Question

There is a small black dot at the centre C of a solid glass sphere of refractive index \[\mu \] . When seen from outside, the dot will appear to be located:
(A) Away from C for all values of \[\mu \]
(B) At C for all values of \[\mu \]
(C) At C for \[\mu =1.5\] , but away from C for \[\mu \ne 1.5\]
(D) At C only for \[\sqrt{2}\le \mu \le 1.5\]

Answer 1

Hint:The formation of the image depends on how the incident rays from the object are refracted from the glass sphere or any refracting surface in question. Here the dot is placed inside the glass sphere, which means that for the light rays incident from the dot, the sphere will act as a concave lens. We have been given a piece of additional information that the dot is at the centre of the glass sphere. Using this information and the value of the refractive index of the sphere, we can answer the question.

Step by Step Solution:
If we recall the laws for tracing the ray diagram for image formation for any object, we can say that there are two very basic rules.
-The ray of light parallel to the principal axis will pass through or appear to pass through the focus of the refracting surface.
-The light ray incident normally on the refracting surface will pass through un-deviated.
From the second point, we have our answer.
Since all light rays travelling along the diameter of the sphere will be incident normally on the mirror because the rays coming from the centre of the curvature are normal to the sphere’s surface. Hence the rays will pass through un-deviated and the refractive index will play no role in deciding the location of the image.

Hence we can say that option (B) is the correct answer or that the dot will appear to be located at C for all values of \[\mu \] .

Note: The examiner has given us the value of the refractive index to try and confuse. Our first assumption on seeing value is that the question is either analytical or a numerical. In reality, the given question was purely logical and we easily reached our answer using the basic rules for image formation. Therefore, it is my suggestion that a logical approach to every question should be your first move.