
- A14 cm below flat surface
- B30 cm below flat surface
- C20 cm below flat surface
- D16 cm below flat surface
View written solutionFree
Correct answer: C
- Interpret the geometry
- Radius of hemispherical glass body:
- Refractive index of glass:
- The curved surface is silvered, so it acts as a spherical mirror.
- The air bubble lies on the axis, below the flat surface.
Since the center of the hemisphere is at the flat face center, the pole of the curved mirror is below the flat surface.
So the bubble is at a distance from the curved mirror pole:
- Image formed by the silvered curved surface (mirror action inside glass)
The silvered curved surface behaves like a concave mirror for rays inside the glass.
For a spherical mirror,
Using mirror formula,
Substitute and :
The negative sign means the image lies behind the mirror (with this sign convention), i.e. on the other side of the pole by .
Since the mirror pole is below the flat surface, the image position relative to the flat surface is:
This is the image formed by the mirror inside glass.
- Seen through the plane flat surface
Now this image at below the flat surface is viewed from air through the plane glass surface.
For refraction at a plane surface, which gives apparent depth relation:
Here real depth in glass , and .
Hence apparent depth from air is
- Final answer
Thus, the image of the air bubble made by the mirror is seen at
So the correct option is C.
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