x=μ2−μ1R
So, the distance of the object can be obtained as: