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At the bottom of a liquid tank with refractive index m. A plane mirror is placed at the bottom. An object is placed inside the liquid at a height h/2 above the mirror. Where will the image of the object appear to an observer looking from above?

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Given- 

  • Refractive index of liquid = m
  • An object is placed at a height = h/2 above the mirror
  • The mirror is at the bottom of the tank
  • The observer is looking from above (in the air)

To find- The apparent position of the image as seen by the observer above the tank.

Solution- Firstly, a mirror forms a real image of the object, and as the object is at h/2 above the mirror, the real image will form at h/2 below the mirror. So, the distance of the image from the surface of the liquid = $$
(h -\frac {h}{2}) + \frac {h}{2} = h
$$

When light comes out of the liquid into the air, it appears to come from a shallower depth. So, $$
\text {Apparent depth} = \frac {\text {Real depth}} {\text {Refractive index}} = \frac {h}{m}
$$

Therefore, the image will appear at a depth of h/m from the surface of the liquid, as seen by the observer in air.

Posted by

Saniya Khatri

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