**Real and Apparent Depth**

An object placed in denser medium when viewed from a rarer medium appears to be at a lesser depth than its real depth. It is due to refraction of light.

Let a point Object O be at the bottom of the beaker containing water. Suppose XY is the plane surface which separates air and water.

A ray OA from O is incident normally to the surface XY and passes without bending along AD. Another ray OB is refracted along with C making an angle of incidence i and angle of refraction r. When seen from the top, the rays seem to be coming from I and, thus, object is seen at point I. Therefore, AO is the real depth and IO is the apparent depth of that object.

From Snell’s law,

aµw = sin r / sin i (where i is the angle of incident, and r is the angle of refraction)

In ΔABO, sin I = AB / OB

And in ΔABI, sin r = AB / IB

Then, aµw = sin i / sin r

= (AB/IB) / (AB/OB)

= OB/IB

If point B is very close to point A then

OB = OA and IB = IA so,

.: aµw= OA/IA = real depth/apparent depth ……(i)

**Apparent Shift:**if the real depth, OA = t, then from equation (i), apparent depth = t/aµw. The apparent shift of the object is given by

d = OI = OA – AI

= Real depth – Apparent depth

= t - t/aµw

or, d = t (1 – 1/aµw)

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